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Sample records for nonlinear boundary damping

  1. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Danxia Wang

    2015-01-01

    Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l‍(ux2dxuxx-ϕ(∫0l‍(ux2dxuxxt=q(x, in  [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.

  2. On the Stochastic Wave Equation with Nonlinear Damping

    International Nuclear Information System (INIS)

    Kim, Jong Uhn

    2008-01-01

    We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping

  3. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    KAUST Repository

    Said-Houari, Belkacem

    2012-09-01

    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.

  4. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    KAUST Repository

    Said-Houari, Belkacem; Nascimento, Flá vio A Falcã o

    2012-01-01

    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.

  5. Damped nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Nicholson, D.R.; Goldman, M.V.

    1976-01-01

    High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time

  6. Non-Linear Slosh Damping Model Development and Validation

    Science.gov (United States)

    Yang, H. Q.; West, Jeff

    2015-01-01

    Propellant tank slosh dynamics are typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control (GN&C) analysis. For a partially-filled smooth wall propellant tank, the critical damping based on classical empirical correlation is as low as 0.05%. Due to this low value of damping, propellant slosh is potential sources of disturbance critical to the stability of launch and space vehicles. It is postulated that the commonly quoted slosh damping is valid only under the linear regime where the slosh amplitude is small. With the increase of slosh amplitude, the critical damping value should also increase. If this nonlinearity can be verified and validated, the slosh stability margin can be significantly improved, and the level of conservatism maintained in the GN&C analysis can be lessened. The purpose of this study is to explore and to quantify the dependence of slosh damping with slosh amplitude. Accurately predicting the extremely low damping value of a smooth wall tank is very challenging for any Computational Fluid Dynamics (CFD) tool. One must resolve thin boundary layers near the wall and limit numerical damping to minimum. This computational study demonstrates that with proper grid resolution, CFD can indeed accurately predict the low damping physics from smooth walls under the linear regime. Comparisons of extracted damping values with experimental data for different tank sizes show very good agreements. Numerical simulations confirm that slosh damping is indeed a function of slosh amplitude. When slosh amplitude is low, the damping ratio is essentially constant, which is consistent with the empirical correlation. Once the amplitude reaches a critical value, the damping ratio becomes a linearly increasing function of the slosh amplitude. A follow-on experiment validated the developed nonlinear damping relationship. This discovery can

  7. Bryan's effect and anisotropic nonlinear damping

    Science.gov (United States)

    Joubert, Stephan V.; Shatalov, Michael Y.; Fay, Temple H.; Manzhirov, Alexander V.

    2018-03-01

    In 1890, G. H. Bryan discovered the following: "The vibration pattern of a revolving cylinder or bell revolves at a rate proportional to the inertial rotation rate of the cylinder or bell." We call this phenomenon Bryan's law or Bryan's effect. It is well known that any imperfections in a vibratory gyroscope (VG) affect Bryan's law and this affects the accuracy of the VG. Consequently, in this paper, we assume that all such imperfections are either minimised or eliminated by some known control method and that only damping is present within the VG. If the damping is isotropic (linear or nonlinear), then it has been recently demonstrated in this journal, using symbolic analysis, that Bryan's law remains invariant. However, it is known that linear anisotropic damping does affect Bryan's law. In this paper, we generalise Rayleigh's dissipation function so that anisotropic nonlinear damping may be introduced into the equations of motion. Using a mixture of numeric and symbolic analysis on the ODEs of motion of the VG, for anisotropic light nonlinear damping, we demonstrate (up to an approximate average), that Bryan's law is affected by any form of such damping, causing pattern drift, compromising the accuracy of the VG.

  8. Simplified Model of Nonlinear Landau Damping

    International Nuclear Information System (INIS)

    Yampolsky, N.A.; Fisch, N.J.

    2009-01-01

    The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.

  9. Modulated Langmuir waves and nonlinear Landau damping

    International Nuclear Information System (INIS)

    Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.

    1975-01-01

    The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)

  10. Special class of nonlinear damping models in flexible space structures

    Science.gov (United States)

    Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

    1991-01-01

    A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

  11. Nonlinear damping based semi-active building isolation system

    Science.gov (United States)

    Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

    2018-06-01

    Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

  12. Global existence and uniform stabilization of a generalized dissipative Klein-Gordon equation type with boundary damping

    International Nuclear Information System (INIS)

    Zhang Zaiyun; Miao Xiujin; Chen Yuezhong; Liu Zhenhai

    2011-01-01

    In this paper, we prove the existence, uniqueness, and uniform stability of strong and weak solutions of the nonlinear generalized Klein-Gordon equation (1.1) 1 (see Sec. I) in bounded domains with nonlinear damped boundary conditions given by (1.1) 3 (see Sec. I) with some restrictions on function f(u), h(∇u), g(u t ), and b(x), we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique.

  13. The Characteristics of Vibration Isolation System with Damping and Stiffness Geometrically Nonlinear

    Science.gov (United States)

    Lu, Ze-Qi; Chen, Li-Qun; Brennan, Michael J.; Li, Jue-Ming; Ding, Hu

    2016-09-01

    The paper concerns an investigation into the use of both stiffness and damping nonlinearity in the vibration isolator to improve its effectiveness. The nonlinear damping and nonlinear stiffness are both achieved by horizontal damping and stiffness as the way of the geometrical nonlinearity. The harmonic balance method is used to analyze the force transmissibility of such vibration isolation system. It is found that as the horizontal damping increasing, the height of the force transmissibility peak is decreased and the high-frequency force transmissibility is almost the same. The results are also validated by some numerical method. Then the RMS of transmissibility under Gaussian white noise is calculated numerically, the results demonstrate that the beneficial effects of the damping nonlinearity can be achieved under random excitation.

  14. Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

    Science.gov (United States)

    Fibich, G.; Ilan, B.; Tsynkov, S.

    2002-01-01

    The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.

  15. Nonlinear time heteronymous damping in nonlinear parametric planetary systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena

    2014-01-01

    Roč. 225, č. 7 (2014), s. 2059-2073 ISSN 0001-5970 Institutional support: RVO:61388998 Keywords : nonlinear dynamics * planetary systems * heteronymous damping Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 1.465, year: 2014

  16. Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

    Directory of Open Access Journals (Sweden)

    S. L. Han

    2012-01-01

    Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

  17. Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms

    Directory of Open Access Journals (Sweden)

    Alex Elías-Zúñiga

    2013-01-01

    Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.

  18. Quantum corrections to nonlinear ion acoustic wave with Landau damping

    Energy Technology Data Exchange (ETDEWEB)

    Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)

    2014-07-15

    Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.

  19. Nonlinear roll damping of a barge with and without liquid cargo in spherical tanks

    Directory of Open Access Journals (Sweden)

    Wenhua Zhao

    2016-01-01

    Full Text Available Damping plays a significant role on the maximum amplitude of a vessel's roll motion, in particular near the resonant frequency. It is a common practice to predict roll damping using a linear radiation–diffraction code and add that to a linearized viscous damping component, which can be obtained through empirical, semi-empirical equations or free decay tests in calm water. However, it is evident that the viscous roll damping is nonlinear with roll velocity and amplitude. Nonlinear liquid cargo motions inside cargo tanks also contribute to roll damping, which when ignored impedes the accurate prediction of maximum roll motions. In this study, a series of free decay model tests is conducted on a barge-like vessel with two spherical tanks, which allows a better understanding of the nonlinear roll damping components considering the effects of the liquid cargo motion. To examine the effects of the cargo motion on the damping levels, a nonlinear model is adopted to calculate the damping coefficients. The liquid cargo motion is observed to affect both the linear and the quadratic components of the roll damping. The flow memory effect on the roll damping is also studied. The nonlinear damping coefficients of the vessel with liquid cargo motions in spherical tanks are obtained, which are expected to contribute in configurations involving spherical tanks.

  20. Nonlinear damping of drift waves by strong flow curvature

    International Nuclear Information System (INIS)

    Sidikman, K.L.; Carreras, B.A.; Garcia, L.; Diamond, P.H.

    1993-01-01

    A single-equation model has been used to study the effect of a fixed poloidal flow (V 0 ) on turbulent drift waves. The electron dynamics come from a laminar kinetic equation in the dissipative trapped-electron regime. In the past, the authors have assumed that the mode frequency is close to the drift-wave frequency. Trapped-electron density fluctuations are then related to potential fluctuations by an open-quotes iδclose quotes term. Flow shear (V 0 ') and curvature (V 0 double-prime) both have a stabilizing effect on linear modes for this open-quotes iδclose quotes model. However, in the nonlinear regime, single-helicity effects inhibit the flow damping. Neither V 0 ' nor V 0 double-prime produces a nonlinear damping effect. The above assumption on the frequency can be relaxed by including the electron time-response in the linear part of the evolution. In this time-dependent model, instability drive due to trapped electrons is reduced when mode frequency is greater than drift-wave frequency. Since V 0 double-prime produces such a frequency shift, its linear effect is enhanced. There is also nonlinear damping, since single-helicity effects do not eliminate the shift. Renormalized theory for this model predicts nonlinear stability for sufficiently large curvature. Single-helicity calculations have already shown nonlinear damping, and this strong V 0 double-prime regime is being explored. In the theory, the Gaussian shape of the nonlinear diffusivity is expanded to obtain a quadratic potential. The implications of this assumption will be tested by solving the full renormalized equation using a shooting method

  1. Nonlinear damping for vibration isolation of microsystems using shear thickening fluid

    Science.gov (United States)

    Iyer, S. S.; Vedad-Ghavami, R.; Lee, H.; Liger, M.; Kavehpour, H. P.; Candler, R. N.

    2013-06-01

    This work reports the measurement and analysis of nonlinear damping of micro-scale actuators immersed in shear thickening fluids (STFs). A power-law damping term is added to the linear second-order model to account for the shear-dependent viscosity of the fluid. This nonlinear model is substantiated by measurements of oscillatory motion of a torsional microactuator. At high actuation forces, the vibration velocity amplitude saturates. The model accurately predicts the nonlinear damping characteristics of the STF using a power-law index extracted from independent rheology experiments. This result reveals the potential to use STFs as adaptive, passive dampers for vibration isolation of microelectromechanical systems.

  2. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson; Said-Houari, Belkacem

    2012-01-01

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  3. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-03-07

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  4. Identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform

    Science.gov (United States)

    Ta, Minh-Nghi; Lardiès, Joseph

    2006-05-01

    We consider the free response of a nonlinear vibrating system. Using the ridges and skeletons of the continuous wavelet transform, we identify weak nonlinearities on damping and stiffness and estimate their physical parameters. The crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform. The method is applied to simulated single-degree-of-freedom systems and multi-degree-of-freedom systems with nonlinearities on damping and stiffness. Experimental validation of the nonlinear identification and parameter estimation method is presented. The experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor.

  5. Spontaneous symmetry breaking in ΡΤ symmetric systems with nonlinear damping

    International Nuclear Information System (INIS)

    Karthiga, S.; Chandrasekar, V.K.; Senthilvelan, M.; Lakshmanan, M.

    2016-01-01

    In this talk, we discuss the remarkable role of position dependent damping in determining the parametric regions of symmetry breaking in nonlinear ΡΤ -symmetric systems. We illustrate the nature of ΡΤ-symmetry preservation and breaking with reference to a remarkable integrable scalar nonlinear system. In the two dimensional cases of such position dependent damped systems, we unveil the existence of a class of novel bi-ΡΤ -symmetric systems which have two fold ΡΤ symmetries. We discuss the dynamics of these systems and show how symmetry breaking occurs, that is whether the symmetry breaking of the two ΡΤ symmetries occurs in pair or occurs one by one. The addition of linear damping in these nonlinearly damped systems induces competition between the two types of damping. This competition results in a ΡΤ phase transition in which the ΡΤ symmetry is broken for lower loss/gain strength and is restored by increasing the loss/gain strength. We also show that by properly designing the form of the position dependent damping, we can tailor the ΡΤ-symmetric regions of the system. (author)

  6. Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

    International Nuclear Information System (INIS)

    Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

    2009-01-01

    In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+αxx+βx 3 +γx=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+αx q x+βx 2q+1 =0, where α, β, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.

  7. Flutter Sensitivity to Boundary Layer Thickness, Structural Damping, and Static Pressure Differential for a Shuttle Tile Overlay Repair Concept

    Science.gov (United States)

    Scott, Robert C.; Bartels, Robert E.

    2009-01-01

    This paper examines the aeroelastic stability of an on-orbit installable Space Shuttle patch panel. CFD flutter solutions were obtained for thick and thin boundary layers at a free stream Mach number of 2.0 and several Mach numbers near sonic speed. The effect of structural damping on these flutter solutions was also examined, and the effect of structural nonlinearities associated with in-plane forces in the panel was considered on the worst case linear flutter solution. The results of the study indicated that adequate flutter margins exist for the panel at the Mach numbers examined. The addition of structural damping improved flutter margins as did the inclusion of nonlinear effects associated with a static pressure difference across the panel.

  8. Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim

    1996-01-01

    in an exponentially decreasing width of the solution in the long-time limit. We also find that a sufficiently large noise variance may cause an initially localized distribution to spread instead of contracting, and that the critical variance necessary to cause dispersion will for small damping be the same......We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead...

  9. Collisionless damping of nonlinear dust ion acoustic wave due to dust charge fluctuation

    International Nuclear Information System (INIS)

    Ghosh, Samiran; Chaudhuri, Tushar K.; Sarkar, Susmita; Khan, Manoranjan; Gupta, M.R.

    2002-01-01

    A dissipation mechanism for the damping of the nonlinear dust ion acoustic wave in a collisionless dusty plasma consisting of nonthermal electrons, ions, and variable charge dust grains has been investigated. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust ion acoustic wave propagation to be described by the damped Korteweg-de Vries equation. Due to the presence of nonthermal electrons, the dust ion acoustic wave admits both positive and negative potential and it suffers less damping than the dust acoustic wave, which admits only negative potential

  10. Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Ciprian G. Gal

    2017-01-01

    Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.

  11. Self-sustained solitons in systems with nonlinear damping

    International Nuclear Information System (INIS)

    Gonzalez, J.A.

    1993-05-01

    The existence and stability of kinks in systems with nonlinear damping are investigated. We discuss the mechanism of a bifurcation after which the kink becomes a non-stationary state. (author). 9 refs

  12. Modified multiple time scale method for solving strongly nonlinear damped forced vibration systems

    Science.gov (United States)

    Razzak, M. A.; Alam, M. Z.; Sharif, M. N.

    2018-03-01

    In this paper, modified multiple time scale (MTS) method is employed to solve strongly nonlinear forced vibration systems. The first-order approximation is only considered in order to avoid complexicity. The formulations and the determination of the solution procedure are very easy and straightforward. The classical multiple time scale (MS) and multiple scales Lindstedt-Poincare method (MSLP) do not give desire result for the strongly damped forced vibration systems with strong damping effects. The main aim of this paper is to remove these limitations. Two examples are considered to illustrate the effectiveness and convenience of the present procedure. The approximate external frequencies and the corresponding approximate solutions are determined by the present method. The results give good coincidence with corresponding numerical solution (considered to be exact) and also provide better result than other existing results. For weak nonlinearities with weak damping effect, the absolute relative error measures (first-order approximate external frequency) in this paper is only 0.07% when amplitude A = 1.5 , while the relative error gives MSLP method is surprisingly 28.81%. Furthermore, for strong nonlinearities with strong damping effect, the absolute relative error found in this article is only 0.02%, whereas the relative error obtained by MSLP method is 24.18%. Therefore, the present method is not only valid for weakly nonlinear damped forced systems, but also gives better result for strongly nonlinear systems with both small and strong damping effect.

  13. Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

    Science.gov (United States)

    Olejnik, Paweł; Awrejcewicz, Jan

    2018-01-01

    A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

  14. Nonlinear damped Schrodinger equation in two space dimensions

    Directory of Open Access Journals (Sweden)

    Tarek Saanouni

    2015-04-01

    Full Text Available In this article, we study the initial value problem for a semi-linear damped Schrodinger equation with exponential growth nonlinearity in two space dimensions. We show global well-posedness and exponential decay.

  15. Travelling Solitons in the Damped Driven Nonlinear Schroedinger Equation

    CERN Document Server

    Barashenkov, I V

    2003-01-01

    The well-known effect of the linear damping on the moving nonlinear Schrodinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable.

  16. Travelling solitons in the damped driven nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Barashenkov, I.V.; Zemlyanaya, E.V.

    2003-01-01

    The well known effect of the linear damping on the moving nonlinear Schroedinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable

  17. On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

    Directory of Open Access Journals (Sweden)

    Koh Kim Jie

    2017-01-01

    Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

  18. Linear time heteronymous damping in nonlinear parametric systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena; Houfek, Martin

    2016-01-01

    Roč. 40, 23-24 (2016), s. 10038-10051 ISSN 0307-904X Institutional support: RVO:61388998 Keywords : nonlinear dynamics of systems * parametric systems * time heteronymous damping * gears Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 2.350, year: 2016

  19. Flutter analysis of an airfoil with nonlinear damping using equivalent linearization

    Directory of Open Access Journals (Sweden)

    Chen Feixin

    2014-02-01

    Full Text Available The equivalent linearization method (ELM is modified to investigate the nonlinear flutter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM, an equivalent system can be deduced and then investigated by linear flutter analysis methods. Different from the routine procedures of the ELM, the frequency rather than the amplitude of limit cycle oscillation (LCO is chosen as an active increment to produce bifurcation charts. Numerical examples show that this modification makes the ELM much more efficient. Meanwhile, the LCOs obtained by the ELM are in good agreement with numerical solutions. The nonlinear damping can delay the occurrence of secondary bifurcation. On the other hand, it has marginal influence on bifurcation characteristics or LCOs.

  20. A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings

    Science.gov (United States)

    Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

    2016-10-01

    In this paper, we address the stability of resonantly forced density waves in dense planetary rings. Goldreich & Tremaine have already argued that density waves might be unstable, depending on the relationship between the ring’s viscosity and the surface mass density. In the recent paper Schmidt et al., we have pointed out that when—within a fluid description of the ring dynamics—the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping, but nonlinearity of the underlying equations guarantees a finite amplitude and eventually a damping of the wave. We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model. This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts density waves to be (linearly) unstable in a ring region where the conditions for viscous overstability are met. Sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. The wave’s damping lengths of the model depend on certain input parameters, such as the distance to the threshold for viscous overstability in parameter space and the ground state surface mass density.

  1. Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping

    Directory of Open Access Journals (Sweden)

    Eleni Bisognin

    2007-01-01

    Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.

  2. On the wave equation with semilinear porous acoustic boundary conditions

    KAUST Repository

    Graber, Philip Jameson; Said-Houari, Belkacem

    2012-01-01

    The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

  3. On the wave equation with semilinear porous acoustic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-05-01

    The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

  4. Modal approach for nonlinear vibrations of damped impacted plates: Application to sound synthesis of gongs and cymbals

    Science.gov (United States)

    Ducceschi, M.; Touzé, C.

    2015-05-01

    This paper presents a modal, time-domain scheme for the nonlinear vibrations of perfect and imperfect plates. The scheme can take into account a large number of degrees-of-freedom and is energy-conserving. The targeted application is the sound synthesis of cymbals and gong-like musical instruments, which are known for displaying a strongly nonlinear vibrating behaviour. This behaviour is typical of a wave turbulence regime, in which the wide-band spectrum of excited modes is observable in the form of an energy cascade. The modal method is selected for its versatility in handling complex damping laws that can be implemented easily by selecting appropriate damping values in each one of the modal equations. In the first part of the paper, the modal method is explained in its generality, and it will be seen that the method is valid for plates with arbitrary geometry and boundary conditions as long as the eigenmodes are known. Secondly, a time-integration, energy-conserving scheme for perfect and imperfect plates is presented, and implementation comments are given in order to treat efficiently the high-dimensionality of the resulting dynamical system. The scheme is run with appropriate parameters in order to produce sound samples. A simple impact law is considered for the excitation, whereas the flexibility of the method is highlighted by showing simulations for free-edge circular plates and simply-supported rectangular plates, together with various damping laws.

  5. Comparison among nonlinear excitation control strategies used for damping power system oscillations

    International Nuclear Information System (INIS)

    Leon, A.E.; Solsona, J.A.; Valla, M.I.

    2012-01-01

    Highlights: ► A description and comparison of nonlinear control strategies for synchronous generators are presented. ► Advantages of using nonlinear controllers are emphasized against the use of classical PSSs. ► We find that a particular selection of IDA gains achieve the same performance that FL controllers. - Abstract: This work is focused on the problem of power system stability. A thorough description of nonlinear control strategies for synchronous generator excitation, which are designed for damping oscillations and improving transient stability on power systems, is presented along with a detailed comparison among these modern strategies and current solutions based on power system stabilizers. The performance related to damping injection in each controller, critical time enhancement, robustness against parametric uncertainties, and control signal energy consumption is analyzed. Several tests are presented to validate discussions on various advantages and disadvantages of each control strategy.

  6. Nonlinear effects in the damping of third-sound pulses

    International Nuclear Information System (INIS)

    Browne, D.A.

    1984-01-01

    We show that nonlinearities in the equations of motion for a third-sound pulse in a thick superfluid film lead to the production of short-wavelength solitons. The soliton damping arises from viscous stresses in the film, rather than from coupling to thermal currents in the vapor and the substrate as in the hydrodynamic regime. These solitons are more strongly damped than a long-wavelength third-sound wave and lead to a larger attenuation of the pulse. We show that this mechanism can account for the discrepancy between attenuation calculated theoretically for the long-wavelength limit and the experimentally observed attenuation of low-amplitude third-sound pulses

  7. TCSC Nonlinear Adaptive Damping Controller Design Based on RBF Neural Network to Enhance Power System Stability

    DEFF Research Database (Denmark)

    Yao, Wei; Fang, Jiakun; Zhao, Ping

    2013-01-01

    the characteristics of the conventional PID, but adjust the parameters of PID controller online using identified Jacobian information from RBFNN. Hence, it has strong adaptability to the variation of the system operating condition. The effectiveness of the proposed controller is tested on a two-machine five-bus power...... system and a four-machine two-area power system under different operating conditions in comparison with the lead-lag damping controller tuned by evolutionary algorithm (EA). Simulation results show that the proposed damping controller achieves good robust performance for damping the low frequency......In this paper, a nonlinear adaptive damping controller based on radial basis function neural network (RBFNN), which can infinitely approximate to nonlinear system, is proposed for thyristor controlled series capacitor (TCSC). The proposed TCSC adaptive damping controller can not only have...

  8. Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects

    Directory of Open Access Journals (Sweden)

    Jie-Yu Chen

    2009-05-01

    Full Text Available In Atomic force microscope (AFM examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.

  9. Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping

    Directory of Open Access Journals (Sweden)

    Jieqiong Wu

    2015-09-01

    Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.

  10. On the dynamic buckling of a weakly damped nonlinear elastic ...

    African Journals Online (AJOL)

    In this paper we determine the dynamic buckling load of a strictly nonlinear but weakly damped elastic oscillatory model structure subjected to small perturbations The loading history is explicitly time dependent and varies slowly with time over a natural period of oscillation of the structure. A multiple timing regular ...

  11. Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior Damping

    International Nuclear Information System (INIS)

    Kaltenbacher, Barbara

    2010-01-01

    In this paper we show boundary observability and boundary stabilizability by linear feedbacks for a class of nonlinear wave equations including the undamped Westervelt model used in nonlinear acoustics. We prove local existence for undamped generalized Westervelt equations with homogeneous Dirichlet boundary conditions as well as global existence and exponential decay with absorbing type boundary conditions.

  12. Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-Propelled Space Vehicles

    Science.gov (United States)

    Ottander, John A.; Hall, Robert A.; Powers, J. F.

    2018-01-01

    A method is presented that allows for the prediction of the magnitude of limit cycles due to adverse control-slosh interaction in liquid propelled space vehicles using non-linear slosh damping. Such a method is an alternative to the industry practice of assuming linear damping and relying on: mechanical slosh baffles to achieve desired stability margins; accepting minimal slosh stability margins; or time domain non-linear analysis to accept time periods of poor stability. Sinusoidal input describing functional analysis is used to develop a relationship between the non-linear slosh damping and an equivalent linear damping at a given slosh amplitude. In addition, a more accurate analytical prediction of the danger zone for slosh mass locations in a vehicle under proportional and derivative attitude control is presented. This method is used in the control-slosh stability analysis of the NASA Space Launch System.

  13. Global well-posedness for nonlinear Schrodinger equations with energy-critical damping

    Directory of Open Access Journals (Sweden)

    Binhua Feng

    2015-01-01

    Full Text Available We consider the Cauchy problem for the nonlinear Schrodinger equations with energy-critical damping. We prove the existence of global in-time solutions for general initial data in the energy space. Our results extend some results from [1,2].

  14. An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

    Science.gov (United States)

    Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

    2018-06-01

    This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

  15. Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.

    Science.gov (United States)

    Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad

    2016-02-01

    In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.

  16. Vibration isolation using nonlinear damping implemented by a feedback-controlled MR damper

    International Nuclear Information System (INIS)

    Ho, C; Lang, Z Q; Billings, S A; Sapiński, B

    2013-01-01

    The main problem of using a conventional linear damper on a vibration isolation system is that the reduction of the resonant peak in many cases inevitably results in the degradation of the high-frequency transmissibility. Instead of using active control methods which normally depend on the model of the controlled plant and where unmodelled dynamics may induce stability concerns, recent studies have revealed that optimal vibration isolation over a wide frequency range can be achieved by using nonlinear damping. The present study is concerned with the realization of the ideal nonlinear damping characteristic using a feedback-controlled MR damper. Both simulation and experimental studies are conducted to demonstrate the advantages of the simple but effective vibration control strategy. This research work has significant implications for the effective use of MR dampers in the vibration control of a wide range of engineering systems. (paper)

  17. On the Effect of Thermoelastic Damping in Nonlinear Micro Electro Mechanical Resonators using Differential Quadrature Method

    Directory of Open Access Journals (Sweden)

    A. Karami Mohammadi

    2015-07-01

    Full Text Available : In this paper, a nonlinear model of clamped-clamped microbeam actuated by electrostatic load with stretching and thermoelastic effects is presented. Free vibration frequency is calculated by discretization based on DQ method. Frequency is a complex value due to the thermoelastic effect that dissipates the energy. By separating the real and imaginary parts of frequency, quality factor of thermoelastic damping is calculated. Both stretching and thermoelastic effects are validated against the results of the reference papers. The variations of thermoelastic damping versus elasticity modulus, coefficient of thermal expansion and geometrical parameters such as thickness, gap distance, and length are investigated and these results are compared in the linear and nonlinear models for high values of voltage. Also, this paper shows that since for high values of electrostatic voltage the linear model reveals a large error for calculating the thermoelastic damping, the nonlinear model should be used for this purpose.

  18. Nonlinear piping damping and response predictions

    International Nuclear Information System (INIS)

    Severud, L.K.; Weiner, E.O.; Lindquist, M.R.; Anderson, M.J.; Wagner, S.E.

    1986-10-01

    The high level dynamic testing of four prototypic piping systems, used to provide benchmarks for analytical prediction comparisons, is overviewed. The size of pipe tested ranged from one-inch to six-inches in diameter and consisted of carbon steel or stainless steel material. Failure of the tested systems included progressive gross deformation or some combination of ratchetting-fatigue. Pretest failure predictions and post test comparisons using simplified elastic and elasto-plastic methods are presented. Detailed non-linear inelastic analyses are also shown, along with a typical ratchet-fatigue failure calculation. A simplified method for calculating modal equivalent viscous damping for snubbers and plastic hinges is also described. Conclusions are made regarding the applicability of the various analytical failure predictive methods and recommendations are made for future analytic and test efforts

  19. Damping characteristic identification of non-linear soil-structural system interaction by phase resonance

    International Nuclear Information System (INIS)

    Poterasu, V.F.

    1984-01-01

    It is presented a method and the phase resonance for damping characteristic identification of non-linear soil-structural interaction. The algorithm can be applied in case of any, not necessarily, damping characteristic of the system examined. For the identification, the system is harmonically excited and are considered the super-harmonic amplitudes for odd and even powers of the x. The response of shear beam system for different levels of base excitation and for different locations of the load is considered. (Author) [pt

  20. An optimal approach to active damping of nonlinear vibrations in composite plates using piezoelectric patches

    International Nuclear Information System (INIS)

    Saviz, M R

    2015-01-01

    In this paper a nonlinear approach to studying the vibration characteristic of laminated composite plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange type of strain–displacements relations, by incorporating higher-order terms arising from nonlinear relations of kinematics into mathematical formulations. The equations of motion are obtained through the energy method, based on Lagrange equations and by using higher-order shear deformation theories with von Karman–type nonlinearities, so that transverse shear strains vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch. Different boundary conditions are investigated. Optimal locations of piezoelectric patches are found using a genetic algorithm to maximize spatial controllability/observability and considering the effect of residual modes to reduce spillover effect. Active attenuation of vibration of laminated composite plate is achieved through an optimal control law with inequality constraint, which is related to the maximum and minimum values of allowable voltage in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the Pontryagin’s minimum principle is implemented in a system with multi-inequality constraint of control inputs. The results are compared with similar ones, proving the accuracy of the model especially for the structures undergoing large deformations. The convergence is studied and nonlinear frequencies are obtained for different thickness ratios. The structural coupling between plate and piezoelectric actuators is analyzed. Some examples with new features are presented, indicating that the piezo-patches significantly improve the damping characteristics of the plate for suppressing the geometrically nonlinear transient vibrations. (paper)

  1. Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands

    Science.gov (United States)

    Todo, Y.; Berk, H. L.; Breizman, B. N.

    2012-09-01

    This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ⩾ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping.

  2. Damping and non-linearity of a levitating magnet in rotation above a superconductor

    International Nuclear Information System (INIS)

    Druge, J; Jean, C; Laurent, O; Méasson, M-A; Favero, I

    2014-01-01

    We study the dissipation of moving magnets in levitation above a superconductor. The rotation motion is analyzed using optical tracking techniques. It displays a remarkable regularity together with long damping time up to several hours. The magnetic contribution to the damping is investigated in detail by comparing 14 distinct magnetic configurations and points towards amplitude-dependent dissipation mechanisms. The non-linear dynamics of the mechanical rotation motion is also revealed and described with an effective Duffing model. The magnetic mechanical damping is consistent with measured hysteretic cycles M(H) that are discussed within a modified critical state model. The obtained picture of the coupling of levitating magnets to their environment sheds light on their potential as ultra-low dissipation mechanical oscillators for high precision physics. (paper)

  3. Boundary induced nonlinearities at small Reynolds numbers

    NARCIS (Netherlands)

    Sbragaglia, M.; Sugiyama, K.

    2007-01-01

    We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag

  4. Nonlinear streak computation using boundary region equations

    Energy Technology Data Exchange (ETDEWEB)

    Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

    2012-08-01

    The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

  5. Relativistic electron beam acceleration by cascading nonlinear Landau damping of electromagnetic waves in a plasma

    International Nuclear Information System (INIS)

    Sugaya, R.; Ue, A.; Maehara, T.; Sugawa, M.

    1996-01-01

    Acceleration and heating of a relativistic electron beam by cascading nonlinear Landau damping involving three or four intense electromagnetic waves in a plasma are studied theoretically based on kinetic wave equations and transport equations derived from relativistic Vlasov endash Maxwell equations. Three or four electromagnetic waves excite successively two or three nonresonant beat-wave-driven relativistic electron plasma waves with a phase velocity near the speed of light [v p =c(1-γ -2 p ) 1/2 , γ p =ω/ω pe ]. Three beat waves interact nonlinearly with the electron beam and accelerate it to a highly relativistic energy γ p m e c 2 more effectively than by the usual nonlinear Landau damping of two electromagnetic waves. It is proved that the electron beam can be accelerated to more highly relativistic energy in the plasma whose electron density decreases temporally with an appropriate rate because of the temporal increase of γ p . copyright 1996 American Institute of Physics

  6. On the energetics of a damped beam-like equation for different boundary conditions

    International Nuclear Information System (INIS)

    Sandilo, S.H.; Sheikh, A.H.; Soomro, A.R.

    2017-01-01

    In this paper, the energy estimates for a damped linear homogeneous beam-like equation will be considered. The energy estimates will be studied for different BCs (Boundary Conditions) for the axially moving continuum. The problem has physical and engineering application. The applications are mostly occurring in models of conveyor belts and band-saw blades. The research study is focused on the Dirichlet, the Neumann and the Robin type of BCs. From physical point of view, the considered mathematical model expounds the transversal vibrations of a moving belt system or moving band-saw blade. It is assumed that a viscous damping parameter and the horizontal velocity are positive and constant. It will be shown in this paper that change in geometry or the physics of the boundaries can affect the stability properties of the system in general and stability depends on the axial direction of the motion. In all cases of the BCs, it will be shown that there is energy decay due to viscous damping parameter and it will also be shown that in some cases there is no conclusion whether the beam energy decreases or increases. The detailed physical interpretation of all terms and expressions is provided and studied in detail. (author)

  7. On the Energetics of a Damped Beam-Like Equation for Different Boundary Conditions

    Directory of Open Access Journals (Sweden)

    SAJAD HUSSAIN SANDILO

    2017-04-01

    Full Text Available In this paper, the energy estimates for a damped linear homogeneous beam-like equation will be considered. The energy estimates will be studied for different BCs (Boundary Conditions for the axially moving continuum. The problem has physical and engineering application. The applications are mostly occurring in models of conveyor belts and band-saw blades. The research study is focused on the Dirichlet, the Neumann and the Robin type of BCs. From physical point of view, the considered mathematical model expounds the transversal vibrations of a moving belt system or moving band-saw blade. It is assumed that a viscous damping parameter and the horizontal velocity are positive and constant. It will be shown in this paper that change in geometry or the physics of the boundaries can affect the stability properties of the system in general and stability depends on the axial direction of the motion. In all cases of the BCs, it will be shown that there is energy decay due to viscous damping parameter and it will also be shown that in some cases there is no conclusion whether the beam energy decreases or increases. The detailed physical interpretation of all terms and expressions is provided and studied in detail.

  8. Nonlinear Transient Growth and Boundary Layer Transition

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2016-01-01

    Parabolized stability equations (PSE) are used in a variational approach to study the optimal, non-modal disturbance growth in a Mach 3 at plate boundary layer and a Mach 6 circular cone boundary layer. As noted in previous works, the optimal initial disturbances correspond to steady counter-rotating streamwise vortices, which subsequently lead to the formation of streamwise-elongated structures, i.e., streaks, via a lift-up effect. The nonlinear evolution of the linearly optimal stationary perturbations is computed using the nonlinear plane-marching PSE for stationary perturbations. A fully implicit marching technique is used to facilitate the computation of nonlinear streaks with large amplitudes. To assess the effect of the finite-amplitude streaks on transition, the linear form of plane- marching PSE is used to investigate the instability of the boundary layer flow modified by spanwise periodic streaks. The onset of bypass transition is estimated by using an N- factor criterion based on the amplification of the streak instabilities. Results show that, for both flow configurations of interest, streaks of sufficiently large amplitude can lead to significantly earlier onset of transition than that in an unperturbed boundary layer without any streaks.

  9. Coupled influence of noise and damped propagation of impurity on linear and nonlinear polarizabilities of doped quantum dots

    International Nuclear Information System (INIS)

    Ganguly, Jayanta; Ghosh, Manas

    2015-01-01

    Highlights: • Linear and nonlinear polarizabilities of quantum dot are studied. • Quantum dot is doped with a repulsive impurity. • Doped system is subject to Gaussian white noise. • Dopant migrates under damped condition. • Noise-damping coupling affects polarizabilities. - Abstract: We investigate the profiles of diagonal components of static and frequency-dependent linear, first, and second nonlinear polarizabilities of repulsive impurity doped quantum dot. We have considered propagation of dopant within an environment that damps the motion. Simultaneous presence of noise inherent to the system has also been considered. The dopant has a Gaussian potential and noise considered is a Gaussian white noise. The doped system is exposed to an external electric field which could be static or time-dependent. Noise undergoes direct coupling with damping and the noise-damping coupling strength appears to be a crucial parameter that designs the profiles of polarizability components. This happens because the coupling strength modulates the dispersive and asymmetric character of the system. The frequency of external field brings about additional features in the profiles of polarizability components. The present investigation highlights some useful features in the optical properties of doped quantum dots

  10. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Stéphane

    2011-12-01

    In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

  11. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Sté phane; Said-Houari, Belkacem

    2011-01-01

    In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

  12. Numerical analysis of non-linear vibrations of a fractionally damped cylindrical shell under the conditions of combinational internal resonance

    Directory of Open Access Journals (Sweden)

    Rossikhin Yury A.

    2018-01-01

    Full Text Available Non-linear damped vibrations of a cylindrical shell embedded into a fractional derivative medium are investigated for the case of the combinational internal resonance, resulting in modal interaction, using two different numerical methods with further comparison of the results obtained. The damping properties of the surrounding medium are described by the fractional derivative Kelvin-Voigt model utilizing the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential equations of the second order are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitude-and-phase modulations for the case of the combinational internal resonance. A good agreement in results is declared.

  13. Nonlinear vibration of a traveling belt with non-homogeneous boundaries

    Science.gov (United States)

    Ding, Hu; Lim, C. W.; Chen, Li-Qun

    2018-06-01

    Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account.

  14. Electromagnetic pulses at the boundary of a nonlinear plasma

    International Nuclear Information System (INIS)

    Satorius, E.H.

    1975-01-01

    An investigation was made of the behavior of strong electromagnetic pulses at the boundary of a nonlinear, cold, collisionless, and uniform plasma. The nonlinearity considered here is due to the nonlinear terms in the fluid equation which is used to describe the plasma. Two cases are studied. First, the case where there is a voltage pulse applied across the plane boundary of a semi-infinite, nonlinear plasma. Two different voltage pulses are considered, i.e., a delta function pulse and a suddenly turned-on sinusoidal pulse. The resulting electromagnetic fields propagating in the nonlinear plasma are found in this case. In the second case, the reflection of incident E-polarized and H-polarized, electromagnetic pulses at various angles of incidence from a nonlinear, semi-infinite plasma are considered. Again, two forms of incident pulses are considered: a delta function pulse and a suddenly turned-on sinusoidal pulse. In case two, the reflected electromagnetic fields are found. In both cases, the method used for finding the fields is to first solve the fluid equation (which describes the plasma) for the nonlinear conduction current in terms of the electric field using a perturbation method (since the nonlinear effects are assumed to be small). Next, this current is substituted into Maxwell's equations, and finally the electromagnetic fields which satisfy the boundary conditions are found. (U.S.)

  15. On the Possibility of Using Nonlinear Elements for Landau Damping in High-Intensity Beams

    Energy Technology Data Exchange (ETDEWEB)

    Alexahin, Y. [Fermilab; Gianfelice-Wendt, E. [Fermilab; Lebedev, V. [Fermilab; Valishev, A. [Fermilab

    2016-09-30

    Direct space-charge force shifts incoherent tunes downwards from the coherent ones breaking the Landau mechanism of coherent oscillations damping at high beam intensity. To restore it nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a “nonlinear integrable optics” insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II (PIP II) parameters the required nonlinear tune shift can be created without destroying the dynamic aperture.

  16. Permanent dipole moments and damping in nonlinear optics. A quantum electrodynamic description

    International Nuclear Information System (INIS)

    Davila-Smith, L.C.

    1999-01-01

    Based on the well-known transformation of the electric-dipole interaction, different nonlinear optical processes are analysed. The transformation provides a convenient means for ascertaining the effects of permanent dipoles on the optical behaviour of systems with a response dominated by two energy levels. By establishing the general validity of the procedure for parametric and non-parametric processes, it is shown how the detailed structure of the optical nonlinearity can be ascertained, based on a novel interpretation of the relevant quantum electrodynamical Feynman diagrams. This transformation is used to analysed a novel five-wave mixing process, which is also developed in this thesis. This process is of considerable interest for its involvement in the generation of even harmonics in isotropic media. Also, the flexibility in the beam geometry affords considerable scope for the study of the polarisation and angular dependence. Finally, a general study of the effects of resonance in matter-radiation interactions is given, justifying the phenomenological incorporation of the damping addenda. The two alternative convention used when the damping is introduced are discussed, showing that both conventions lead to different physical results. Based on these studies the resonance effects are considered in relation to different multiphoton processes. (author)

  17. Collective states of externally driven, damped nonlinear Schroedinger solitons

    International Nuclear Information System (INIS)

    Barashenkov, I.V.; Smirnov, Yu.S.

    1997-01-01

    We study bifurcations of localized stationary solitons of the externally driven, damped nonlinear Schroedinger equation iΨ t + Ψ xx + 2|Ψ| 2 Ψ=-iγΨ-h e iΩt , in the region of large γ (γ>1/2). For each pair of h and γ, there are two coexisting solitons, Ψ + and Ψ - . As the driver's strength h increases for the fixed γ, the Ψ + soliton merges with the flat background while the Ψ - forms a stationary collective state with two 'psi-pluses': Ψ - → Ψ (+ - +) . We obtain other stationary solutions and identify them as multisoliton complexes Ψ (++) , Ψ (--) , Ψ (-+) , Ψ (---) , Ψ (-+- ) etc. The corresponding intersoliton separations are compared to predictions of a variational approximation

  18. Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

    Science.gov (United States)

    Liu, Ping; Shi, Junping

    2018-01-01

    The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.

  19. Extended Rayleigh Damping Model

    Directory of Open Access Journals (Sweden)

    Naohiro Nakamura

    2016-07-01

    Full Text Available In dynamic analysis, frequency domain analysis can be used if the entire structure is linear. However, time history analysis is generally used if nonlinear elements are present. Rayleigh damping has been widely used in time history response analysis. Many articles have reported the problems associated with this damping and suggested remedies. A basic problem is that the frequency area across which the damping ratio is almost constant is too narrow. If the area could be expanded while incurring only a small increase in computational cost, this would provide an appropriate remedy for this problem. In this study, a novel damping model capable of expanding the constant frequency area by more than five times was proposed based on the study of a causal damping model. This model was constructed by adding two terms to the Rayleigh damping model and can be applied to the linear elements in the time history analysis of a nonlinear structure. The accuracy and efficiency of the model were confirmed using example analyses.

  20. Collisional damping of Langmuir waves in the collisionless limit

    International Nuclear Information System (INIS)

    Auerbach, S.P.

    1977-01-01

    Linear Langmuir wave damping by collisions is studied in the limit of collision frequency ν approaching zero. In this limit, collisions are negligible, except in a region in velocity space, the boundary layer, centered about the phase velocity. If kappa, the ratio of the collisional equilibration time in the boundary layer to the Landau damping time, is small, the boundary layer width scales as ν/sup 1/3/, and the perturbed distribution function scales as ν/sup -1/3/. The damping rate is thus independent of ν, although essentially all the damping occurs in the collision-dominated boundary layer. Solution of the Fokker--Planck equation shows that the damping rate is precisely the Landau (collisionless) rate. The damping rate is independent of kappa, although the boundary layer thickness is not

  1. On the solution of the equations for nonlinear interaction of three damped waves

    International Nuclear Information System (INIS)

    1976-01-01

    Three-wave interactions are analyzed in a coherent wave description assuming different linear damping (or growth) of the individual waves. It is demonstrated that when two of the coefficients of dissipation are equal, the set of equations can be reduced to a single equivalent equation, which in the nonlinearly unstable case, where one wave is undamped, asymptotically takes the form of an equation defining the third Painleve transcendent. It is then possible to find an asymptotic expansion near the time of explosion. This solution is of principal interest since it indicates that the solution of the general three-wave system, where the waves undergo different individual dissipations, belongs to a higher class of functions, which reduces to Jacobian elliptic functions only in the case where all waves suffer the same damping [fr

  2. On the solvability of initial boundary value problems for nonlinear ...

    African Journals Online (AJOL)

    In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...

  3. Geometrically nonlinear transient vibrations of actively damped anti-symmetric angle ply laminated composite shallow shell using active fibre composite (AFC) actuators

    Science.gov (United States)

    Ashok, M. H.; Shivakumar, J.; Nandurkar, Santosh; Khadakbhavi, Vishwanath; Pujari, Sanjay

    2018-02-01

    In present work, the thin laminated composite shallow shell as smart structure with AFC material’s ACLD treatment is analyzed for geometrically nonlinear transient vibrations. The AFC material is used to make the constraining layer of the ACLD treatment. Golla-Hughes-McTavish (GHM) is used to model the constrained viscoelastic layer of the ACLD treatment in time domain. Along with a simple first-order shear deformation theory the Von Kármán type non-linear strain displacement relations are used for deriving this electromechanical coupled problem. A 3-dimensional finite element model of smart composite panels integrated with the ACLD treated patches has been modelled to reveal the performance of ACLD treated patches on improving the damping properties of slender anti-symmetric angle-ply laminated shallow shell, in controlling the transient vibrations which are geometrically nonlinear. The mathematical results explain that the ACLD treated patches considerably enhance the damping properties of anti-symmetric angle-ply panels undergoing geometrically nonlinear transient vibrations.

  4. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

    Directory of Open Access Journals (Sweden)

    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  5. Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition

    Directory of Open Access Journals (Sweden)

    Qiansheng Tang

    2016-01-01

    Full Text Available Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.

  6. Effect of Stress Amplitude on the Damping of Recycled Aggregate Concrete.

    Science.gov (United States)

    Liang, Chaofeng; Liu, Tiejun; Xiao, Jianzhuang; Zou, Dujian; Yang, Qiuwei

    2015-08-14

    Damping characterizes the energy dissipation capacity of materials and structures, and it is affected by several external factors such as vibrating frequency, stress history, temperature, and stress amplitude. This study investigates the relationship between the damping and the stress amplitude of environment-friendly recycled aggregate concrete (RAC). First, a function model of a member's loss factor and stress amplitude was derived based on Lazan's damping-stress function. Then, the influence of stress amplitude on the loss tangent of RAC was experimentally investigated. Finally, parameters used to determine the newly derived function were obtained by numerical fitting. It is shown that the member's loss factor is affected not only by the stress amplitude but also by factors such as the cross section shapes, boundary conditions, load types, and loading positions. The loss tangent of RAC increases with the stress amplitude, even at low stress amplitude. The damping energy exponent of RAC is not identically equal to 2.0, indicating that the damping is nonlinear. It is also found that the energy dissipation capacity of RAC is superior to that of natural aggregate concrete (NAC), and the energy dissipation capacity can be further improved by adding modified admixtures.

  7. Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions

    Directory of Open Access Journals (Sweden)

    Qingkai Kong

    2012-02-01

    Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with  Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.

  8. On Landau damping

    KAUST Repository

    Mouhot, Clément

    2011-09-01

    Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation; new functional inequalities; a control of non-linear echoes; sharp "deflection" estimates; and a Newton approximation scheme. Our results hold for any potential no more singular than Coulomb or Newton interaction; the limit cases are included with specific technical effort. As a side result, the stability of homogeneous equilibria of the non-linear Vlasov equation is established under sharp assumptions. We point out the strong analogy with the KAM theory, and discuss physical implications. Finally, we extend these results to some Gevrey (non-analytic) distribution functions. © 2011 Institut Mittag-Leffler.

  9. Oscillation criteria for third order nonlinear delay differential equations with damping

    Directory of Open Access Journals (Sweden)

    Said R. Grace

    2015-01-01

    Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.

  10. Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

    2017-06-01

    Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

  11. On a non-linear pseudodifferential boundary value problem

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong.

    1989-12-01

    A pseudodifferential boundary value problem for operators with symbols taking values in Sobolev spaces and with non-linear right-hand side was studied. Existence and uniqueness theorems were proved. (author). 11 refs

  12. Boundary control of nonlinear coupled heat systems using backstepping

    KAUST Repository

    Bendevis, Paul

    2016-10-20

    A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.

  13. Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions

    Energy Technology Data Exchange (ETDEWEB)

    Amour, Rabia; Tribeche, Mouloud [Faculty of Physics, Theoretical Physics Laboratory (TPL), Plasma Physics Group (PPG), University of Bab-Ezzouar, USTHB, B.P. 32, El Alia, Algiers 16111 (Algeria)

    2014-12-15

    The charge variation induced nonlinear dust-acoustic wave damping in a charge varying dusty plasma with nonextensive ions is considered. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust acoustic wave propagation to be described by a damped Korteweg-de Vries (dK-dV) equation the coefficients of which depend sensitively on the nonextensive parameter q. The damping term, solely due to the dust charge variation, is affected by the ion nonextensivity. For the sake of completeness, the possible effects of nonextensivity and collisionless damping on weakly nonlinear wave packets described by the dK-dV equation are succinctly outlined by deriving a nonlinear Schrödinger-like equation with a complex nonlinear coefficient.

  14. Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions

    International Nuclear Information System (INIS)

    Amour, Rabia; Tribeche, Mouloud

    2014-01-01

    The charge variation induced nonlinear dust-acoustic wave damping in a charge varying dusty plasma with nonextensive ions is considered. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust acoustic wave propagation to be described by a damped Korteweg-de Vries (dK-dV) equation the coefficients of which depend sensitively on the nonextensive parameter q. The damping term, solely due to the dust charge variation, is affected by the ion nonextensivity. For the sake of completeness, the possible effects of nonextensivity and collisionless damping on weakly nonlinear wave packets described by the dK-dV equation are succinctly outlined by deriving a nonlinear Schrödinger-like equation with a complex nonlinear coefficient

  15. Improving the Validity of Squeeze Film Air-Damping Model of MEMS Devices with Border Effect

    Directory of Open Access Journals (Sweden)

    Cheng Bai

    2014-01-01

    Full Text Available Evaluation of squeezed film air damping is critical in the design and control of dynamic MEMS devices. The published squeezed film air damping models are generally derived from the analytical solutions of Reynolds equation or its other modified forms under the supposition of trivial pressure boundary conditions on the peripheral borders. These treatments ignoring the border effect can not give faithful result for structure with smaller air venting gap or the double-gimbaled structure in which the inner frame and outer one affect the air venting. In this paper, we use Green’s function to solve the nonlinear Reynolds equation with inhomogeneous boundary conditions. For two typical normal motion cases of parallel plate, the analytical models of squeeze film damping force with border effect are established. The viscous and inertial losses with real values and image values acoustic impedance are all included in the model. These models reduced the time consumption while giving satisfactory result. Without multifield coupling analysis, the estimation of the dynamic behavior of MEMS device is also allowed, and the simulation of the system performance is more convenient.

  16. Nonlinear interaction of the surface waves at a plasma boundary

    International Nuclear Information System (INIS)

    Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.

    1976-01-01

    Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)

  17. The Influence on Modal Parameters of Thin Cylindrical Shell under Bolt Looseness Boundary

    Directory of Open Access Journals (Sweden)

    Hui Li

    2016-01-01

    Full Text Available The influence on modal parameters of thin cylindrical shell (TCS under bolt looseness boundary is investigated. Firstly, bolt looseness boundary of the shell is divided into two types, that is, different bolt looseness numbers and different bolt looseness levels, and natural frequencies and mode shapes are calculated by finite element method to roughly master vibration characteristics of TCS under these conditions. Then, the following measurements and identification techniques are used to get precise frequency, damping, and shape results; for example, noncontact laser Doppler vibrometer and vibration shaker with excitation level being precisely controlled are used in the test system; “preexperiment” is adopted to determine the required tightening torque and verify fixed constraint boundary; the small-segment FFT processing technique is employed to accurately measure nature frequency and laser rotating scanning technique is used to get shape results with high efficiency. Finally, based on the measured results obtained by the above techniques, the influence on modal parameters of TCS under two types of bolt looseness boundaries is analyzed and discussed. It can be found that bolt looseness boundary can significantly affect frequency and damping results which might be caused by changes of nonlinear stiffness and damping and in bolt looseness positions.

  18. Single-ion nonlinear mechanical oscillator

    International Nuclear Information System (INIS)

    Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

    2010-01-01

    We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

  19. Entanglement Dynamics of Linear and Nonlinear Interaction of Two Two-Level Atoms with a Quantized Phase-Damped Field in the Dispersive Regime

    Science.gov (United States)

    Tavassoly, M. K.; Daneshmand, R.; Rustaee, N.

    2018-06-01

    In this paper we study the linear and nonlinear (intensity-dependent) interactions of two two-level atoms with a single-mode quantized field far from resonance, while the phase-damping effect is also taken into account. To find the analytical solution of the atom-field state vector corresponding to the considered model, after deducing the effective Hamiltonian we evaluate the time-dependent elements of the density operator using the master equation approach and superoperator method. Consequently, we are able to study the influences of the special nonlinearity function f (n) = √ {n}, the intensity of the initial coherent state field and the phase-damping parameter on the degree of entanglement of the whole system as well as the field and atom. It is shown that in the presence of damping, by passing time, the amount of entanglement of each subsystem with the rest of system, asymptotically reaches to its stationary and maximum value. Also, the nonlinear interaction does not have any effect on the entanglement of one of the atoms with the rest of system, but it changes the amplitude and time period of entanglement oscillations of the field and the other atom. Moreover, this may cause that, the degree of entanglement which may be low (high) at some moments of time becomes high (low) by entering the intensity-dependent function in the atom-field coupling.

  20. Positive solutions of a three-point boundary-value problem for differential equations with damping and actively bounded delayed forcing term

    Directory of Open Access Journals (Sweden)

    George L. Karakostas

    2006-08-01

    Full Text Available We provide sufficient conditions for the existence of positive solutions of a three-point boundary value problem concerning a second order delay differential equation with damping and forcing term whose the delayed part is an actively bounded function, a meaning introduced in [19]. By writing the damping term as a difference of two factors one can extract more information on the solutions. (For instance, in an application, given in the last section, we can give the exact value of the norm of the solution.

  1. Effect of state-dependent delay on a weakly damped nonlinear oscillator.

    Science.gov (United States)

    Mitchell, Jonathan L; Carr, Thomas W

    2011-04-01

    We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.

  2. Damping characteristics of reinforced concrete structures

    International Nuclear Information System (INIS)

    Hisano, M.; Nagashima, I.; Kawamura, S.

    1987-01-01

    Reinforced concrete structures in a nuclear power plant are not permitted to go far into the inelasticity generally, even when subjected to strong ground motion. Therefore it is important to evaluate the damping appropriately in linear and after cracking stage before yielding in the dynamic response analysis. Next three dampings are considered of reinforced concrete structures. 1) Internal damping in linear range material damping of concrete without cracks;2) Hysteretic damping in inelastic range material hysteretic damping of concrete due to cracking and yielding;3) Damping due to the energy dissipation into the ground. Among these damping material damping affects dynamic response of a nuclear power plant on hard rock site where damping due to energy dissipation into the ground is scarcely expected. However material damping in linear and slightly nonlinear range have only been assumed without enough experimental data. In this paper such damping is investigated experimentally by the shaking table tests of reinforced concrete box-walls which modeled roughly the outer wall structure of a P.W.R. type nuclear power plant

  3. Landau damping of dust acoustic solitary waves in nonthermal plasmas

    Science.gov (United States)

    Ghai, Yashika; Saini, N. S.; Eliasson, B.

    2018-01-01

    Dust acoustic (DA) solitary and shock structures have been investigated under the influence of Landau damping in a dusty plasma containing two temperature nonthermal ions. Motivated by the observations of Geotail spacecraft that reported two-temperature ion population in the Earth's magnetosphere, we have investigated the effect of resonant wave-particle interactions on DA nonlinear structures. The Korteweg-de Vries (KdV) equation with an additional Landau damping term is derived and its analytical solution is presented. The solution has the form of a soliton whose amplitude decreases with time. Further, we have illustrated the influence of Landau damping and nonthermality of the ions on DA shock structures by a numerical solution of the Landau damping modified KdV equation. The study of the time evolution of shock waves suggests that an initial shock-like pulse forms an oscillatory shock at later times due to the balance of nonlinearity, dispersion, and dissipation due to Landau damping. The findings of the present investigation may be useful in understanding the properties of nonlinear structures in the presence of Landau damping in dusty plasmas containing two temperature ions obeying nonthermal distribution such as in the Earth's magnetotail.

  4. Ambient-temperature high damping capacity in TiPd-based martensitic alloys

    Energy Technology Data Exchange (ETDEWEB)

    Xue, Dezhen [Multi-disciplinary Materials Research Center, Frontier Institute of Science and Technology, State Key Laboratory for Mechanical Behavior of Materials, Xi' an Jiaotong University, Xi' an 710049 (China); Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Zhou, Yumei, E-mail: zhouyumei@mail.xjtu.edu.cn [Multi-disciplinary Materials Research Center, Frontier Institute of Science and Technology, State Key Laboratory for Mechanical Behavior of Materials, Xi' an Jiaotong University, Xi' an 710049 (China); Ding, Xiangdong [Multi-disciplinary Materials Research Center, Frontier Institute of Science and Technology, State Key Laboratory for Mechanical Behavior of Materials, Xi' an Jiaotong University, Xi' an 710049 (China); Otsuka, Kazuhiro [Ferroic Physics Group, National Institute for Materials Science, Tsukuba 305-0047, Ibaraki (Japan); Lookman, Turab [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Sun, Jun [Multi-disciplinary Materials Research Center, Frontier Institute of Science and Technology, State Key Laboratory for Mechanical Behavior of Materials, Xi' an Jiaotong University, Xi' an 710049 (China); Ren, Xiaobing [Multi-disciplinary Materials Research Center, Frontier Institute of Science and Technology, State Key Laboratory for Mechanical Behavior of Materials, Xi' an Jiaotong University, Xi' an 710049 (China); Ferroic Physics Group, National Institute for Materials Science, Tsukuba 305-0047, Ibaraki (Japan)

    2015-04-24

    Shape memory alloys (SMAs) have attracted considerable attention for their high damping capacities. Here we investigate the damping behavior of Ti{sub 50}(Pd{sub 50−x}D{sub x}) SMAs (D=Fe, Co, Mn, V) by dynamic mechanical analysis. We find that these alloys show remarkably similar damping behavior. There exists a sharp damping peak associated with the B2–B19 martensitic transformation and a high damping plateau (Q{sup −1}~0.02–0.05) over a wide ambient-temperature range (220–420 K) due to the hysteretic twin boundary motion. After doping hydrogen into the above alloys, a new relaxation-type damping peak appears in the martensite phase over 270–360 K. Such a peak is considered to originate from the interaction of hydrogen atoms with twin boundaries and the corresponding damping capacity (Q{sup −1}~0.05–0.09) is enhanced by roughly twice that of the damping plateau for each alloy. Moreover, the relaxation peaks are at higher temperatures for the TiPd-based alloys (270–370 K) than for the TiNi-based alloys (190–260 K). We discuss the influence of hydrogen diffusion, mobility of twin boundaries and hydrogen–twin boundary interaction on the temperature range of the relaxation peak. Our results suggest that a martensite, with appropriate values for twinning shear and hydrogen doping level, provides a route towards developing high damping SMAs for applications in desired temperature ranges.

  5. Ambient-temperature high damping capacity in TiPd-based martensitic alloys

    International Nuclear Information System (INIS)

    Xue, Dezhen; Zhou, Yumei; Ding, Xiangdong; Otsuka, Kazuhiro; Lookman, Turab; Sun, Jun; Ren, Xiaobing

    2015-01-01

    Shape memory alloys (SMAs) have attracted considerable attention for their high damping capacities. Here we investigate the damping behavior of Ti 50 (Pd 50−x D x ) SMAs (D=Fe, Co, Mn, V) by dynamic mechanical analysis. We find that these alloys show remarkably similar damping behavior. There exists a sharp damping peak associated with the B2–B19 martensitic transformation and a high damping plateau (Q −1 ~0.02–0.05) over a wide ambient-temperature range (220–420 K) due to the hysteretic twin boundary motion. After doping hydrogen into the above alloys, a new relaxation-type damping peak appears in the martensite phase over 270–360 K. Such a peak is considered to originate from the interaction of hydrogen atoms with twin boundaries and the corresponding damping capacity (Q −1 ~0.05–0.09) is enhanced by roughly twice that of the damping plateau for each alloy. Moreover, the relaxation peaks are at higher temperatures for the TiPd-based alloys (270–370 K) than for the TiNi-based alloys (190–260 K). We discuss the influence of hydrogen diffusion, mobility of twin boundaries and hydrogen–twin boundary interaction on the temperature range of the relaxation peak. Our results suggest that a martensite, with appropriate values for twinning shear and hydrogen doping level, provides a route towards developing high damping SMAs for applications in desired temperature ranges

  6. Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber-reinforced composites

    International Nuclear Information System (INIS)

    Panda, Satyajit; Ray, M C

    2008-01-01

    In this paper, a geometrically nonlinear dynamic analysis has been presented for functionally graded (FG) plates integrated with a patch of active constrained layer damping (ACLD) treatment and subjected to a temperature field. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber-reinforced composite (PFRC) material. The temperature field is assumed to be spatially uniform over the substrate plate surfaces and varied through the thickness of the host FG plates. The temperature-dependent material properties of the FG substrate plates are assumed to be graded in the thickness direction of the plates according to a power-law distribution while the Poisson's ratio is assumed to be a constant over the domain of the plate. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla–Hughes–McTavish (GHM) method. Based on the first-order shear deformation theory, a three-dimensional finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG substrate plates under the thermal environment. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear vibrations of FG plates in the absence or the presence of the temperature gradient across the thickness of the plates. It is found that the ACLD treatment is more effective in controlling the geometrically nonlinear vibrations of FG plates than in controlling their linear vibrations. The analysis also reveals that the ACLD patch is more effective for controlling the nonlinear vibrations of FG plates when it is attached to the softest surface of the FG plates than when it is bonded to the stiffest surface of the plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also discussed

  7. Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber-reinforced composites

    Science.gov (United States)

    Panda, Satyajit; Ray, M. C.

    2008-04-01

    In this paper, a geometrically nonlinear dynamic analysis has been presented for functionally graded (FG) plates integrated with a patch of active constrained layer damping (ACLD) treatment and subjected to a temperature field. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber-reinforced composite (PFRC) material. The temperature field is assumed to be spatially uniform over the substrate plate surfaces and varied through the thickness of the host FG plates. The temperature-dependent material properties of the FG substrate plates are assumed to be graded in the thickness direction of the plates according to a power-law distribution while the Poisson's ratio is assumed to be a constant over the domain of the plate. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla-Hughes-McTavish (GHM) method. Based on the first-order shear deformation theory, a three-dimensional finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG substrate plates under the thermal environment. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear vibrations of FG plates in the absence or the presence of the temperature gradient across the thickness of the plates. It is found that the ACLD treatment is more effective in controlling the geometrically nonlinear vibrations of FG plates than in controlling their linear vibrations. The analysis also reveals that the ACLD patch is more effective for controlling the nonlinear vibrations of FG plates when it is attached to the softest surface of the FG plates than when it is bonded to the stiffest surface of the plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also discussed.

  8. Nonlinear electrorheological instability of two Rivlin-Ericksen elastico-viscous fluids

    CERN Document Server

    El-Dib, Y O

    2003-01-01

    The behaviour of surface waves propagating between two Rivlin-Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients. This equation is accomplished by utilizing the cubic nonlinearity. The use of the Gardner-Morikawa transformation yields a simplified linear dispersion relation so that the periodic solution for the linear form is utilized. The ...

  9. Damage Evaluation of Critical Components of Tilted Support Spring Nonlinear System under a Rectangular Pulse

    Directory of Open Access Journals (Sweden)

    Ningning Duan

    2015-01-01

    Full Text Available Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear packaging system with critical components were obtained under a rectangular pulse. To evaluate the damage characteristics of shocks to packaged products with critical components, a concept of the damage boundary surface was presented and applied to a titled support spring system, with the dimensionless critical acceleration of the system, the dimensionless critical velocity, and the frequency parameter ratio of the system taken as the three basic parameters. Based on the numerical results, the effects of the frequency parameter ratio, the mass ratio, the dimensionless peak pulse acceleration, the angle of the system, and the damping ratio on the damage boundary surface of critical components were discussed. It was demonstrated that with the increase of the frequency parameter ratio, the decrease of the angle, and/or the increase of the mass ratio, the safety zone of critical components can be broadened, and increasing the dimensionless peak pulse acceleration or the damping ratio may lead to a decrease of the damage zone for critical components. The results may lead to a thorough understanding of the design principles for the tilted support spring nonlinear system.

  10. Initial boundary value problems of nonlinear wave equations in an exterior domain

    International Nuclear Information System (INIS)

    Chen Yunmei.

    1987-06-01

    In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

  11. Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer.

    Science.gov (United States)

    Wedin, Håkan; Cherubini, Stefania; Bottaro, Alessandro

    2015-07-01

    The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K̂ of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K̂=0). This leads to a Reynolds number of approximately Re(c)=54400 for the onset of linearly unstable waves, and close to Re(g)=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985); J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Re(c)=796 and Re(g)=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re(-ρ), where the value of ρ depends on the permeability coefficient K̂. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for

  12. Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

    Science.gov (United States)

    Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

    2018-04-01

    The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

  13. A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2013-01-01

    Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

  14. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Kaikina, Elena I., E-mail: ekaikina@matmor.unam.mx [Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán (Mexico)

    2013-11-15

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.

  15. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    International Nuclear Information System (INIS)

    Kaikina, Elena I.

    2013-01-01

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time

  16. Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

    Directory of Open Access Journals (Sweden)

    Ying Li

    2017-01-01

    Full Text Available The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton’s second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff’s fractional material model are much larger than those predicted by Mote’s fractional material model.

  17. Modelling of Dampers and Damping in Structures

    DEFF Research Database (Denmark)

    Høgsberg, Jan Riess

    2006-01-01

    and the maximum attainable damping are found by maximizing the expression for the damping ratio. The theory is formulated for linear damper models, but may also be applied for non-linear dampers in terms of equivalent linear parameters for stiffness and damping, respectively. The format of the expressions......, and thereby the damping, of flexible structures are generally described in terms of the dominant vibration modes. A system reduction technique, where the damped vibration mode is constructed as a linear combination of the undamped mode shape and the mode shape obtained by locking the damper, is applied....... This two-component representation leads to a simple solution for the modal damping representing the natural frequency and the associated damping ratio. It appears from numerical examples that this system reduction technique provides very accurate results. % Analytical expressions for the optimal tuning...

  18. Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

    Science.gov (United States)

    Lázaro, Mario

    2018-01-01

    In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.

  19. On the physical solutions to the heat equation subjected to nonlinear boundary conditions

    International Nuclear Information System (INIS)

    Gama, R.M.S. da.

    1990-01-01

    This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)

  20. Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

    OpenAIRE

    Nakamura, Gen; Vashisth, Manmohan

    2017-01-01

    In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

  1. Enhanced damping for bridge cables using a self-sensing MR damper

    Science.gov (United States)

    Chen, Z. H.; Lam, K. H.; Ni, Y. Q.

    2016-08-01

    This paper investigates enhanced damping for protecting bridge stay cables from excessive vibration using a newly developed self-sensing magnetorheological (MR) damper. The semi-active control strategy for effectively operating the self-sensing MR damper is formulated based on the linear-quadratic-Gaussian (LQG) control by further considering a collocated control configuration, limited measurements and nonlinear damper dynamics. Due to its attractive feature of sensing-while-damping, the self-sensing MR damper facilitates the collocated control. On the other hand, only the sensor measurements from the self-sensing device are employed in the feedback control. The nonlinear dynamics of the self-sensing MR damper, represented by a validated Bayesian NARX network technique, are further accommodated in the control formulation to compensate for its nonlinearities. Numerical and experimental investigations are conducted on stay cables equipped with the self-sensing MR damper operated in passive and semi-active control modes. The results verify that the collocated self-sensing MR damper facilitates smart damping for inclined cables employing energy-dissipative LQG control with only force and displacement measurements at the damper. It is also demonstrated that the synthesis of nonlinear damper dynamics in the LQG control enhances damping force tracking efficiently, explores the features of the self-sensing MR damper, and achieves better control performance over the passive MR damping control and the Heaviside step function-based LQG control that ignores the damper dynamics.

  2. Fluid Damping Variation of a Slender Rod in Axial Flow Field

    Energy Technology Data Exchange (ETDEWEB)

    Park, Nam-Gyu; Yoo, Jong-Sung; Jung, Yil-Sup [KEPCO Nuclear Fuel Co., Daejeon (Korea, Republic of)

    2016-10-15

    This study proposed an analytic damping model considering the axial flow condition. In addition, the specific damping values with respect to the flow speeds are calculated. The flow induced damping is beneficial to fuel integrity in that impact energy due to severe accidents such as earthquake dissipates rapidly. A nuclear fuel bundle is composed of many slender fuel rods which contain fission material. The slender rod is typical structure in the fuel, therefore fluid damping estimation on the rod should be an important clue leading to fuel bundle damping identification. Severe accidents could cause fuel assembly vibration in the core, but large motion could be damped out rapidly when a strong damping mechanism is involved. This paper suggested a mathematical model of the slender structure. The physical meaning of the model is described, and the simulation results with the model are also provided. Actual damping due to the fluid is nonlinear, therefore further works are required to explain the detail behavior with the nonlinearity. The model validation test is on-going in KEPCO Nuclear Fuel, but it is believed that performance of the model is well correlated to the published work.

  3. Temperature dependent elasticity and damping in dehydrated sandstone

    Science.gov (United States)

    Darling, T. W.; Struble, W.

    2013-12-01

    Work reported previously at this conference, outlining our observation of anomalously large elastic softening and damping in dehydrated Berea sandstone at elevated temperatures, has been analysed to study shear and compressional effects separately. Modeling of the sample using COMSOL software was necessary to identify modes, as the vibration spectrum of the sample is poorly approximated by a uniform isotropic solid. The first torsional mode of our evacuated, dry, core softens at nearly twice the rate of Young's modulus modes (bending and compressional) and is also damped nearly twice as strongly as temperature increases. We consider two possible models for explaining this behavior, based on the assumption that the mechanical properties of the sandstone are dominated by the framework of quartz grains and polycrystalline cementation, neglecting initially the effects of clay and feldspar inclusions. The 20cm x 2.54cm diameter core is dry such that the pressure of water vapor in the experiment chamber is below 1e-6 Torr at 70C, suggesting that surface water beyond a small number of monolayers is negligible. Our models consider (1) enhanced sliding of grain boundaries in the cementation at elevated temperature and reduced internal water content, and (2) strain microcracking of the cementatioin at low water content due to anisotropic expansion in the quartz grains. In model (1) interfaces parallel to polyhedral grain surfaces were placed in the cement bonds and assigned frictional properties. Model (2) has not yet been implemented. The overall elasticity of a 3-D several-grain model network was determined by modeling quasistatic loading and measuring displacements. Initial results with a small number of grains/bonds suggests that only the first model provides softening and damping for all the modes, however the details of the effects of defect motioin at individual interfaces as the source for the frictional properties is still being evaluated. Nonlinear effects are

  4. An enhanced nonlinear damping approach accounting for system constraints in active mass dampers

    Science.gov (United States)

    Venanzi, Ilaria; Ierimonti, Laura; Ubertini, Filippo

    2015-11-01

    Active mass dampers are a viable solution for mitigating wind-induced vibrations in high-rise buildings and improve occupants' comfort. Such devices suffer particularly when they reach force saturation of the actuators and maximum extension of their stroke, which may occur in case of severe loading conditions (e.g. wind gust and earthquake). Exceeding actuators' physical limits can impair the control performance of the system or even lead to devices damage, with consequent need for repair or substitution of part of the control system. Controllers for active mass dampers should account for their technological limits. Prior work of the authors was devoted to stroke issues and led to the definition of a nonlinear damping approach, very easy to implement in practice. It consisted of a modified skyhook algorithm complemented with a nonlinear braking force to reverse the direction of the mass before reaching the stroke limit. This paper presents an enhanced version of this approach, also accounting for force saturation of the actuator and keeping the simplicity of implementation. This is achieved by modulating the control force by a nonlinear smooth function depending on the ratio between actuator's force and saturation limit. Results of a numerical investigation show that the proposed approach provides similar results to the method of the State Dependent Riccati Equation, a well-established technique for designing optimal controllers for constrained systems, yet very difficult to apply in practice.

  5. Damping of Resonantly Forced Density Waves in Dense Planetary Rings

    Science.gov (United States)

    Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

    2016-10-01

    We address the stability of resonantly forced density waves in dense planetary rings.Already by Goldreich and Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the ring's viscosity and the surface mass density. In the recent paper (Schmidt et al. 2016) we have pointed out that when - within a fluid description of the ring dynamics - the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping.We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model.This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts linear instability of density waves in a ring region where the conditions for viscous overstability are met. In this case, sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. In general the model wave damping lengths depend on a set of input parameters, such as the distance to the threshold for viscous overstability and the ground state surface mass density.Our new model compares reasonably well with the streamline model for nonlinear density waves of Borderies et al. 1986.Deviations become substantial in the highly nonlinear regime, corresponding to strong satellite forcing.Nevertheless, we generally observe good or at least qualitative agreement between the wave amplitude profiles of both models. The streamline approach is superior at matching the total wave profile of waves observed in Saturn's rings, while our new damping relation is a comparably handy tool to gain insight in the evolution of the wave amplitude with distance from resonance, and the different regimes of

  6. Ceramic coatings: A phenomenological modeling for damping behavior related to microstructural features

    International Nuclear Information System (INIS)

    Tassini, N.; Patsias, S.; Lambrinou, K.

    2006-01-01

    Recent research has shown that both stiffness and damping of ceramic coatings exhibit different non-linearities. These properties strongly depend on the microstructure, which is characterized by heterogeneous sets of elastic elements with mesoscopic sizes and shapes, as in non-linear mesoscopic elastic materials. To predict the damping properties of this class of materials, we have implemented a phenomenological model that characterizes their elastic properties. The model is capable of reproducing the basic features of the observed damping behavior for zirconia coatings prepared by air plasma spraying and electron-beam physical-vapor-deposition

  7. Induced scattering due to nonlinear Landau and cyclotron damping of electromagnetic and electrostatic waves in a magnetized plasma

    International Nuclear Information System (INIS)

    Sugaya, Reiji

    1989-01-01

    General expressions of the matrix elements for nonlinear wave-particle scattering (nonlinear Landau and cyclotron damping) of electromagnetic and electrostatic waves in a homogeneous magnetized plasma are derived from the Vlasov-Maxwell equations. The kinetic wave equations obtained for electromagnetic waves are expressed by four-order tensors in the rotating and cartesian coordinates. No restrictions are imposed on the propagation angle to a uniform magnetic field, the Larmor radius, the frequencies, or the wave numbers. By electrostatic approximation of the dielectric tensor and the matrix elements the kinetic wave equations can be applied to the case in which two scattering waves are electrostatic or they are partially electrostatic. Further, the matrix elements in the limit of parallel or perpendicular propagation to the magnetic field are given. (author)

  8. Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

    KAUST Repository

    Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model

  9. Simple model with damping of the mode-coupling instability

    Energy Technology Data Exchange (ETDEWEB)

    Pestrikov, D V [AN SSSR, Novosibirsk (Russian Federation). Inst. Yadernoj Fiziki

    1996-08-01

    In this paper we use a simple model to study the suppression of the transverse mode-coupling instability. Two possibilities are considered. One is due to the damping of particular synchrobetatron modes, and another - due to Landau damping, caused by the nonlinearity of betatron oscillations. (author)

  10. Damping Measurements of Plasma Modes

    Science.gov (United States)

    Anderegg, F.; Affolter, M.; Driscoll, C. F.

    2010-11-01

    For azimuthally symmetric plasma modes in a magnesium ion plasma, confined in a 3 Tesla Penning-Malmberg trap with a density of n ˜10^7cm-3, we measure a damping rate of 2s-1plasma column, alters the frequency of the mode from 16 KHz to 192 KHz. The oscillatory fluid displacement is small compared to the wavelength of the mode; in contrast, the fluid velocity, δvf, can be large compared to v. The real part of the frequency satisfies a linear dispersion relation. In long thin plasmas (α> 10) these modes are Trivelpiece-Gould (TG) modes, and for smaller values of α they are Dubin spheroidal modes. However the damping appears to be non-linear; initially large waves have weaker exponential damping, which is not yet understood. Recent theoryootnotetextM.W. Anderson and T.M. O'Neil, Phys. Plasmas 14, 112110 (2007). calculates the damping of TG modes expected from viscosity due to ion-ion collisions; but the measured damping, while having a similar temperature and density dependence, is about 40 times larger than calculated. This discrepancy might be due to an external damping mechanism.

  11. The Duffing oscillator with damping

    DEFF Research Database (Denmark)

    Johannessen, Kim

    2015-01-01

    An analytical solution to the differential equation describing the Duffing oscillator with damping is presented. The damping term of the differential equation and the initial conditions satisfy an algebraic equation, and thus the solution is specific for this type of damping. The nonlinear term...... of the differential equation is allowed to be considerable compared to the linear term. The solution is expressed in terms of the Jacobi elliptic functions by including a parameter-dependent elliptic modulus. The analytical solution is compared to the numerical solution, and the agreement is found to be very good....... It is established that the period of oscillation is shorter compared to that of a linearized model but increasing with time and asymptotically approaching the period of oscillation of the linear damped model. An explicit expression for the period of oscillation has been derived, and it is found to be very accurate....

  12. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

    Science.gov (United States)

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

    2014-01-01

    In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

  13. Semilinear damped wave equation in locally uniform spaces

    Czech Academy of Sciences Publication Activity Database

    Michálek, Martin; Pražák, D.; Slavík, J.

    2017-01-01

    Roč. 16, č. 5 (2017), s. 1673-1695 ISSN 1534-0392 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : damped wave equations * nonlinear damping * unbounded domains Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.801, year: 2016 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14110

  14. On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

    Directory of Open Access Journals (Sweden)

    Jun Wang

    2011-01-01

    Full Text Available A nonlinear time-varying (NLTV dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

  15. Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

    Science.gov (United States)

    Rahman, M. A.; Ahmed, U.; Uddin, M. S.

    2013-08-01

    A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

  16. Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at

    Directory of Open Access Journals (Sweden)

    Swati Mukhopadhyay

    2013-12-01

    Full Text Available The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter.

  17. The influence of compressibility on nonlinear spectral energy transfer - Part 2: Effect on hypersonic boundary layer transition

    Science.gov (United States)

    Mittal, Ankita; Girimaji, Sharath

    2017-11-01

    We examine the effect of compressible spectral energy transfer in the nonlinear regime of transition to turbulence of hypersonic boundary layers. The nature of spectral energy transfer between perturbation modes is profoundly influenced by two compressibility mechanisms. First and foremost, the emergence of nonlinear pressure-dilatation mechanism leads to kinetic-internal energy exchange within the perturbation field. Such interchange is absent in incompressible flow as pressure merely reorients the perturbation amplitude vector while conserving kinetic energy. Secondly, the nature of triadic interactions also changes due to variability in density. In this work, we demonstrate that the efficiency of nonlinear spectral energy transfer is diminished in compressible boundary layers. Emergence of new perturbation modes or `broad-banding' of the perturbation field is significantly delayed in comparison to incompressible boundary layer undergoing transition. A significant amount of perturbation energy is transformed to internal energy and thus unavailable for `tripping' the flow into turbulent state. These factors profoundly change the nature of the nonlinear stage of transition in compressible boundary layer leading to delayed onset of full-fledged turbulence.

  18. The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

    International Nuclear Information System (INIS)

    Anderies, J M; Carpenter, S R; Steffen, Will; Rockström, Johan

    2013-01-01

    We present a minimal model of land use and carbon cycle dynamics and use it to explore the relationship between non-linear dynamics and planetary boundaries. Only the most basic interactions between land cover and terrestrial, atmospheric, and marine carbon stocks are considered in the model. Our goal is not to predict global carbon dynamics as it occurs in the actual Earth System. Rather, we construct a conceptually reasonable heuristic model of a feedback system between different carbon stocks that captures the qualitative features of the actual Earth System and use it to explore the topology of the boundaries of what can be called a ‘safe operating space’ for humans. The model analysis illustrates the existence of dynamic, non-linear tipping points in carbon cycle dynamics and the potential complexity of planetary boundaries. Finally, we use the model to illustrate some challenges associated with navigating planetary boundaries. (letter)

  19. The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

    Science.gov (United States)

    Anderies, J. M.; Carpenter, S. R.; Steffen, Will; Rockström, Johan

    2013-12-01

    We present a minimal model of land use and carbon cycle dynamics and use it to explore the relationship between non-linear dynamics and planetary boundaries. Only the most basic interactions between land cover and terrestrial, atmospheric, and marine carbon stocks are considered in the model. Our goal is not to predict global carbon dynamics as it occurs in the actual Earth System. Rather, we construct a conceptually reasonable heuristic model of a feedback system between different carbon stocks that captures the qualitative features of the actual Earth System and use it to explore the topology of the boundaries of what can be called a ‘safe operating space’ for humans. The model analysis illustrates the existence of dynamic, non-linear tipping points in carbon cycle dynamics and the potential complexity of planetary boundaries. Finally, we use the model to illustrate some challenges associated with navigating planetary boundaries.

  20. Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

    Directory of Open Access Journals (Sweden)

    Imran Talib

    2015-12-01

    Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

  1. Damping and Frequency Shift of Large Amplitude Electron Plasma Waves

    DEFF Research Database (Denmark)

    Thomsen, Kenneth; Juul Rasmussen, Jens

    1983-01-01

    The initial evolution of large-amplitude one-dimensional electron waves is investigated by applying a numerical simulation. The initial wave damping is found to be strongly enhanced relative to the linear damping and it increases with increasing amplitude. The temporal evolution of the nonlinear...

  2. Magnon damping in two-dimensional Heisenberg ferromagnetic system

    International Nuclear Information System (INIS)

    Cheng, T.-M.; Li Lin; Ze Xianyu

    2006-01-01

    A magnon-phonon interaction model is set up for a two-dimensional insulating ferromagnetic system. By using Matsubara function theory we have studied the magnon damping -I m Σ* (1) (k->) and calculated the magnon damping -I m Σ* (1) (k->) curve on the main symmetric point and line in the Brillouin zone for various parameters in the system. It is concluded that at the boundary of Brillouin zone there is a strong magnon damping. However, the magnon damping is very weak on the zone of small wave vector and the magnon damping reaches maximal value at very low temperature. The contributions of longitudinal phonon and transverse phonon on the magnon damping are compared and the influences of various parameters are also discussed

  3. Spike-like solitary waves in incompressible boundary layers driven by a travelling wave.

    Science.gov (United States)

    Feng, Peihua; Zhang, Jiazhong; Wang, Wei

    2016-06-01

    Nonlinear waves produced in an incompressible boundary layer driven by a travelling wave are investigated, with damping considered as well. As one of the typical nonlinear waves, the spike-like wave is governed by the driven-damped Benjamin-Ono equation. The wave field enters a completely irregular state beyond a critical time, increasing the amplitude of the driving wave continuously. On the other hand, the number of spikes of solitary waves increases through multiplication of the wave pattern. The wave energy grows in a sequence of sharp steps, and hysteresis loops are found in the system. The wave energy jumps to different levels with multiplication of the wave, which is described by winding number bifurcation of phase trajectories. Also, the phenomenon of multiplication and hysteresis steps is found when varying the speed of driving wave as well. Moreover, the nature of the change of wave pattern and its energy is the stability loss of the wave caused by saddle-node bifurcation.

  4. Nonlinear analysis for dual-frequency concurrent energy harvesting

    Science.gov (United States)

    Yan, Zhimiao; Lei, Hong; Tan, Ting; Sun, Weipeng; Huang, Wenhu

    2018-05-01

    The dual-frequency responses of the hybrid energy harvester undergoing the base excitation and galloping were analyzed numerically. In this work, an approximate dual-frequency analytical method is proposed for the nonlinear analysis of such a system. To obtain the approximate analytical solutions of the full coupled distributed-parameter model, the forcing interactions is first neglected. Then, the electromechanical decoupled governing equation is developed using the equivalent structure method. The hybrid mechanical response is finally separated to be the self-excited and forced responses for deriving the analytical solutions, which are confirmed by the numerical simulations of the full coupled model. The forced response has great impacts on the self-excited response. The boundary of Hopf bifurcation is analytically determined by the onset wind speed to galloping, which is linearly increased by the electrical damping. Quenching phenomenon appears when the increasing base excitation suppresses the galloping. The theoretical quenching boundary depends on the forced mode velocity. The quenching region increases with the base acceleration and electrical damping, but decreases with the wind speed. Superior to the base-excitation-alone case, the existence of the aerodynamic force protects the hybrid energy harvester at resonance from damages caused by the excessive large displacement. From the view of the harvested power, the hybrid system surpasses the base-excitation-alone system or the galloping-alone system. This study advances our knowledge on intrinsic nonlinear dynamics of the dual-frequency energy harvesting system by taking advantage of the analytical solutions.

  5. Nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2014-06-01

    Full Text Available This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented.

  6. On the Stability of Three-Dimensional Boundary Layers. Part 1; Linear and Nonlinear Stability

    Science.gov (United States)

    Janke, Erik; Balakumar, Ponnampalam

    1999-01-01

    The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment.

  7. Landau damping dynamic aperture and octupole in LHC

    CERN Document Server

    Gareyte, Jacques; Ruggiero, F

    1997-01-01

    Maximization of the dynamic aperture and Landau damping of the collective instabilities are partly conflicting requirements. On the one hand, the non-linearities of the lattice must be minimized at large oscillation amplitude to guarantee the stability of the single particle motion. On the other hand, a spread of the betatron frequencies is necessary to guarantee the stability of the collective motion of bunches of particles; this requires the introduction of non-linearities effective at small amplitudes. We show in this note that the `natural' spread of betatron tunes due to the field imperfections is inadequate or Landau damping. An octupole scheme is required to provide collective stability at high energy. At low energy it may be used to find the optimum between the correction of the octupolar field imperfections and Landau damping. The solution of the stability problem taking into account the two degrees of freedom of the transverse motion allows a significant saving in octupole strength: 144 octupoles wi...

  8. Barotropic FRW cosmologies with Chiellini damping

    Energy Technology Data Exchange (ETDEWEB)

    Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, SLP (Mexico); Mancas, Stefan C., E-mail: stefan.mancas@erau.edu [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Chen, Pisin, E-mail: pisinchen@phys.ntu.edu.tw [Leung Center for Cosmology and Particle Astrophysics (LeCosPA) and Department of Physics, National Taiwan University, Taipei 10617, Taiwan (China)

    2015-05-08

    It is known that barotropic FRW equations written in the conformal time variable can be reduced to simple linear equations for an exponential function involving the conformal Hubble rate. Here, we show that an interesting class of barotropic universes can be obtained in the linear limit of a special type of nonlinear dissipative Ermakov–Pinney equations with the nonlinear dissipation built from Chiellini's integrability condition. These cosmologies, which evolutionary are similar to the standard ones, correspond to barotropic fluids with adiabatic indices rescaled by a particular factor and have amplitudes of the scale factors inverse proportional to the adiabatic index. - Highlights: • Chiellini-damped Ermakov–Pinney equations are used in barotropic FRW cosmological context. • Chiellini-damped scale factors of the barotropic FRW universes are introduced. • These scale factors are similar to the undamped ones.

  9. Emergent large mechanical damping in ferroelastic-martensitic systems driven by disorder

    Science.gov (United States)

    Ni, Yan; Zhang, Zhen; Fang, Minxia; Hao, Yanshuang; Ding, Xiangdong; Otsuka, Kazuhiro; Ren, Xiaobing

    2018-05-01

    Disorders and point defects strongly interplay with the phase transition and alter the properties of ferroelastic-martensitic systems. Unusual static and quasistatic behaviors, such as time-dependent phase transitions, are discovered when disorders are introduced. However, the role of disorders on the ferroelastic system in vibrational environments at moderate frequency is rarely known, investigation of which could further shed light on their application as mechanical damping materials. Here we present the emergence of large damping capacity in ferroelastic-martensitic systems [including both the T i50 -xN i50 +x alloy and (C a1 -xS rx) Ti O3 ceramics] by introducing disorder (i.e., substitutional Ni and Sr, respectively). As the level disorder increases, the damping capacity of both systems raises and eventually reaches a maximum when long-range-ordered martensite tends to vanish. Moreover, near the disorder-induced phase boundary, we observe a large mechanical damping in ferroelastic ceramics (C a1 -xS rx) Ti O3 with a figure of merit ˜2 GP a1 /2 . Microscopic and dynamic investigations indicate that such damping plateau could result from the competing evolution of density and mobility of domain boundaries when disorder is introduced. Our work provides a degree of freedom to develop ferroelastic damping materials and a potential way to tune domain-boundary-mediated functionalities for other ferroic materials.

  10. Halo Mitigation Using Nonlinear Lattices

    CERN Document Server

    Sonnad, Kiran G

    2005-01-01

    This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It is well established that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC is analysed using the Lie Transform perturbation theory showing that by averaging over a lattice period, one can reuduce the focusing force to a form that is identical to that used in the PIC simula...

  11. Dynamic stability of a lightly damped column trapped by a ...

    African Journals Online (AJOL)

    In this paper we initiate an analytical approach for determining the dynamic buckling load of a finite viscously damped column acted upon by a harmonically slowly varying explicitly time dependent load. The viscous damping is considered light and the column rests on an elastic foundation that produces a nonlinear ...

  12. Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

    Science.gov (United States)

    Midya, Bikashkali; Konotop, Vladimir V.

    2017-07-01

    We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e., the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn, the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications, the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.

  13. Laser light triggers increased Raman amplification in the regime of nonlinear Landau damping

    International Nuclear Information System (INIS)

    Depierreux, S.; Goyon, C.; Masson-Laborde, P.E.; Yahia, V.; Loisel, G.; Labaune, C.

    2014-01-01

    Stimulated Raman backscattering (SRS) has many unwanted effects in megajoule-scale inertially confined fusion (ICF) plasmas. Moreover, attempts to harness SRS to amplify short laser pulses through backward Raman amplification have achieved limited success. In high temperature fusion plasmas, SRS usually occurs in a kinetic regime where the nonlinear response of the Langmuir wave to the laser drive and its host of complicating factors make it difficult to predict the degree of amplification that can be achieved under given experimental conditions. Here we present experimental evidence of reduced Landau damping with increasing Langmuir wave amplitude and determine its effects on Raman amplification. The threshold for trapping effects to influence the amplification is shown to be very low. Above threshold, the complex SRS dynamics results in increased amplification factors, which partly explains previous ICF experiments. These insights could aid the development of more efficient backward Raman amplification schemes in this regime. (authors)

  14. Dissipative quantum trajectories in complex space: Damped harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

    2016-10-15

    Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

  15. Dissipative quantum trajectories in complex space: Damped harmonic oscillator

    International Nuclear Information System (INIS)

    Chou, Chia-Chun

    2016-01-01

    Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

  16. Nonlinear evolution of Mack modes in a hypersonic boundary layer

    Science.gov (United States)

    Chokani, Ndaona

    2005-01-01

    In hypersonic boundary layer flows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layer transition. In the case of low-level freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Cross-bicoherence measurements, derived from hot-wire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phase-locked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, cross-bicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the low-frequency, phase-locked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.

  17. On small vibrations of a damped Stieltjes string

    Directory of Open Access Journals (Sweden)

    Olga Boyko

    2015-01-01

    Full Text Available Inverse problem of recovering masses, coefficients of damping and lengths of the intervals between the masses using two spectra of boundary value problems and the total length of the Stieltjes string (an elastic thread bearing point masses is considered. For the case of point-wise damping at the first counting from the right end mass the problem of recovering the masses, the damping coefficient and the lengths of the subintervals by one spectrum and the total length of the string is solved.

  18. Sum-frequency nonlinear Cherenkov radiation generated on the boundary of bulk medium crystal.

    Science.gov (United States)

    Wang, Xiaojing; Cao, Jianjun; Zhao, Xiaohui; Zheng, Yuanlin; Ren, Huaijin; Deng, Xuewei; Chen, Xianfeng

    2015-12-14

    We demonstrated experimentally a method to generate the sum-frequency Nonlinear Cherenkov radiation (NCR) on the boundary of bulk medium by using two synchronized laser beam with wavelength of 1300 nm and 800 nm. It is also an evidence that the polarization wave is always confined to the boundary. Critical conditions of surface sum-frequency NCR under normal and anomalous dispersion condition is discussed.

  19. Bifurcation characteristics in parametric systems with combined damping

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena

    Vol.16, č. 3 (2009), s. 1-9 ISSN 1802-1484 R&D Projects: GA ČR(CZ) GA101/07/0884 Institutional research plan: CEZ:AV0Z20760514 Keywords : non-linear dynamics * parametric systems * impact effects * linear and non-linear damping Subject RIV: BI - Acoustics http://www.im.fme.vutbr.cz/pdf/16_3_221.full.pdf

  20. On Nonlinear Inverse Problems of Heat Transfer with Radiation Boundary Conditions: Application to Dehydration of Gypsum Plasterboards Exposed to Fire

    OpenAIRE

    Belmiloudi, A.; Mahé, F.

    2014-01-01

    International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...

  1. Fully nonlinear time-domain simulation of a backward bent duct buoy floating wave energy converter using an acceleration potential method

    Directory of Open Access Journals (Sweden)

    Kyoung-Rok Lee

    2013-12-01

    Full Text Available A floating Oscillating Water Column (OWC wave energy converter, a Backward Bent Duct Buoy (BBDB, was simulated using a state-of-the-art, two-dimensional, fully-nonlinear Numerical Wave Tank (NWT technique. The hydrodynamic performance of the floating OWC device was evaluated in the time domain. The acceleration potential method, with a full-updated kernel matrix calculation associated with a mode decomposition scheme, was implemented to obtain accurate estimates of the hydrodynamic force and displacement of a freely floating BBDB. The developed NWT was based on the potential theory and the boundary element method with constant panels on the boundaries. The mixed Eulerian-Lagrangian (MEL approach was employed to capture the nonlinear free surfaces inside the chamber that interacted with a pneumatic pressure, induced by the time-varying airflow velocity at the air duct. A special viscous damping was applied to the chamber free surface to represent the viscous energy loss due to the BBDB's shape and motions. The viscous damping coefficient was properly selected using a comparison of the experimental data. The calculated surface elevation, inside and outside the chamber, with a tuned viscous damping correlated reasonably well with the experimental data for various incident wave conditions. The conservation of the total wave energy in the computational domain was confirmed over the entire range of wave frequencies.

  2. Climate variability and vadose zone controls on damping of transient recharge

    Science.gov (United States)

    Corona, Claudia R.; Gurdak, Jason J.; Dickinson, Jesse; Ferré, T.P.A.; Maurer, Edwin P.

    2017-01-01

    Increasing demand on groundwater resources motivates understanding of the controls on recharge dynamics so model predictions under current and future climate may improve. Here we address questions about the nonlinear behavior of flux variability in the vadose zone that may explain previously reported teleconnections between global-scale climate variability and fluctuations in groundwater levels. We use hundreds of HYDRUS-1D simulations in a sensitivity analysis approach to evaluate the damping depth of transient recharge over a range of periodic boundary conditions and vadose zone geometries and hydraulic parameters that are representative of aquifer systems of the conterminous United States (U.S). Although the models were parameterized based on U.S. aquifers, findings from this study are applicable elsewhere that have mean recharge rates between 3.65 and 730 mm yr–1. We find that mean infiltration flux, period of time varying infiltration, and hydraulic conductivity are statistically significant predictors of damping depth. The resulting framework explains why some periodic infiltration fluxes associated with climate variability dampen with depth in the vadose zone, resulting in steady-state recharge, while other periodic surface fluxes do not dampen with depth, resulting in transient recharge. We find that transient recharge in response to the climate variability patterns could be detected at the depths of water levels in most U.S. aquifers. Our findings indicate that the damping behavior of transient infiltration fluxes is linear across soil layers for a range of texture combinations. The implications are that relatively simple, homogeneous models of the vadose zone may provide reasonable estimates of the damping depth of climate-varying transient recharge in some complex, layered vadose zone profiles.

  3. Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions

    Directory of Open Access Journals (Sweden)

    A. Sakabekov

    2016-01-01

    Full Text Available We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.

  4. Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

    KAUST Repository

    Eleiwi, Fadi

    2015-07-01

    This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.

  5. Discrete-time nonlinear damping backstepping control with observers for rejection of low and high frequency disturbances

    Science.gov (United States)

    Kim, Wonhee; Chen, Xu; Lee, Youngwoo; Chung, Chung Choo; Tomizuka, Masayoshi

    2018-05-01

    A discrete-time backstepping control algorithm is proposed for reference tracking of systems affected by both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. A discrete time DOB, which is constructed based on infinite impulse response filters is applied to compensate for narrow band disturbances at high frequencies. A discrete-time nonlinear damping backstepping controller with an augmented observer is proposed to track the desired output and to compensate for low frequency broadband disturbances along with a disturbance observer, for rejecting narrow band high frequency disturbances. This combination has the merit of simultaneously compensating both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. The performance of the proposed method is validated via experiments.

  6. Dynamic characteristics of a novel damped outrigger system

    Science.gov (United States)

    Tan, Ping; Fang, Chuangjie; Zhou, Fulin

    2014-06-01

    This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analytical model is developed by modeling the effect of the damped outrigger as a general rotational spring acting on a Bernoulli-Euler beam. The equivalent rotational spring stiffness incorporating the combined effects of dampers and axial stiffness of perimeter columns is derived. The dynamic stiffness method (DSM) is applied to formulate the governing equation of the damped outrigger system. The accuracy and efficiency are verified in comparison with those obtained from compatibility equations and boundary equations. Parametric analysis of three non-dimensional factors is conducted to evaluate the influences of various factors, such as the stiffness ratio of the core to the beam, position of the damped outrigger, and the installed damping coefficient. Results show that the modal damping ratio is significantly influenced by the stiffness ratio of the core to the column, and is more sensitive to damping than the position of the damped outrigger. The proposed analytical model in combination with DSM can be extended to the study of structures with more outriggers.

  7. Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

    Science.gov (United States)

    Cai, Wei; Wang, Jian-Zhong

    1993-01-01

    We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

  8. Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

    CERN Document Server

    Gazzola, Filippo; Sweers, Guido

    2010-01-01

    This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

  9. A purely nonlinear route to transition approaching the edge of chaos in a boundary layer

    International Nuclear Information System (INIS)

    Cherubini, S; De Palma, P; Robinet, J-Ch; Bottaro, A

    2012-01-01

    The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Λ and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow. (paper)

  10. Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities

    Directory of Open Access Journals (Sweden)

    J. Gwinner

    2013-01-01

    Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

  11. New implementation method for essential boundary condition to extended element-free Galerkin method. Application to nonlinear problem

    International Nuclear Information System (INIS)

    Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki

    2011-01-01

    A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem. (author)

  12. POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

    Directory of Open Access Journals (Sweden)

    FAOUZI HADDOUCHI

    2015-11-01

    Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

  13. Squeeze-Film Air Damping of a Five-Axis Electrostatic Bearing for Rotary Micromotors.

    Science.gov (United States)

    Wang, Shunyue; Han, Fengtian; Sun, Boqian; Li, Haixia

    2017-05-13

    Air-film damping, which dominates over other losses, plays a significant role in the dynamic response of many micro-fabricated devices with a movable mass suspended by various bearing mechanisms. Modeling the damping characteristics accurately will be greatly helpful to the bearing design, control, and test in various micromotor devices. This paper presents the simulated and experimental squeeze-film air damping results of an electrostatic bearing for use in a rotary high-speed micromotor. It is shown that the boundary condition to solve the three-dimensional Reynolds equation, which governs the squeeze-film damping in the air gap between the rotor and its surrounding stator sealed in a three-layer evacuated cavity, behaves with strong cross-axis coupling characteristics. To accurately characterize the damping effect, a set of multiphysics finite-element simulations are performed by computing both the rotor velocity and the distribution of the viscous damping force acting on the rotor. The damping characteristics varying with several key structure parameters are simulated and discussed to optimize the device structure for desirable rotor dynamics. An electrical measurement method is also proposed and applied to validate the numerical results of the damping coefficients experimentally. Given that the frequency response of the electric bearing is critically dependent on the damping coefficients at atmospheric pressure, a solution to the air-film damping measurement problem is presented by taking approximate curve fitting of multi-axis experimental frequency responses. The measured squeeze-film damping coefficients for the five-axis electric bearing agrees well with the numerical solutions. This indicates that numerical multiphysics simulation is an effective method to accurately examine the air-film damping effect for complex device geometry and arbitrary boundary condition. The accurate damping coefficients obtained by FEM simulation will greatly simplify the design

  14. Design of Weighted Wide Area Damping Controller (WWADC Based PSS for Damping Inter-Area Low Frequency Oscillations

    Directory of Open Access Journals (Sweden)

    Saleh M. Bamasak

    2017-09-01

    Full Text Available Wide Area Measurement System (WAMS can extend and effectively improve the power system stabilizers (PSS capability in damping the inter-area low frequency oscillations in interconnected bulk power systems. This paper proposes the implementation of Weighted Wide Area Damping Controller (WWADC in which weighted factors are introduced for each remote feedback signals. Modal analysis approach is implemented for the purpose of identifying the optimal location as well as the input signals’ optimal combination of WWADC. Based on the linearized model, Differential Evolution (DE algorithm is applied to search for optimal controller parameters and optimal weighted factors. The successful application of the proposed approach is achieved in two power networks; the two-area 4-machine system and the IEEE-39 bus 10-machine system. The analysis of the eigenvalue and non-linear time domain simulations indicate that damping the inter-area oscillations and improving the system stability irrespective of the severity and the location of the disturbances can be effectively achieved by WADC

  15. Hyperchaotic circuit with damped harmonic oscillators

    DEFF Research Database (Denmark)

    Lindberg, Erik; Murali, K.; Tamasevicius, A.

    2001-01-01

    A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...... capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...... by means of numerical integration of the appropriate differential equations....

  16. Nonlinear Dynamics of Vortices in Different Types of Grain Boundaries

    Science.gov (United States)

    Sheikhzada, Ahmad K.

    As a major component of linear particle accelerators, superconducting radio-frequency (SRF) resonator cavities are required to operate with lowest energy dissipation and highest accelerating gradient. SRF cavities are made of polycrystalline materials in which grain boundaries can limit maximum RF currents and produce additional power dissipation sources due to local penetration of Josephson vortices. The essential physics of vortex penetration and mechanisms of dissipation of vortices driven by strong RF currents along networks of grain boundaries and their contribution to the residual surface resistance have not been well understood. To evaluate how GBs can limit the performance of SRF materials, particularly Nb and Nb3Sn, we performed extensive numerical simulations of nonlinear dynamics of Josephson vortices in grain boundaries under strong dc and RF fields. The RF power due to penetration of vortices both in weakly-coupled and strongly-coupled grain boundaries was calculated as functions of the RF field and frequency. The result of this calculation manifested a quadratic dependence of power to field amplitude at strong RF currents, an illustration of resistive behavior of grain boundaries. Our calculations also showed that the surface resistance is a complicated function of field controlled by penetration and annihilation of vortices and antivortices in strong RF fields which ultimately saturates to normal resistivity of grain boundary. We found that Cherenkov radiation of rapidly moving vortices in grain boundaries can produce a new instability causing generation of expanding vortex-antivortex pair which ultimately drives the entire GB in a resistive state. This effect is more pronounced in polycrystalline thin film and multilayer coating structures in which it can cause significant increase in power dissipation and results in hysteresis effects in I-V characteristics, particularly at low temperatures.

  17. Nonlinear Dynamics of Vortices in Different Types of Grain Boundaries

    Energy Technology Data Exchange (ETDEWEB)

    Sheikhzada, Ahmad [Old Dominion Univ., Norfolk, VA (United States)

    2017-05-01

    As a major component of linear particle accelerators, superconducting radio-frequency (SRF) resonator cavities are required to operate with lowest energy dissipation and highest accelerating gradient. SRF cavities are made of polycrystalline materials in which grain boundaries can limit maximum RF currents and produce additional power dissipation sources due to local penetration of Josephson vortices. The essential physics of vortex penetration and mechanisms of dissipation of vortices driven by strong RF currents along networks of grain boundaries and their contribution to the residual surface resistance have not been well understood. To evaluate how GBs can limit the performance of SRF materials, particularly Nb and Nb3Sn, we performed extensive numerical simulations of nonlinear dynamics of Josephson vortices in grain boundaries under strong dc and RF fields. The RF power due to penetration of vortices both in weakly-coupled and strongly-coupled grain boundaries was calculated as functions of the RF field and frequency. The result of this calculation manifested a quadratic dependence of power to field amplitude at strong RF currents, an illustration of resistive behavior of grain boundaries. Our calculations also showed that the surface resistance is a complicated function of field controlled by penetration and annihilation of vortices and antivortices in strong RF fields which ultimately saturates to normal resistivity of grain boundary. We found that Cherenkov radiation of rapidly moving vortices in grain boundaries can produce a new instability causing generation of expanding vortex-antivortex pair which ultimately drives the entire GB in a resistive state. This effect is more pronounced in polycrystalline thin film and multilayer coating structures in which it can cause significant increase in power dissipation and results in hysteresis effects in I-V characteristics, particularly at low temperatures.

  18. A Parameter Estimation Method for Nonlinear Systems Based on Improved Boundary Chicken Swarm Optimization

    Directory of Open Access Journals (Sweden)

    Shaolong Chen

    2016-01-01

    Full Text Available Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.

  19. Experimental Investigation of Stiffness Characteristics and Damping Properties of a Metallic Rubber Material

    Science.gov (United States)

    Lu, Ch. Zh.; Li, Jingyuan; Zhou, Bangyang; Li, Shuang

    2017-09-01

    The static stiffness and dynamic damping properties of a metallic rubber material (MR) were investigated, which exhibited a nonlinear deformation behavior. Its static stiffness is analyzed and discussed. The effects of structural parameters of MR and experimental conditions on its shock absorption capacity were examined by dynamic tests. Results revealed excellent elastic and damping properties of the material. Its stiffness increased with density, but decreased with thickness. The damping property of MR varied with its density, thickness, loading frequency, and amplitude.

  20. On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

    Science.gov (United States)

    Hall, P.; Malik, M. R.

    1984-01-01

    The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

  1. On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

    Science.gov (United States)

    Hall, P.; Malik, M. R.

    1986-01-01

    The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

  2. Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

    Directory of Open Access Journals (Sweden)

    Salih Yalcinbas

    2016-01-01

    Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

  3. Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions.

    Science.gov (United States)

    Bardhan, Jaydeep P; Knepley, Matthew G

    2014-10-07

    We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

  4. Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

    International Nuclear Information System (INIS)

    Bardhan, Jaydeep P.; Knepley, Matthew G.

    2014-01-01

    We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry

  5. Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Bardhan, Jaydeep P. [Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115 (United States); Knepley, Matthew G. [Computation Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

    2014-10-07

    We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

  6. Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability

    Science.gov (United States)

    Robinett, Rush D.; Wilson, David G.

    2009-10-01

    This paper presents a new nonlinear control methodology for slewing spacecraft, which provides both necessary and sufficient conditions for stability by identifying the stability boundaries, rigid body modes, and limit cycles. Conservative Hamiltonian system concepts, which are equivalent to static stability of airplanes, are used to find and deal with the static stability boundaries: rigid body modes. The application of exergy and entropy thermodynamic concepts to the work-rate principle provides a natural partitioning through the second law of thermodynamics of power flows into exergy generator, dissipator, and storage for Hamiltonian systems that is employed to find the dynamic stability boundaries: limit cycles. This partitioning process enables the control system designer to directly evaluate and enhance the stability and performance of the system by balancing the power flowing into versus the power dissipated within the system subject to the Hamiltonian surface (power storage). Relationships are developed between exergy, power flow, static and dynamic stability, and Lyapunov analysis. The methodology is demonstrated with two illustrative examples: (1) a nonlinear oscillator with sinusoidal damping and (2) a multi-input-multi-output three-axis slewing spacecraft that employs proportional-integral-derivative tracking control with numerical simulation results.

  7. Nonlinear characterization of a bolted, industrial structure using a modal framework

    Science.gov (United States)

    Roettgen, Daniel R.; Allen, Matthew S.

    2017-02-01

    This article presents measurements from a sub assembly of an off-the-shelf automotive exhaust system containing a bolted-flange connection and uses a recently proposed modal framework to develop a nonlinear dynamic model for the structure. The nonlinear identification and characterization methods used are reviewed to highlight the strengths of the current approach and the areas where further development is needed. This marks the first use of these new testing and nonlinear identification tools, and the associated modal framework, on production hardware with a realistic joint and realistic torque levels. To screen the measurements for nonlinearities, we make use of a time frequency analysis routine designed for transient responses called the zeroed early-time fast Fourier transform (ZEFFT). This tool typically reveals the small frequency shifts and distortions that tend to occur near each mode that is affected by the nonlinearity. The damping in this structure is found to be significantly nonlinear and a Hilbert transform is used to characterize the damping versus amplitude behavior. A model is presented that captures these effects for each mode individually (e.g. assuming negligible nonlinear coupling between modes), treating each mode as a single degree-of-freedom oscillator with a spring and viscous damping element in parallel with a four parameter Iwan model. The parameters of this model are identified for each of the structure's modes that exhibited nonlinearity and the resulting nonlinear model is shown to capture the stiffness and damping accurately over a large range of response amplitudes.

  8. Electron dynamics with radiation and nonlinear wigglers

    International Nuclear Information System (INIS)

    Jowett, J.M.

    1986-06-01

    The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches

  9. Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

    Science.gov (United States)

    Andres, Jeanne Therese H; Cardoso, Silvana S S

    2012-09-01

    We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

  10. Positive solutions for a nonlinear periodic boundary-value problem with a parameter

    Directory of Open Access Journals (Sweden)

    Jingliang Qiu

    2012-08-01

    Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

  11. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Dilna, N.; Rontó, András

    2010-01-01

    Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

  12. Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

    Science.gov (United States)

    Bardhan, Jaydeep P.; Knepley, Matthew G.

    2014-01-01

    We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry. PMID:25296776

  13. A Hartman–Nagumo inequality for the vector ordinary -Laplacian and applications to nonlinear boundary value problems

    Directory of Open Access Journals (Sweden)

    Ureña Antonio J

    2002-01-01

    Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.

  14. Unwrapped phase inversion with an exponential damping

    KAUST Repository

    Choi, Yun Seok

    2015-07-28

    Full-waveform inversion (FWI) suffers from the phase wrapping (cycle skipping) problem when the frequency of data is not low enough. Unless we obtain a good initial velocity model, the phase wrapping problem in FWI causes a result corresponding to a local minimum, usually far away from the true solution, especially at depth. Thus, we have developed an inversion algorithm based on a space-domain unwrapped phase, and we also used exponential damping to mitigate the nonlinearity associated with the reflections. We construct the 2D phase residual map, which usually contains the wrapping discontinuities, especially if the model is complex and the frequency is high. We then unwrap the phase map and remove these cycle-based jumps. However, if the phase map has several residues, the unwrapping process becomes very complicated. We apply a strong exponential damping to the wavefield to eliminate much of the residues in the phase map, thus making the unwrapping process simple. We finally invert the unwrapped phases using the back-propagation algorithm to calculate the gradient. We progressively reduce the damping factor to obtain a high-resolution image. Numerical examples determined that the unwrapped phase inversion with a strong exponential damping generated convergent long-wavelength updates without low-frequency information. This model can be used as a good starting model for a subsequent inversion with a reduced damping, eventually leading to conventional waveform inversion.

  15. Effect of Landau damping on kinetic Alfven and ion-acoustic solitary waves in a magnetized nonthermal plasma with warm ions

    International Nuclear Information System (INIS)

    Bandyopadhyay, Anup; Das, K.P.

    2002-01-01

    The evolution equations describing both kinetic Alfven wave and ion-acoustic wave in a nonthermal magnetized plasma with warm ions including weak nonlinearity and weak dispersion with the effect of Landau damping have been derived. These equations reduce to two coupled equations constituting the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation for both kinetic Alfven wave and ion-acoustic wave, including an extra term accounting for the effect of Landau damping. When the coefficient of the nonlinear term of the evolution equation for ion-acoustic wave vanishes, the nonlinear behavior of ion-acoustic wave, including the effect of Landau damping, is described by two coupled equations constituting the modified KdV-ZK (MKdV-ZK) equation, including an extra term accounting for the effect of Landau damping. It is found that there is no effect of Landau damping on the solitary structures of the kinetic Alfven wave. Both the macroscopic evolution equations for the ion-acoustic wave admits solitary wave solutions, the former having a sech 2 profile and the latter having a sech profile. In either case, it is found that the amplitude of the ion-acoustic solitary wave decreases slowly with time

  16. Global existence and decay of solutions of a nonlinear system of wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.

  17. Global existence and decay of solutions of a nonlinear system of wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-03-01

    This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.

  18. Optimal analytic method for the nonlinear Hasegawa-Mima equation

    Science.gov (United States)

    Baxter, Mathew; Van Gorder, Robert A.; Vajravelu, Kuppalapalle

    2014-05-01

    The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.

  19. Suggestions for new transverse oscillations damping systems in large synchrotrons and colliders

    International Nuclear Information System (INIS)

    Ivanov, I.N.; Melnikov, V.A.

    1994-01-01

    Due to the high requirements on beam quality, modern synchrotrons and colliders require special systems for transverse oscillation damping (TDS). New system for the correction of injection errors and multibunch instabilities is proposed. The special beam monitor on the basis of the axial-slotted lines is developed for the transverse beam velocity measuring. The special nonlinear regime of damping is suggested to decrease the operating time of TDS. 2 refs., 4 figs., 2 tabs

  20. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  1. Nonlinear observer-based Lyapunov boundary control of distributed heat transfer mechanisms for membrane distillation plant

    KAUST Repository

    Eleiwi, Fadi

    2016-09-19

    This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer. (C) 2016 Elsevier Ltd. All rights reserved.

  2. Comparative study of popular objective functions for damping power system oscillations in multimachine system.

    Science.gov (United States)

    Islam, Naz Niamul; Hannan, M A; Shareef, Hussain; Mohamed, Azah; Salam, M A

    2014-01-01

    Power oscillation damping controller is designed in linearized model with heuristic optimization techniques. Selection of the objective function is very crucial for damping controller design by optimization algorithms. In this research, comparative analysis has been carried out to evaluate the effectiveness of popular objective functions used in power system oscillation damping. Two-stage lead-lag damping controller by means of power system stabilizers is optimized using differential search algorithm for different objective functions. Linearized model simulations are performed to compare the dominant mode's performance and then the nonlinear model is continued to evaluate the damping performance over power system oscillations. All the simulations are conducted in two-area four-machine power system to bring a detailed analysis. Investigated results proved that multiobjective D-shaped function is an effective objective function in terms of moving unstable and lightly damped electromechanical modes into stable region. Thus, D-shape function ultimately improves overall system damping and concurrently enhances power system reliability.

  3. Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2012-06-01

    Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.

  4. Mathematical and numerical study of nonlinear boundary problems related to plasma physics

    International Nuclear Information System (INIS)

    Sermange, M.

    1982-06-01

    After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr

  5. Application of small panel damping measurements to larger walls

    Science.gov (United States)

    Hastings, Mardi C.; Godfrey, Richard; Babcock, G. Madison

    1996-05-01

    Damping properties of a viscoelastic material were determined using a standard resonant beam technique. The damping material was then applied to 1 by 2 foot gypsum panels in a constrained layer construction. Damping loss factors in panels with and without the constrained layer were determined based on reverberation times after excitation at third-octave band center frequencies. The constrained damping layer had been designed to increase damping by an order of magnitude above that of a single gypsum panel at 2000 Hz; however, relative to a gypsum panel of the same overall thickness as the panel with the constrained layer, loss factors increased only by a factor of three to five. Next modal damping loss factors in 9 by 14 foot gypsum single and double walls were calculated from the experimentally determined quality factor for each modal resonance. Results showed that below 2500 Hz, modes in 1 by 2 foot gypsum panels had nearly the same damping loss factors as modes in a 9 by 14 foot gypsum wall of the same thickness; however, loss factors for the wall were an order of magnitude lower than those of the 1 by 2 foot panels at frequencies above 2500 Hz, the coincidence frequency for 5/8-inch thick gypsum plates. Thus it was inconclusive whether or not damping loss factors measured using small panels could be used to estimate the effect of a constrained damping layer on transmission loss through a 9 by 14 foot wall unless boundary conditions and modal frequencies were the same for each size.

  6. Nonlinear interaction of s-polarized surface waves at the boundary of a semibounded magnetized plasma

    International Nuclear Information System (INIS)

    Amein, W.H.; El-Siragy, N.M.; Nagy, O.Z.; Sayed, Y.A.

    1981-01-01

    Nonlinear interaction of S-Polarized surface waves at the boundary of a semibounded magnetized plasma is investigated. The expressions of the amplitudes of the generated waves are found. It is shown that, the generated waves with combined frequencies are equally radiated from the transient layer into plasma and vacuum

  7. Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

    Indian Academy of Sciences (India)

    In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

  8. Breatherlike excitations in discrete lattices with noise and nonlinear damping

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus

    1997-01-01

    We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects...

  9. Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

    Energy Technology Data Exchange (ETDEWEB)

    Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)

    2016-07-01

    A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

  10. Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

    Directory of Open Access Journals (Sweden)

    Suheel Abdullah Malik

    2014-01-01

    Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

  11. Magnetically tuned mass dampers for optimal vibration damping of large structures

    International Nuclear Information System (INIS)

    Bourquin, Frederic; Siegert, Dominique; Caruso, Giovanni; Peigney, Michael

    2014-01-01

    This paper deals with the theoretical and experimental analysis of magnetically tuned mass dampers, applied to the vibration damping of large structures of civil engineering interest. Two devices are analysed, for which both the frequency tuning ratio and the damping coefficient can be easily and finely calibrated. They are applied for the damping of the vibrations along two natural modes of a mock-up of a bridge under construction. An original analysis, based on the Maxwell receding image method, is developed for estimating the drag force arising inside the damping devices. It also takes into account self-inductance effects, yielding a complex nonlinear dependence of the drag force on the velocity. The analysis highlights the range of velocities for which the drag force can be assumed of viscous type, and shows its dependence on the involved geometrical parameters of the dampers. The model outcomes are then compared to the corresponding experimental calibration curves. A dynamic model of the controlled structure equipped with the two damping devices is presented, and used for the development of original optimization expressions and for determining the corresponding maximum achievable damping. Finally, several experimental results are presented, concerning both the free and harmonically forced vibration damping of the bridge mock-up, and compared to the corresponding theoretical predictions. The experimental results reveal that the maximum theoretical damping performance can be achieved, when both the tuning frequencies and damping coefficients of each device are finely calibrated according to the optimization expressions. (paper)

  12. Boundary control of fluid flow through porous media

    DEFF Research Database (Denmark)

    Hasan, Agus; Foss, Bjarne; Sagatun, Svein Ivar

    2010-01-01

    The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper,......, some stabilizing controllers are constructed for various cases using Lyapunov design.......The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper...

  13. DAMPING OF MAGNETOHYDRODYNAMIC TURBULENCE IN PARTIALLY IONIZED PLASMA: IMPLICATIONS FOR COSMIC RAY PROPAGATION

    International Nuclear Information System (INIS)

    Xu, Siyao; Yan, Huirong; Lazarian, A.

    2016-01-01

    We study the damping processes of both incompressible and compressible magnetohydrodynamic (MHD) turbulence in a partially ionized medium. We start from the linear analysis of MHD waves, applying both single-fluid and two-fluid treatments. The damping rates derived from the linear analysis are then used in determining the damping scales of MHD turbulence. The physical connection between the damping scale of MHD turbulence and the cutoff boundary of linear MHD waves is investigated. We find two branches of slow modes propagating in ions and neutrals, respectively, below the damping scale of slow MHD turbulence, and offer a thorough discussion of their propagation and dissipation behavior. Our analytical results are shown to be applicable in a variety of partially ionized interstellar medium (ISM) phases and the solar chromosphere. The importance of neutral viscosity in damping the Alfvenic turbulence in the interstellar warm neutral medium and the solar chromosphere is demonstrated. As a significant astrophysical utility, we introduce damping effects to the propagation of cosmic rays in partially ionized ISM. The important role of turbulence damping in both transit-time damping and gyroresonance is identified.

  14. Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

    International Nuclear Information System (INIS)

    Koteras, J.R.

    1996-01-01

    The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

  15. Measurement of Resonance driving terms in the ATF Damping Ring

    CERN Document Server

    Tomás, R; Kuroda, S; Naito, T; Okugi, T; Urakawa, J; Zimmermann, F

    2008-01-01

    The measurement of resonance driving terms in the Damping Ring of the Accelerator Test Facility in KEK could help finding possible machine imperfections and even to optimize single particle stability through the minimization of non-linearities. The first experimental attempts of this enterprise are reported in this note.

  16. Non-linear dynamic response of reactor containment

    International Nuclear Information System (INIS)

    Takemori, T.; Sotomura, K.; Yamada, M.

    1975-01-01

    A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

  17. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  18. Nonlinear free vibration control of beams using acceleration delayed-feedback control

    International Nuclear Information System (INIS)

    Alhazza, Khaled A; Alajmi, Mohammed; Masoud, Ziyad N

    2008-01-01

    A single-mode delayed-feedback control strategy is developed to reduce the free vibrations of a flexible beam using a piezoelectric actuator. A nonlinear variational model of the beam based on the von Kàrmàn nonlinear type deformations is considered. Using Galerkin's method, the resulting governing partial differential equations of motion are reduced to a system of nonlinear ordinary differential equations. A linear model using the first mode is derived and is used to characterize the damping produced by the controller as a function of the controller's gain and delay. Three-dimensional figures showing the damping magnitude as a function of the controller gain and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated and compared. To validate the single-mode approximation, numerical simulations are performed using a three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the first-mode vibration

  19. Phase-locking phenomena and excitation of damped and driven nonlinear oscillators

    DEFF Research Database (Denmark)

    Shagalov, A.G.; Juul Rasmussen, Jens; Naulin, Volker

    2009-01-01

    Resonant phase-locking phenomena ('autoresonance') in the van der Pol Duffing oscillator forced by a small amplitude periodic driving with slowly varying frequency have been studied. We show that autoresonance occurs for oscillators with sufficiently small damping, when the system may have bi-stable...

  20. Non-parametric system identification from non-linear stochastic response

    DEFF Research Database (Denmark)

    Rüdinger, Finn; Krenk, Steen

    2001-01-01

    An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable...... of the energy at mean-level crossings, which yields the damping relative to white noise intensity. Finally, an estimate of the noise intensity is extracted by estimating the absolute damping from the autocovariance functions of a set of modified phase plane variables at different energy levels. The method...

  1. Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Alsaedi Ahmed

    2009-01-01

    Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

  2. Nonlinear Dynamics of Nanomechanical Resonators

    Science.gov (United States)

    Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym

    2007-03-01

    Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004).

  3. Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

    Directory of Open Access Journals (Sweden)

    Alex Elías-Zúñiga

    2013-01-01

    oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.

  4. Global Well-Posedness for Cubic NLS with Nonlinear Damping

    KAUST Repository

    Antonelli, Paolo

    2010-11-04

    We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.

  5. The short circumference damping ring design for the ILC

    CERN Document Server

    Korostelev, Maxim S; Kuriki, Masao; Kuroda, Shigeru; Naito, Takashi; Ross, Marc; Urakawa, Junji; Zimmermann, Frank

    2005-01-01

    The ILC damping ring tentative design is driven by the operational scenario of the main linac, the beam-dynamics demand of producing a stable and high-quality beam, the injection/extraction scheme and the kicker performance. In this paper, a short circumference damping ring design based on TME cells is described. The ring accommodates injection kickers which provide a flat top of 280 nsec and a 60 nsec rise and fall time and very fast strip-line kickers for beam extraction with a 2 nsec rise and fall time for 3-MHz operation. The potential impact of collective effects and the possible degradation of the dynamic aperture by nonlinear-wiggler fields are estimated.

  6. Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2017-01-01

    The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

  7. Structural Damping with Friction Beams

    Directory of Open Access Journals (Sweden)

    L. Gaul

    2008-01-01

    Full Text Available In the last several years, there has been increasing interest in the use of friction joints for enhancing damping in structures. The joints themselves are responsible for the major part of the energy dissipation in assembled structures. The dissipated work in a joint depends on both the applied normal force and the excitation force. For the case of a constant amplitude excitation force, there is an optimal normal force which maximizes the damping. A ‘passive’ approach would be employed in this instance. In most cases however, the excitation force, as well as the interface parameters such as the friction coefficient, normal pressure distribution, etc., are not constant. In these cases, a ‘semi-active’ approach, which implements an active varying normal force, is necessary. For the ‘passive’ and ‘semi-active’ approaches, the normal force has to be measured. Interestingly, since the normal force in a friction joint influences the local stiffness, the natural frequencies of the assembled structure can be tuned by adjusting the normal force. Experiments and simulations are performed for a simple laboratory structure consisting of two superposed beams with friction in the interface. Numerical simulation of the friction interface requires non-linear models. The response of the double beam system is simulated using a numerical algorithm programmed in MATLAB which models point-to-point friction with the Masing friction model. Numerical predictions and measurements of the double beam free vibration response are compared. A practical application is then described, in which a friction beam is used to damp the vibrations of the work piece table on a milling machine. The increased damping of the table reduces vibration amplitudes, which in turn results in enhanced surface quality of the machined parts, reduction in machine tool wear, and potentially higher feed rates. Optimal positioning of the friction beams is based on knowledge of the mode

  8. Optics design of Intrabeam Scattering dominated damping rings

    CERN Document Server

    Antoniou, Fanouria; Papaphilippou, Ioannis

    A e+/e- linear collider, the Compact Linear Collider (CLIC) is under design at CERN, aiming to explore the terascale particle physics regime. The collider has been optimized at 3 TeV center of mass energy and targets a luminosity of 1034 cm-2 s-1. In order to achieve this high luminosity, high intensity bunches with ultra low emittances, in all three planes, are required. The generation of ultra low emittance is achieved in the Damping Rings (DR) complex of the collider. The large input beam emittances, especially the ones coming from the positron source, and the requirement of ultra low emittance production in a fast repetition time of 20 ms, imply that the beam damping is done in two stages. Thus, a main-damping ring (DR) and a predamping ring (PDR) are needed, for each particle species. The high bunch brightness gives rise to several collective effects, with Intra-beam scattering (IBS) being the main limitation to the ultra-low emittance. This thesis elaborates the lattice design and non-linear optimizatio...

  9. Comparison of a nonlinear dynamic model of a piping system to test data

    International Nuclear Information System (INIS)

    Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.

    1983-01-01

    Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)

  10. Study of damping characteristics of fibre reinforced composite aerospace structure

    International Nuclear Information System (INIS)

    Khan, M.Z.; Saleh, S.; Munir, A.

    2006-01-01

    Composite materials are used in a variety of high demanding structural applications. Apart from their other preferable properties, they have high-energy dissipation characteristics, which is important aspect when we repeatedly wiggle the system back and forth. It is important to have thorough understanding of material damping behavior; in general materials damping tends to be complex nonlinear function of vibration amplitude, frequency of loading and material formulation. There are number of mathematical models available in literature to obtain hysteresis curves. One approach for identifying damping characteristics used mechanical hysteresis curves. In present work, a phenomenon was observed during testing of fibre reinforced composite beam of an aerospace structure, that for increase load in structure, the path of Force vs. Displacement curve is different than the path of unloading. A plot is generated which indicate the hysteresis loop representing the steady state dynamic behavior of material. The area enclosed by such curves is proportional to energy dissipation per cycle. However, the specific shape of the curve also has important implications for characterizing the specific functional form of the damping. Therefore, it is important to develop methods for accurately accounting for such effects. The current work explores the damping characteristics both theoretically and experimentally. (author)

  11. Nonlinear dissipative devices in structural vibration control: A review

    Science.gov (United States)

    Lu, Zheng; Wang, Zixin; Zhou, Ying; Lu, Xilin

    2018-06-01

    Structural vibration is a common phenomenon existing in various engineering fields such as machinery, aerospace, and civil engineering. It should be noted that the effective suppression of structural vibration is conducive to enhancing machine performance, prolonging the service life of devices, and promoting the safety and comfort of structures. Conventional linear energy dissipative devices (linear dampers) are largely restricted for wider application owing to their low performance under certain conditions, such as the detuning effect of tuned mass dampers subjected to nonstationary excitations and the excessively large forces generated in linear viscous dampers at high velocities. Recently, nonlinear energy dissipative devices (nonlinear dampers) with broadband response and high robustness are being increasingly used in practical engineering. At the present stage, nonlinear dampers can be classified into three groups, namely nonlinear stiffness dampers, nonlinear-stiffness nonlinear-damping dampers, and nonlinear damping dampers. Corresponding to each nonlinear group, three types of nonlinear dampers that are widely utilized in practical engineering are reviewed in this paper: the nonlinear energy sink (NES), particle impact damper (PID), and nonlinear viscous damper (NVD), respectively. The basic concepts, research status, engineering applications, and design approaches of these three types of nonlinear dampers are summarized. A comparison between their advantages and disadvantages in practical engineering applications is also conducted, to provide a reference source for practical applications and new research.

  12. Pipe damping

    International Nuclear Information System (INIS)

    Ware, A.G.

    1985-01-01

    Studies are being conducted at the Idaho National Engineering Laboratory to determine whether an increase in the damping values used in seismic structural analyses of nuclear piping systems is justified. Increasing the allowable damping would allow fewer piping supports which could lead to safer, more reliable, and less costly piping systems. Test data from availble literature were examined to determine the important parameters contributing to piping system damping, and each was investigated in separate-effects tests. From the combined results a world pipe damping data bank was established and multiple regression analyses performed to assess the relative contributions of the various parameters. The program is being extended to determine damping applicable to higher frequency (33 to 100 Hz) fluid-induced loadings. The goals of the program are to establish a methodology for predicting piping system damping and to recommend revised guidelines for the damping values to be included in analyses

  13. Temporal Damping Effect of the Yucca Mountain Fractured Saturated Rock on Transient Infiltration Pulses

    International Nuclear Information System (INIS)

    K. Zhang; Y.S. Wu; L. Pan

    2006-01-01

    Performance assessment of the Yucca Mountain unsaturated zone (UZ) as the site for an underground repository of high-level radioactive waste relies on the crucial assumption that water percolation processes in the unsaturated zone can be approximated as a steady-state condition. Justification of such an assumption is based on temporal damping effects of several geological units within the unsaturated tuff formation. In particular, the nonwelded tuff of the Paintbrush Group (PTn unit) at Yucca Mountain, because of its highly porous nature, has been conceptualized to have a significant capacity for temporally damping transient percolation fluxes. The objective of this study is to investigate these damping effects, using a three-dimensional (3-D) mountain-scale model as well as several one-dimensional (1-D) models. The 3-D model incorporates a wide variety of the updated field data for the highly heterogeneous unsaturated formation at Yucca Mountain. The model is first run to steady state and calibrated using field-measured data and then transient pulse infiltrations are applied to the model top boundary. Subsequent changes in percolation fluxes at the bottom of and within the PTn unit are examined under episodic infiltration boundary conditions. The 1-D model is used to examine the long-term response of the flow system to higher infiltration pulses, while the damping effect is also investigated through modeling tracer transport in the UZ under episodic infiltration condition. Simulation results show the existence of damping effects within the PTn unit and also indicate that the assumption of steady-state flow conditions below the PTn unit is reasonable. However, the study also finds that some fast flow paths along faults exist, causing vertical-flux quick responses at the PTn bottom to the episodic infiltration at the top boundary

  14. Numerical Investigation of Damping of Torsional Beam Vibrations by Viscous Bimoments

    DEFF Research Database (Denmark)

    Hoffmeyer, David; Høgsberg, Jan Becker

    2017-01-01

    Damping of torsional beam vibrations of slender beam–structures with thin–walled cross–sections is investigated. Analytical results from solving the differential equation governing torsion with viscous bimoments imposed at the boundary, are compared with a numerical approach with three...

  15. Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

    Science.gov (United States)

    Kanoglu, U.; Aydin, B.

    2014-12-01

    The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

  16. Optimization of piezoelectric cantilever energy harvesters including non-linear effects

    International Nuclear Information System (INIS)

    Patel, R; McWilliam, S; Popov, A A

    2014-01-01

    This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations. (paper)

  17. Nonlinear Electron Waves in Strongly Magnetized Plasmas

    DEFF Research Database (Denmark)

    Pécseli, Hans; Juul Rasmussen, Jens

    1980-01-01

    Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....

  18. Tuning of damping controller for UPFC using quantum particle swarm optimizer

    Energy Technology Data Exchange (ETDEWEB)

    Shayeghi, H., E-mail: hshayeghi@gmail.co [Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil (Iran, Islamic Republic of); Shayanfar, H.A. [Center of Excellence for Power System Automation and Operation, Electrical Engineering Department, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Jalilzadeh, S.; Safari, A. [Technical Engineering Department, Zanjan University, Zanjan (Iran, Islamic Republic of)

    2010-11-15

    On the basis of the linearized Phillips-Herffron model of a single machine power system, we design optimally the unified power flow controller (UPFC) based damping controller in order to enhance power system low frequency oscillations. The problem of robustly UPFC based damping controller is formulated as an optimization problem according to the time domain-based objective function which is solved using quantum-behaved particle swarm optimization (QPSO) technique that has fewer parameters and stronger search capability than the particle swarm optimization (PSO), as well as is easy to implement. To ensure the robustness of the proposed damping controller, the design process takes into account a wide range of operating conditions and system configurations. The effectiveness of the proposed controller is demonstrated through non-linear time-domain simulation and some performance indices studies under various disturbance conditions of over a wide range of loading conditions. The results analysis reveals that the designed QPSO based UPFC controller has an excellent capability in damping power system low frequency oscillations in comparison with the designed classical PSO (CPSO) based UPFC controller and enhance greatly the dynamic stability of the power systems. Moreover, the system performance analysis under different operating conditions show that the {delta}{sub E} based damping controller is superior to the m{sub B} based damping controller.

  19. Nonlinear traveling waves in rotating Rayleigh-Bacute enard convection: Stability boundaries and phase diffusion

    International Nuclear Information System (INIS)

    Liu, Y.; Ecke, R.E.

    1999-01-01

    We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bacute enard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio Γ=5. We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates 60<Ω<420. The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for Ω=274. The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated. copyright 1999 The American Physical Society

  20. Non-linear processes in the Earth atmosphere boundary layer

    Science.gov (United States)

    Grunskaya, Lubov; Valery, Isakevich; Dmitry, Rubay

    2013-04-01

    The work is connected with studying electromagnetic fields in the resonator Earth-Ionosphere. There is studied the interconnection of tide processes of geophysical and astrophysical origin with the Earth electromagnetic fields. On account of non-linear property of the resonator Earth-Ionosphere the tides (moon and astrophysical tides) in the electromagnetic Earth fields are kinds of polyharmonic nature. It is impossible to detect such non-linear processes with the help of the classical spectral analysis. Therefore to extract tide processes in the electromagnetic fields, the method of covariance matrix eigen vectors is used. Experimental investigations of electromagnetic fields in the atmosphere boundary layer are done at the distance spaced stations, situated on Vladimir State University test ground, at Main Geophysical Observatory (St. Petersburg), on Kamchatka pen., on Lake Baikal. In 2012 there was continued to operate the multichannel synchronic monitoring system of electrical and geomagnetic fields at the spaced apart stations: VSU physical experimental proving ground; the station of the Institute of Solar and Terrestrial Physics of Russian Academy of Science (RAS) at Lake Baikal; the station of the Institute of volcanology and seismology of RAS in Paratunka; the station in Obninsk on the base of the scientific and production society "Typhoon". Such investigations turned out to be possible after developing the method of scanning experimental signal of electromagnetic field into non- correlated components. There was used a method of the analysis of the eigen vectors ofthe time series covariance matrix for exposing influence of the moon tides on Ez. The method allows to distribute an experimental signal into non-correlated periodicities. The present method is effective just in the situation when energetical deposit because of possible influence of moon tides upon the electromagnetic fields is little. There have been developed and realized in program components

  1. On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

    Science.gov (United States)

    Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

    1994-01-01

    It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

  2. Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

    Science.gov (United States)

    Ahmad, Shahid

    1991-01-01

    An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons

  3. Existence of Positive Solutions to a Singular Semipositone Boundary Value Problem of Nonlinear Fractional Differential Systems

    Directory of Open Access Journals (Sweden)

    Xiaofeng Zhang

    2017-12-01

    Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.

  4. A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

    Science.gov (United States)

    Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

    2017-02-01

    The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

  5. Study on global performances and mooring-induced damping of a semi-submersible

    Science.gov (United States)

    Xiong, Ling-zhi; Yang, Jian-min; Lv, Hai-ning; Zhao, Wen-hua; Kou, Yu-feng

    2016-10-01

    The harsh environmental conditions bring strong nonlinearities to the hydrodynamic performances of the offshore floating platforms, which challenge the reliable prediction of the platform coupled with the mooring system. The present study investigates a typical semi-submersible under both the operational and the survival conditions through numerical and experimental methods. The motion responses, the mooring line tensions, and the wave loads on the longitudinal mid-section are investigated by both the fully non-linearly coupled numerical simulation and the physical experiment. Particularly, in the physical model test, the wave loads distributed on the semi-submersible's mid-section were measured by dividing the model into two parts, namely the port and the starboard parts, which were rigidly connected by three six-component force transducers. It is concluded that both the numerical and physical model can have good prediction of the semi-submersible's global responses. In addition, an improved numerical approach is proposed for the estimation of the mooring-induced damping, and is validated by both the experimental and the published results. The characteristics of the mooring-induced damping are further summarized in various sea states, including the operational and the survival environments. In order to obtain the better prediction of the system response in deep water, the mooring-induced damping of the truncated mooring lines applied in the physical experiment are compensated by comparing with those in full length. Furthermore, the upstream taut and the downstream slack mooring lines are classified and investigated to obtain the different mooring line damping performances in the comparative study.

  6. Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

    Science.gov (United States)

    Do, K. D.

    2018-05-01

    Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

  7. Global Optimization of Damping Ring Designs Using a Multi-Objective Evolutionary Algorithm

    CERN Document Server

    Emery, Louis

    2005-01-01

    Several damping ring designs for the International Linear Collider have been proposed recently. Some of the specifications, such as circumference and bunch train, are not fixed yet. Designers must make a choice anyway, select a geometry type (dog-bone or circular), an arc cell type (TME or FODO), and optimize linear and nonlinear part of the optics. The design process include straightforward steps (usually the linear optics), and some steps not so straightforward (when nonlinear optics optimization is affected by the linear optics). A first attempt at automating this process for the linear optics is reported. We first recognize that the optics is defined by just a few primary parameters (e.g., phase advance per cell) that determine the rest (e.g., quadrupole strength). In addition to the exact specification of circumference, equilibrium emittance and damping time there are some other quantities which could be optimized that may conflict with each other. A multiobjective genetic optimizer solves this problem b...

  8. Direct heuristic dynamic programming for damping oscillations in a large power system.

    Science.gov (United States)

    Lu, Chao; Si, Jennie; Xie, Xiaorong

    2008-08-01

    This paper applies a neural-network-based approximate dynamic programming method, namely, the direct heuristic dynamic programming (direct HDP), to a large power system stability control problem. The direct HDP is a learning- and approximation-based approach to addressing nonlinear coordinated control under uncertainty. One of the major design parameters, the controller learning objective function, is formulated to directly account for network-wide low-frequency oscillation with the presence of nonlinearity, uncertainty, and coupling effect among system components. Results include a novel learning control structure based on the direct HDP with applications to two power system problems. The first case involves static var compensator supplementary damping control, which is used to provide a comprehensive evaluation of the learning control performance. The second case aims at addressing a difficult complex system challenge by providing a new solution to a large interconnected power network oscillation damping control problem that frequently occurs in the China Southern Power Grid.

  9. Breather type solutions of the vector nonlinear Schroedinger equation with quasi-constant boundary conditions

    International Nuclear Information System (INIS)

    Makhan'kov, V.G.; Slavov, S.I.

    1989-01-01

    Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs

  10. Global format for energy-momentum based time integration in nonlinear dynamics

    DEFF Research Database (Denmark)

    Krenk, Steen

    2014-01-01

    A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...

  11. Sound Power Minimization of Circular Plates Through Damping Layer Placement

    Science.gov (United States)

    Wodtke, H.-W.; Lamancusa, J. S.

    1998-09-01

    Damping layers, widely used for noise and vibration control of thin-walled structures, can be designed to provide an optimal trade-off between performance and weight which is of particular importance in the automotive and aircraft industry. The goal of the presented work is the minimization of sound power radiated from plates under broadband excitation by redistribution of unconstrained damping layers. The total radiated sound power is assumed to be represented by the sound power radiated at the structural resonances. Resonance tracking is performed by means of single-degree-of-freedom (SDOF)-approximations based on near-resonance responses and their frequency derivatives. Axisymmetric vibrations of circular plates under several boundary and forcing conditions are considered. Frequency dependent Young's modulus and loss factor of the damping material are taken into account. Vibration analysis is based on the finite element method (FEM) while acoustic radiation is treated by means of Rayleigh's integral formula. It is shown that, starting from a uniform damping layer distribution, substantial reduction in radiated sound power can be achieved through redistribution of the damping layers. Depending on the given situation, these reductions are not only due to amplitude reductions but also to changes in vibration shapes and frequencies.

  12. Nonlinear soil-structure interaction analysis based on the boundary-element method in time domain with application to embedded foundation

    International Nuclear Information System (INIS)

    Wolf, J.P.; Darbre, G.R.

    1985-01-01

    The computational procedure of the so-called truncated indirect boundary-element method is derived. The latter, which is non-local in space and time, represents a rigorous generally applicable procedure for taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basement and separation of the side wall is investigated. (orig.)

  13. Nonlinear analysis for a ship with a general roll-damping model

    Energy Technology Data Exchange (ETDEWEB)

    El-Bassiouny, A F [Mathematics Department, Faculty of Science, Benha University, Benha 13518 (Egypt)

    2007-05-15

    The qualitative behaviour of the response of a ship rolling in longitudinal waves whose amplitude or frequency (parameters) are slowly varied is presented. An analytical and numerical technique is used to predict the qualitative change taking place in the stable solutions of a ship model as one of the parameters is slowly changed. The analysis took into consideration linear, cubic and quantic terms in the polynomial expansion of the relative roll angle. The damping moment consists of the linear term associated with radiation and viscous damping and a cubic term due to frictional resistance and eddies behind bilge keels and hard bilge corners. Two methods (the averaging and the multiple time scales) are used to investigate a first-order approximate analytical solution. The modulation equations of the amplitudes and phases are obtained. These equations are used to determine steady state solutions. Numerical calculations are presented which illustrate the behaviour of the steady state response amplitude as a function of the detuning parameter. The stability of the proposed solution is determined applying Liapunov's first method. The effects of different parameters on the system behaviour are investigated numerically. The results obtained by the two methods are in excellent agreement.

  14. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2014-01-01

    Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

  15. Kinetic theory of collective exitations and damping in Bose-Einstein condensed gases

    NARCIS (Netherlands)

    Al Khawaja, U.; Stoof, H.T.C.

    2000-01-01

    We calculate the frequencies and damping rates of the low-lying collective modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex nonlinear Schrödinger equation to determine the dynamics of the condensate atoms. In this manner we take into account both collisions between

  16. Kinetic theory of collective excitations and damping in Bose-Einstein condensed gases

    NARCIS (Netherlands)

    Al Khawaja, U.; Stoof, H.T.C.

    2000-01-01

    We calculate the frequencies and damping rates of the low-lying collective modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex nonlinear Schrödinger equation to determine the dynamics of the condensate atoms, and couple it to a Boltzmann equation for the noncondensate

  17. Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

    International Nuclear Information System (INIS)

    Semenova, V.N.

    2016-01-01

    A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

  18. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    1978-01-01

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

  19. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

  20. Some aspects of floor spectra of 1DOF nonlinear primary structures

    International Nuclear Information System (INIS)

    Politopoulos, I.; Feau, C.

    2007-01-01

    In this paper the influence of the nonlinear behaviour of the primary structure on floor spectra is investigated by means of simple models. The general trends of floor spectra for different types of nonlinear behaviour of one degree of freedom (1DOF) primary structure are shown and we point out their common futures and their differences. A special attention is given to the cases of elastoplastic and nonlinear elastic behaviours and methods to determine an equivalent linear oscillator are proposed. The properties (frequency and damping) of this equivalent linear oscillator are quite different from the properties of equivalent linear oscillators commonly considered in practice. In particular, in the case of elastoplastic behaviour, there is no frequency shift and damping is smaller than assumed by other methods commonly used. In the case of nonlinear elastic behaviour, the concept of an equivalent frequency which is a random variable is used. Finally, a design floor spectrum of primary structures, exhibiting energy dissipating nonlinear behaviour is proposed. (authors)

  1. Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

    International Nuclear Information System (INIS)

    Glowinski, R.; Le Tallec, P.

    1984-01-01

    The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

  2. Nonlinear resonance in Duffing oscillator with fixed and integrative ...

    Indian Academy of Sciences (India)

    We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...

  3. Nonlinear resonance in Duffing oscillator with fixed and integrative ...

    Indian Academy of Sciences (India)

    2012-03-02

    Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...

  4. General decay of solutions of a nonlinear system of viscoelastic wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2011-04-16

    This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.

  5. General decay of solutions of a nonlinear system of viscoelastic wave equations

    KAUST Repository

    Said-Houari, Belkacem; Messaoudi, Salim A.; Guesmia, Aï ssa

    2011-01-01

    This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.

  6. Effects of extreme wind shear on aeroelastic modal damping of wind turbines

    DEFF Research Database (Denmark)

    Skjoldan, P.F.; Hansen, Morten Hartvig

    2013-01-01

    Wind shear is an important contributor to fatigue loads on wind turbines. Because it causes an azimuthal variation in angle of attack, it can also affect aerodynamic damping. In this paper, a linearized model of a wind turbine, based on the nonlinear aeroelastic code BHawC, is used to investigate...

  7. Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

    Directory of Open Access Journals (Sweden)

    Mitsuhiro Nakao

    2014-01-01

    Full Text Available We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.

  8. Quadratic Damping

    Science.gov (United States)

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  9. Effects of Collisionality on the Nonlinear Characteristics of Boundary Turbulence and Blob/hole Transport in Tokamak Plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Li, J.; Yasuaki, K., E-mail: lijq@energy.kyoto-u.ac.jp [Kyoto University, Kyoto (Japan); Cheng, J.; Longwen, Y.; Jiaqi, D. [Southwestern Institute of Physics, Chengdu (China)

    2012-09-15

    Full text: Blob/hole dynamics near tokamak separatrix is of striking importance in determining the boundary transport. Based on simulations using an extended 2-region (edge/SOL) fluid model, we found that blob/hole dynamics are sensitively influenced by the plasma collisionality, i.e., ion-electron and ion-neutral collisions. Namely, the holes are enhanced in highly collisional edge whereas the blobs are weakened at the SOL, causing larger particle convection. These blob/hole dynamics are closely correlated with potential dipoles. The trends are experimentally evidenced on the HL-2A tokamak. Moreover, as the neutral-ion collision increases, the blobs at the SOL tend to develop into streamers propagating outwards with reduced amplitude while the holes inwards are suppressed, showing a key role in nonlinear structure regulation and resultant transport suppression. Results suggest that adjusting the plasma collisionality by fueling, e.g., gas puffing, could serve as a method to nonlinearly select turbulent structures, i.e., blobs, holes or streamers, to access the control of boundary transport. (author)

  10. Injection and Extraction Lines for the ILC Damping Rings

    International Nuclear Information System (INIS)

    Reichel, Ina

    2007-01-01

    The current design for the injection and extraction lines into and out of the ILC Damping Rings is presented as well as the design for the abort line. Due to changes of the geometric boundary conditions by other subsystems of the ILC, a modular approach has been used to be able to respond to recurring layout changes while reusing previously designed parts

  11. Effect of microalloying with rare-earth on recrystallization behaviour and damping properties of Mg sheets

    International Nuclear Information System (INIS)

    Ma, Ning; Peng, Qiuming; Pan, Junling; Li, Hui; Xiao, Wenlong

    2014-01-01

    Highlights: • Rare earth additions accelerate recovery, but retard recrystallization. • Internal peak at mediate temperatures corresponds to grain boundary relaxation. • Internal peak at elevated temperature is a recrystallization peak. • Grain size, basal texture and dislocation density affect damping remarkably. - Abstract: The effect of a small amount of rare earth elements (RE: Nd and Dy, 0.5 wt.%) on recrystallization behaviour, microstructural evolution and damping properties of deformed Mg sheets have been investigated. The recrystallization behaviour was analyzed in terms of the Johnson–Mehl–Avrami–Kolmogorov model via the variation of microhardness. The Avrami exponent of pure Mg sheet ranged from 1.02 to 1.16, and it was reduced by adding REs. The acceleration of recovery and retardation of recrystallization were detected by the presence of REs. Three point bending was carried out to assess damping properties. At the temperature of ∼150 °C, the damping peak corresponds to grain boundary relaxation, which was affected by grain size, basal texture and the variation of dislocation density on basal plane. At elevated temperatures, a non-thermal activated peak was mainly dependent upon annealing condition, where its height and temperature were increased by adding REs, assigning to be a recrystallization peak

  12. Investigation of superstructure damping identification for the HDR containment building

    International Nuclear Information System (INIS)

    Hsieh, B.J.; Kot, C.A.; Srinivasan, M.G.

    1985-01-01

    A method for the estimation of first mode structural damping, developed by other investigators, was applied to shaker test data of the HDR containment building. Due to inadequate precision in the experimental phase measurements no valid results could be obtained. Based on modal analysis it was also noted that for systems such as the HDR building, contributions of higher modes are not negligible as was assumed in the original approach. Therefore, the procedure for the determination of superstructure damping using experimental data was extended to include the effects of higher modes. The extended method does not lead to any higher order nonlinear equations than the first mode approximation and was found to be as simple to apply as the original approach

  13. Spatially Localized Particle Energization by Landau Damping in Current Sheets

    Science.gov (United States)

    Howes, G. G.; Klein, K. G.; McCubbin, A. J.

    2017-12-01

    Understanding the mechanisms of particle energization through the removal of energy from turbulent fluctuations in heliospheric plasmas is a grand challenge problem in heliophysics. Under the weakly collisional conditions typical of heliospheric plasma, kinetic mechanisms must be responsible for this energization, but the nature of those mechanisms remains elusive. In recent years, the spatial localization of plasma heating near current sheets in the solar wind and numerical simulations has gained much attention. Here we show, using the innovative and new field-particle correlation technique, that the spatially localized particle energization occurring in a nonlinear gyrokinetic simulation has the velocity space signature of Landau damping, suggesting that this well-known collisionless damping mechanism indeed actively leads to spatially localized heating in the vicinity of current sheets.

  14. Boundary controllability for a nonlinear beam equation

    Directory of Open Access Journals (Sweden)

    Xiao-Min Cao

    2015-09-01

    Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.

  15. Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

    Science.gov (United States)

    Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles

    2011-01-01

    Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

  16. Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

    Directory of Open Access Journals (Sweden)

    Chen Yuming

    2011-01-01

    Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

  17. Power Oscillation Damping Controller for Wind Power Plant Utilizing Wind Turbine Inertia as Energy Storage

    DEFF Research Database (Denmark)

    Knüppel, Thyge; Nielsen, Jørgen Nygård; Jensen, Kim Høj

    2011-01-01

    For a wind power plant (WPP) the upper limit for active power output is bounded by the instantaneous wind conditions and therefore a WPP must curtail its power output when system services with active power are delivered. Here, a power oscillation damping controller (POD) for WPPs is presented...... that utilizes the stored kinetic energy in the wind turbine (WT) mechanical system as energy storage from which damping power can be exchanged. This eliminates the need for curtailed active power production. Results are presented using modal analysis and induced torque coefficients (ITC) to depict the torques...... induced on the synchronous generators from the POD. These are supplemented with nonlinear time domain simulations with and without an auxiliary POD for the WPP. The work is based on a nonlinear, dynamic model of the 3.6 MW Siemens Wind Power wind turbine....

  18. Decoherence and Landau-Damping

    Energy Technology Data Exchange (ETDEWEB)

    Ng, K.Y.; /Fermilab

    2005-12-01

    The terminologies, decoherence and Landau damping, are often used concerning the damping of a collective instability. This article revisits the difference and relation between decoherence and Landau damping. A model is given to demonstrate how Landau damping affects the rate of damping coming from decoherence.

  19. Comparison of modal spectral and non-linear time history analysis of a piping system

    International Nuclear Information System (INIS)

    Gerard, R.; Aelbrecht, D.; Lafaille, J.P.

    1987-01-01

    A typical piping system of the discharge line of the chemical and volumetric control system, outside the containment, between the penetration and the heat exchanger, an operating power plant was analyzed using four different methods: Modal spectral analysis with 2% constant damping, modal spectral analysis using ASME Code Case N411 (PVRC damping), linear time history analysis, non-linear time history analysis. This paper presents an estimation of the conservatism of the linear methods compared to the non-linear analysis. (orig./HP)

  20. Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

    Science.gov (United States)

    Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh

    2018-02-01

    The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

  1. DYNAMICS OF VIBRATION FEEDERS WITH A NONLINEAR ELASTIC CHARACTERISTIC

    Directory of Open Access Journals (Sweden)

    V. I. Dyrda

    2017-04-01

    Full Text Available Purpose. Subject to the smooth and efficient operation of each production line, is the use of vehicles transporting high specification. It worked well in practice for transporting construction machines, which are used during the vibration. The use of vibration machines requires optimization of their operation modes. In the form of elastic link in them are increasingly using rubber-metallic elements, which are characterized by nonlinear damping properties. So it is necessary to search for new, more modern, methods of calculation of dynamic characteristics of the vibration machines on the properties of rubber as a cushioning material. Methodology. The dynamics of vibration machine that is as elastic rubber block units and buffer shock absorbers limiting the amplitude of the vibrations of the working body. The method of determining amplitude-frequency characteristics of the vibrating feeder is based on the principle of Voltaire, who in the calculations of the damping properties of the dampers will allow for elastic-hereditary properties of rubber. When adjusting the basic dynamic stiffness of the elastic ties and vibratory buffers, using the principle of heredity rubber properties, determine the dependence of the amplitude of the working body of the machine vibrations. This method is called integro-operator using the fractional-exponential kernels of relaxation. Findings. Using the derived formula for determining the amplitude of the resonance curve is constructed one-mass nonlinear system. It is established that the use of the proposed method of calculation will provide a sufficiently complete description of the damping parameters of rubber-metallic elements and at the same time be an effective means of calculating the amplitude-frequency characteristics of nonlinear vibration systems. Originality. The authors improved method of determining damping characteristics of rubber-metallic elements and the amplitude-frequency characteristics of nonlinear

  2. Overview on methods for formulating explicit damping matrices for non-classically damped structures

    International Nuclear Information System (INIS)

    Xu, J.

    1998-04-01

    In computing the dynamic response of a connected system with multiple components having dissimilar damping characteristics, which is often referred to as nonclassically damped system such as nuclear power plant piping systems supported by stiff structures, one needs to define the system-level damping based upon the damping information of components. This is frequently done in practice using approximate methods expressed as composite modal damping with weighting functions. However, when the difference in damping among components is substantial, the composite modal damping may become inappropriate in the characterization of the damping behavior of such systems. In recent years, several new methods have emerged with the expectation that they could produce more exact system-level damping for a group of nonclassically damped structures which are comprised of components that possess classical modal damping. In this paper, an overview is presented to examine these methods in the light of their theoretical basis, the technical merits, and practical applications. To this end, a synthesis method is described, which was shown to reduce to the other methods in the literature

  3. A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems

    Directory of Open Access Journals (Sweden)

    Antônio Marcos Gonçalves de Lima

    Full Text Available AbstractMany authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency- and temperature-dependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very costly, sometimes unfeasible. It is especially true when the viscoelastic materials are used to reduce vibrations of nonlinear systems. As a matter of fact, which the resolution of the resulting nonlinear equations of motion with frequency- and temperature-dependent viscoelastic damping forces is an interesting, but hard-to-solve problem. Those difficulties motivate the present study, in which a time-domain condensation strategy of viscoelastic systems is addressed, where the viscoelastic behavior is modeled by using a four parameter fractional derivative model. After the discussion of various theoretical aspects, the exact and reduced time responses are calculated for a three-layer sandwich plate by considering nonlinear boundary conditions.

  4. On the experimental prediction of the stability threshold speed caused by rotating damping

    Science.gov (United States)

    Vervisch, B.; Derammelaere, S.; Stockman, K.; De Baets, P.; Loccufier, M.

    2016-08-01

    An ever increasing demand for lighter rotating machinery and higher operating speeds results in a raised probability of instabilities. Rotating damping is one of the reasons, instability occurs. Rotating damping, or rotor internal damping, is the damping related to all rotating parts while non-rotating damping appearing in the non-rotating parts. The present study describes a rotating setup, designed to investigate rotating damping experimentally. An efficient experimental procedure is presented to predict the stability threshold of a rotating machine. The setup consists of a long thin shaft with a disk in the middle and clamped boundary conditions. The goal is to extract the system poles as a function of the rotating speed. The real parts of these poles are used to construct the decay rate plot, which is an indication for the stability. The efficiency of the experimental procedure relies on the model chosen for the rotating shaft. It is shown that the shaft behavior can be approximated by a single degree of freedom model that incorporates a speed dependent damping. As such low measurement effort and only one randomly chosen measurement location are needed to construct the decay rate plot. As an excitation, an automated impact hammer is used and the response is measured by eddy current probes. The proposed method yields a reliable prediction of the stability threshold speed which is validated through measurements.

  5. Unimodal optimal passive electromechanical damping of elastic structures

    International Nuclear Information System (INIS)

    Ben Mekki, O; Bourquin, F; Merliot, E; Maceri, F

    2013-01-01

    In this paper, a new electromechanical damper is presented and used, made of a pendulum oscillating around an alternator axis and connected by a gear to the vibrating structure. In this way, the mechanical energy of the oscillating mass can be transformed into electrical energy to be dissipated when the alternator is branched on a resistor. This damping device is intrinsically non-linear, and the problem of the optimal parameters and of the best placement of this damper on the structure is studied. The optimality criterion chosen here is the maximum exponential time decay rate (ETDR) of the structural response. This criterion leads to new design formulas. The case of a bridge under construction is considered and the analytical results are compared with experimental ones, obtained on a mock-up made of a vertical tower connected to a free-end horizontal beam, to simulate the behavior of a cable-stayed bridge during the erection phase. Up to three electromechanical dampers are placed in order to study the multi-modal damping. The satisfactory agreement between the theoretical model and the experiments suggests that a multi-modal passive damping of electromagnetic type could be effective on lightweight flexible structures, when dampers are suitably placed. (paper)

  6. MEMS linear and nonlinear statics and dynamics

    CERN Document Server

    Younis, Mohammad I

    2011-01-01

    MEMS Linear and Nonlinear Statics and Dynamics presents the necessary analytical and computational tools for MEMS designers to model and simulate most known MEMS devices, structures, and phenomena. This book also provides an in-depth analysis and treatment of the most common static and dynamic phenomena in MEMS that are encountered by engineers. Coverage also includes nonlinear modeling approaches to modeling various MEMS phenomena of a nonlinear nature, such as those due to electrostatic forces, squeeze-film damping, and large deflection of structures. The book also: Includes examples of nume

  7. Nonlinear theory of the collisional Rayleigh-Taylor instability in equatorial spread F

    International Nuclear Information System (INIS)

    Chaturvedi, P.K.; Ossakow, S.L.

    1977-01-01

    The nonlinear behavior of the collisional Rayleigh-Taylor instability is studied in equatorial Spread F by including a dominant two-dimensional nonlinearity. It is found that on account of this nonlinearity the instability saturates by generating damped higher spatial harmonics. The saturated power spectrum for the density fluctuations is discussed. A comparison between experimental observations and theory is presented

  8. A Study of the Nonlinear Landau Damping in the Fourier Transformed VelocitySpace

    Czech Academy of Sciences Publication Activity Database

    Sedláček, Zdeněk

    2002-01-01

    Roč. 34, 1-2 (2002), s. 63-87 ISSN 0041-1450 Institutional research plan: CEZ:AV0Z2043910 Keywords : Landau damping * Van Kampen-Case eigenmodes * BGK modes * free streaming Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.453, year: 2002

  9. A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

    Science.gov (United States)

    Brovont, Aaron D.

    The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

  10. Finite-dimensional attractor for a composite system of wave/plate equations with localized damping

    International Nuclear Information System (INIS)

    Bucci, Francesca; Toundykov, Daniel

    2010-01-01

    The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping

  11. Nonlinear Seismic Behavior of Different Boundary Conditions of Transmission Line Systems under Earthquake Loading

    Directory of Open Access Journals (Sweden)

    Li Tian

    2016-01-01

    Full Text Available Nonlinear seismic behaviors of different boundary conditions of transmission line system under earthquake loading are investigated in this paper. The transmission lines are modeled by cable element accounting for the nonlinearity of the cable. For the suspension type, three towers and two span lines with spring model (Model 1 and three towers and four span lines’ model (Model 2 are established, respectively. For the tension type, three towers and two span lines’ model (Model 3 and three towers and four span lines’ model (Model 4 are created, respectively. The frequencies of the transmission towers and transmission lines of the suspension type and tension type are calculated, respectively. The responses of the suspension type and tension type are investigated using nonlinear time history analysis method, respectively. The results show that the responses of the transmission tower and transmission line of the two models of the suspension type are slightly different. However, the responses of transmission tower and transmission line of the two models of the tension type are significantly different. Therefore, in order to obtain accurate results, a reasonable model should be considered. The results could provide a reference for the seismic analysis of the transmission tower-line system.

  12. Linear and nonlinear development of controlled disturbances in the supersonic boundary layer on a swept wing at Mach 2.5

    International Nuclear Information System (INIS)

    Kolosov, G L; Kosinov, A D

    2016-01-01

    Experimental data on the linear and nonlinear wave train development in 3D supersonic boundary layer over a 45° swept-wing at Mach number 2.5 are presented. Travelling artificial disturbances were introduced in the boundary layer by periodical glow discharge at frequencies 10 and 20 kHz. The spatial-temporal and spectral-wave characteristics of the wave train of unstable disturbances in the linear region are obtained. It is shown that the additional peaks in β '-spectra arise for both subharmonic and fundamental frequencies. The experiments indicate the presence of subharmonic resonance mechanism in 3D boundary layer at Mach number 2.5. (paper)

  13. Leading edge effect in laminar boundary layer excitation by sound

    International Nuclear Information System (INIS)

    Leehey, P.; Shapiro, P.

    1980-01-01

    Essentially plane pure tone sound waves were directed downstream over a heavily damped smooth flat plate installed in a low turbulence (0.04%) subsonic wind tunnel. Laminar boundary layer disturbance growth rates were measured with and without sound excitation and compared with numerical results from spatial stability theory. The data indicate that the sound field and Tollmien-Schlichting (T-S) waves coexist with comparable amplitudes when the latter are damped; moreover, the response is linear. Higher early growth rates occur for excitation by sound than by stream turbulence. Theoretical considerations indicate that the boundary layer is receptive to sound excitation primarily at the test plate leading edge. (orig.)

  14. TCSC robust damping controller design based on particle swarm optimization for a multi-machine power system

    Energy Technology Data Exchange (ETDEWEB)

    Shayeghi, H., E-mail: hshayeghi@gmail.co [Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil (Iran, Islamic Republic of); Shayanfar, H.A. [Center of Excellence for Power System Automation and Operation, Electrical Engineering Department, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Jalilzadeh, S.; Safari, A. [Technical Engineering Department, Zanjan University, Zanjan (Iran, Islamic Republic of)

    2010-10-15

    In this paper, a new approach based on the particle swarm optimization (PSO) technique is proposed to tune the parameters of the thyristor controlled series capacitor (TCSC) power oscillation damping controller. The design problem of the damping controller is converted to an optimization problem with the time-domain-based objective function which is solved by a PSO technique which has a strong ability to find the most optimistic results. To ensure the robustness of the proposed stabilizers, the design process takes a wide range of operating conditions into account. The performance of the newly designed controller is evaluated in a four-machine power system subjected to the different types of disturbances in comparison with the genetic algorithm based damping controller. The effectiveness of the proposed controller is demonstrated through the nonlinear time-domain simulation and some performance indices studies. The results analysis reveals that the tuned PSO based TCSC damping controller using the proposed fitness function has an excellent capability in damping power system inter-area oscillations and enhances greatly the dynamic stability of the power systems. Moreover, it is superior to the genetic algorithm based damping controller.

  15. Experimental Study on the Influence on Vibration Characteristics of Thin Cylindrical Shell with Hard Coating under Cantilever Boundary Condition

    Directory of Open Access Journals (Sweden)

    Hui Li

    2017-01-01

    Full Text Available This research has experimentally investigated the influence on vibration characteristics of thin cantilever cylindrical shell (TCS with hard coating under cantilever boundary condition. Firstly, the theoretical model of TCS with hard coating is established to calculate its natural frequencies and modal shapes so as to roughly understand vibration characteristic of TCS when it is coated with hard coating material. Then, by considering its nonlinear stiffness and damping influences, an experiment system is established to accurately measure vibration parameters of the shell, and the corresponding test methods and identification techniques are also proposed. Finally, based on the measured data, the influences on natural frequencies, modal shapes, damping ratios, and vibration responses of TCS with hard coating are analyzed and discussed in detail. It can be found that hard coating can play an important role in vibration reduction of TCS, and for the most modes of TCS, hard coating will result in the decrease of natural frequencies, but the decreased level is not very big, and its damping effects on the higher frequency range of the shell are weak and ineffective. Therefore, in order to make better use of this coating material, we must carefully choose the concerned antivibration frequency range of the shell; otherwise it may lead to some negative effects.

  16. Investigation of nonlinear 2D bottom transportation dynamics in coastal zone on optimal curvilinear boundary adaptive grids

    Directory of Open Access Journals (Sweden)

    Sukhinov Alexander

    2017-01-01

    Full Text Available One of the practically important tasks of hydrophysics for sea coastal systems is the problem of modeling and forecasting bottom sediment transportation. A number of problems connected to ship safety traffic, water medium condition near the coastal line etc. depends on forecasting bottom deposit transportation under natural and technogenic influences. Coastal systems are characterized by a complicated form of coastline - the presence of long, narrow and curvilinear peninsulas and bays. Water currents and waves near the beach are strongly depend on complicated coastal line and in turn, exert on the bottom sediment transportation near the shore. The use of rectangular grids in the construction of discrete models leads to significant errors in both the specification of boundary conditions and in the modeling of hydrophysical processes in the coastal zone. In this paper, we consider the construction of a finite-element approximation of the initial-boundary value problem for the spatially two-dimensional linearized equation of sediment transportation using optimal boundary-adaptive grid. First, the linearization of a spatially two-dimensional nonlinear parabolic equation on the time grid is performed-when the coefficients of the equation that are nonlinearly dependent on the bottom relief function are set on the previous time layer, and the corresponding initial conditions are used on the first time layer. The algorithm for constructing the grid is based on the procedure for minimizing the generalized Dirichlet functional. On the constructed grid, finite element approximation using bilinear basis functions is performed, which completes the construction of a discrete model for the given problem. The using of curvilinear boundary adaptive grids leads to decreasing of total grid number in 5-20 times and respectively the total modeling time and/or it allows to improve modeling accuracy.

  17. Optimizing parameter of particle damping based on Leidenfrost effect of particle flows

    Science.gov (United States)

    Lei, Xiaofei; Wu, Chengjun; Chen, Peng

    2018-05-01

    Particle damping (PD) has strongly nonlinearity. With sufficiently vigorous vibration conditions, it always plays excellent damping performance and the particles which are filled into cavity are on Leidenfrost state considered in particle flow theory. For investigating the interesting phenomenon, the damping effect of PD on this state is discussed by the developed numerical model which is established based on principle of gas and solid. Furtherly, the numerical model is reformed and applied to study the relationship of Leidenfrost velocity with characteristic parameters of PD such as particle density, diameter, mass packing ratio and diameter-length ratio. The results indicate that particle density and mass packing ratio can drastically improve the damping performance as opposed as particle diameter and diameter-length ratio, mass packing ratio and diameter-length ratio can low the excited intensity for Leidenfrost state. For discussing the application of the phenomenon in engineering, bound optimization by quadratic approximation (BOBYQA) method is employed to optimize mass packing ratio of PD for minimize maximum amplitude (MMA) and minimize total vibration level (MTVL). It is noted that the particle damping can drastically reduce the vibrating amplitude for MMA as Leidenfrost velocity equal to the vibrating velocity relative to maximum vibration amplitude. For MTVL, larger mass packing ratio is best option because particles at relatively wide frequency range is adjacent to Leidenfrost state.

  18. Modified computation of the nozzle damping coefficient in solid rocket motors

    Science.gov (United States)

    Liu, Peijin; Wang, Muxin; Yang, Wenjing; Gupta, Vikrant; Guan, Yu; Li, Larry K. B.

    2018-02-01

    In solid rocket motors, the bulk advection of acoustic energy out of the nozzle constitutes a significant source of damping and can thus influence the thermoacoustic stability of the system. In this paper, we propose and test a modified version of a historically accepted method of calculating the nozzle damping coefficient. Building on previous work, we separate the nozzle from the combustor, but compute the acoustic admittance at the nozzle entry using the linearized Euler equations (LEEs) rather than with short nozzle theory. We compute the combustor's acoustic modes also with the LEEs, taking the nozzle admittance as the boundary condition at the combustor exit while accounting for the mean flow field in the combustor using an analytical solution to Taylor-Culick flow. We then compute the nozzle damping coefficient via a balance of the unsteady energy flux through the nozzle. Compared with established methods, the proposed method offers competitive accuracy at reduced computational costs, helping to improve predictions of thermoacoustic instability in solid rocket motors.

  19. Nonlinear radiative heat transfer in magnetohydrodynamic (MHD stagnation point flow of nanofluid past a stretching sheet with convective boundary condition

    Directory of Open Access Journals (Sweden)

    Wubshet Ibrahim

    2015-12-01

    Full Text Available Two-dimensional boundary layer flow of nanofluid fluid past a stretching sheet is examined. The paper reveals the effect of non-linear radiative heat transfer on magnetohydrodynamic (MHD stagnation point flow past a stretching sheet with convective heating. Condition of zero normal flux of nanoparticles at the wall for the stretched flow is considered. The nanoparticle fractions on the boundary are considered to be passively controlled. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. Prandtl number Pr, velocity ratio parameter A, magnetic parameter M, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Moreover, the problem is governed by temperature ratio parameter (Nr=TfT∞ and radiation parameter Rd. Similarity transformation is used to reduce the governing non-linear boundary-value problems into coupled higher order non-linear ordinary differential equation. These equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results are obtained for velocity, temperature and concentration, as well as the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A increase. The local Nusselt number −θ′(0 decreases as the values of thermophoresis parameter Nt and radiation parameter Nr increase and it increases as the values of both Biot number Bi and Prandtl number Pr increase. Furthermore, radiation has a positive effect on temperature and concentration profiles.

  20. An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

    Science.gov (United States)

    Macías-Díaz, J. E.

    2018-06-01

    In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

  1. The damped wave equation with unbounded damping

    Science.gov (United States)

    Freitas, Pedro; Siegl, Petr; Tretter, Christiane

    2018-06-01

    We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of the semigroup generator and the associated quadratic operator function, the convergence of non-real eigenvalues in the asymptotic regime of diverging damping on a subdomain, and we investigate the appearance of essential spectrum on the negative real axis. We further show that the presence of the latter prevents exponential estimates for the semigroup and turns out to be a robust effect that cannot be easily canceled by adding a positive potential. These analytic results are illustrated by examples.

  2. A PSO based unified power flow controller for damping of power system oscillations

    Energy Technology Data Exchange (ETDEWEB)

    Shayeghi, H. [Technical Engineering Dept., Univ. of Mohaghegh Ardabili, Daneshgah Street, P.O. Box 179, Ardabil (Iran); Shayanfar, H.A. [Center of Excellence for Power Automation and Operation, Electrical Engineering Dept., Iran Univ. of Science and Technology, Tehran (Iran); Jalilzadeh, S.; Safari, A. [Technical Engineering Dept., Zanjan Univ., Zanjan (Iran)

    2009-10-15

    On the basis of the linearized Phillips-Herffron model of a single-machine power system, we approach the problem of select the best input control signal of the unified power flow controller (UPFC) and design optimal UPFC based damping controller in order to enhance the damping of the power system low frequency oscillations. The potential of the UPFC supplementary controllers to enhance the dynamic stability is evaluated. This controller is tuned to simultaneously shift the undamped electromechanical modes to a prescribed zone in the s-plane. The problem of robustly UPFC based damping controller is formulated as an optimization problem according to the eigenvalue-based multiobjective function comprising the damping factor, and the damping ratio of the undamped electromechanical modes to be solved using particle swarm optimization technique (PSO) that has a strong ability to find the most optimistic results. To ensure the robustness of the proposed damping controller, the design process takes into account a wide range of operating conditions and system configurations. The effectiveness of the proposed controller is demonstrated through eigenvalue analysis, nonlinear time-domain simulation and some performance indices studies. The results analysis reveals that the tuned PSO based UPFC controller using the proposed multiobjective function has an excellent capability in damping power system low frequency oscillations and enhance greatly the dynamic stability of the power systems. Moreover, the system performance analysis under different operating conditions show that the {delta}{sub E} based controller is superior to the m{sub B} based controller. (author)

  3. Study of a nonlinear system with shocks under broadband excitation. Application to a steam generator tube

    International Nuclear Information System (INIS)

    Thenint, Th.

    2011-01-01

    The steam generator is a heat exchanger and participates to the nuclear safety. Energy is transferred from the primary to the secondary fluid through many U-tubes maintained vertically by support plates. A sludge deposit tends to modify the boundary conditions and the secondary fluid flow. A fluid-elastic instability can then occur and lead to quick tube ruin. This thesis seeks a better understanding of the effect of contact nonlinearity on the dynamics of a tube in-air intermittently impacting the support plates and its consequences in regards with instability. The use of discretized contact conditions with circular obstacles distributed over the thickness of the plates and the use of enriched reduction bases allow quick and relevant nonlinear numerical simulations. These simulations are well correlated with experimental measurements and valid even with strong nonlinearity or negative modal damping. The evolution of power spectral densities (PSD) with growing excitation amplitude is analyzed: padding of the anti-resonances, peak shift and spread. It is then shown that an apparent stiffness associated with a permanent bilateral contact is pertinent to describe these transitions. In the case of an unstable linear system, one demonstrates that the nonlinearity keeps the responses bounded or stabilised, thus paving the way for future work with real or simulated fluid flows. (author)

  4. Landau Damping of Beam Instabilities by Electron Lenses

    Energy Technology Data Exchange (ETDEWEB)

    Shiltsev, V. [Fermilab; Alexahin, Yuri; Burov, A. [Fermilab; Valishev, A. [Fermilab

    2017-06-26

    Modern and future particle accelerators employ increasingly higher intensity and brighter beams of charged particles and become operationally limited by coherent beam instabilities. Usual methods to control the instabilities, such as octupole magnets, beam feedback dampers and use of chromatic effects, become less effective and insufficient. We show that, in contrast, Lorentz forces of a low-energy, a magnetically stabilized electron beam, or "electron lens", easily introduces transverse nonlinear focusing sufficient for Landau damping of transverse beam instabilities in accelerators. It is also important that, unlike other nonlinear elements, the electron lens provides the frequency spread mainly at the beam core, thus allowing much higher frequency spread without lifetime degradation. For the parameters of the Future Circular Collider, a single conventional electron lens a few meters long would provide stabilization superior to tens of thousands of superconducting octupole magnets.

  5. Fast relaxation transients in a kicked damped oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Urquizu, Merce [Laboratori d' Estudis Geofisics ' Eduard Fontsere' , IEC, Barcelona (Spain); Correig, Antoni M. [Departament d' Astronomical i Meteorologia, Laboratori d' Estudis Geofisics Eduard Fontsere, UB Marti Franques 1, E-08028 Barcelona (Spain) and Laboratori d' Estudis Geofisics ' Eduard Fontsere' , IEC, Barcelona (Spain)]. E-mail: ton.correig@am.ub.es

    2007-08-15

    Although nonlinear relaxation transients are very common in nature, very few studies are devoted to its characterization, mainly due to its short time duration. In this paper, we present a study about the nature of relaxation transients in a kicked damped oscillator, in which transients are generated in terms of continuous fast changes in the parameters of the system. We have found that transient dynamics can be described, rather than in terms of bifurcation dynamics, in terms of instantaneous stretching factors, which are related to the stability of fixed points of the corresponding stroboscopic maps.

  6. Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations

    International Nuclear Information System (INIS)

    Civalek, Ö.

    2014-01-01

    In the present study nonlinear static and dynamic responses of shallow spherical shells resting on Winkler–Pasternak elastic foundations are carried out. The formulation of the shells is based on the Donnell theory. The nonlinear governing equations of motion of shallow shells are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the Winkler and Pasternak foundation parameters on nonlinear static and dynamic response of shells are investigated. Some results are also presented for circular plate as special case. Damping effect on nonlinear dynamic response of shells is studied. It is important to state that the increase in damping parameter causes decrease in the dynamic response of the shells. It is shown that the shear parameter of the foundation has a significant influence on the dynamic and static response of the shells. Also, the response of the shell is decreased with the increasing value of the shear parameter of the foundation. Parametric studies considering different geometric variables have also been investigated. -- Highlights: • Nonlinear responses of shallow spherical shells are presented. • The effects of foundation parameters are investigated. • Damping effect on nonlinear dynamic response of shells is also studied

  7. Longitudinal vortices in a transitioning boundary layer

    International Nuclear Information System (INIS)

    Anders, J.B.; Backwelder, R.F.

    1980-01-01

    Naturally occurring spanwise variations of the streamwise velocity component, characteristic of longitudinal vortices embedded in a transitioning boundary layer were explored using hot-wire anemometers. A vibrating ribbon introduced stable or unstable Tollmien-Schlichting waves into the laminar boundary layer. These damped or growing disturbances always developed a strong three-dimensional pattern even though no spanwise perturbations were artificially induced. Changing the radius of the leading edge and other modifications to the flat plate, wind tunnel and boundary layer did not alter the spanwise wavelength of the vortices. (orig.)

  8. An evaluation of an operating BWR piping system damping during earthquake by applying auto regressive analysis

    International Nuclear Information System (INIS)

    Kitada, Y.; Makiguchi, M.; Komori, A.; Ichiki, T.

    1985-01-01

    The records of three earthquakes which had induced significant earthquake response to the piping system were obtained with the earthquake observation system. In the present paper, first, the eigenvalue analysis results for the natural piping system based on the piping support (boundary) conditions are described and second, the frequency and the damping factor evaluation results for each vibrational mode are described. In the present study, the Auto Regressive (AR) analysis method is used in the evaluation of natural frequencies and damping factors. The AR analysis applied here has a capability of direct evaluation of natural frequencies and damping factors from earthquake records observed on a piping system without any information on the input motions to the system. (orig./HP)

  9. Generalized viscothermoelasticity theory of dual-phase-lagging model for damping analysis in circular micro-plate resonators

    Science.gov (United States)

    Grover, D.; Seth, R. K.

    2018-05-01

    Analysis and numerical results are presented for the thermoelastic dissipation of a homogeneous isotropic, thermally conducting, Kelvin-Voigt type circular micro-plate based on Kirchhoff's Love plate theory utilizing generalized viscothermoelasticity theory of dual-phase-lagging model. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized dual-phase-lagging model and coupled viscothermoelastic plates. The scaled thermoelastic damping has been illustrated in case of circular plate and axisymmetric circular plate for fixed aspect ratio for clamped and simply supported boundary conditions. It is observed that the damping of vibrations significantly depend on time delay and mechanical relaxation times in addition to thermo-mechanical coupling in circular plate under resonance conditions and plate dimensions.

  10. Study on optimum aseismic design of complex structure system focusing on damping effect

    International Nuclear Information System (INIS)

    Takahashi, Yoshitaka; Suzuki, Kohei

    1995-01-01

    Optimum design technique for the purpose of aseismic design of complex plant structures such as piping and boiler structures is proposed. Particular attention is focused on the evaluation of the optimum damping and stiffness of the structures and components. Pseudo least square algorithm is introduced to determine the optimum design parameters. Under the requirement of certain allowable maximum response to a given earthquake excitation, optimum stiffness and damping values of the structure can be simultaneously calculated by this proposed method. The applicability of the method is demonstrated through three structural models; (1) linear multi-storied building model in which stiffness and damping constant of each floor are optimized; (2) nonlinear multi-storied building model having the isolated floor in which hysteretic energy absorber of the isolator is optimized; (3) combined boiler-supporting structure model connected by the inelastic seismic ties with each other is optimized. In this model, optimum values of damping characteristic of the seismic ties are evaluated. This work is particularly important for the aseismic design of complex plant structures like integrated boiler-supporting structure in thermal power plant and piping-containment vessel structure in nuclear power plant

  11. Fuel Assembly Damping Summary

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Kanghee; Kang, Heungseok; Oh, Dongseok; Yoon, Kyungho; Kim, Hyungkyu; Kim, Jaeyong [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2013-10-15

    This paper summary the fuel assembly damping data in air/in still water/under flow, released from foreign fuel vendors, compared our data with the published data. Some technical issues in fuel assembly damping measurement testing are also briefly discussed. Understanding of each fuel assembly damping mechanisms according to the surrounding medium and flow velocity can support the fuel design improvement in fuel assembly dynamics and structural integrity aspect. Because the upgraded requirements of the newly-developed advanced reactor system will demands to minimize fuel design margin in integrity evaluation, reduction in conservatism of fuel assembly damping can contribute to alleviate the fuel design margin for sure. Damping is an energy dissipation mechanism in a vibrating mechanical structure and prevents a resonant structure from having infinite vibration amplitudes. The sources of fuel assembly damping are various from support friction to flow contribution, and it can be increased by the viscosity or drag of surrounding fluid medium or the average velocity of water flowing. Fuel licensing requires fuel design evaluation in transient or accidental condition. Dynamic response analysis of fuel assembly is to show fuel integrity and requires information on assembly-wise damping in dry condition and under wet or water flowing condition. However, damping measurement test for the full-scale fuel assembly prototype is not easy to carry out because of the scale (fuel prototype, test facility), unsteadiness of test data (scattering, random sampling and processing), instrumentation under water flowing (water-proof response measurement), and noise. LWR fuel technology division in KAERI is preparing the infra structure for damping measurement test of full-scale fuel assembly, to support fuel industries and related research activities. Here is a preliminary summary of fuel assembly damping, published in the literature. Some technical issues in fuel assembly damping

  12. Multiple Positive Solutions of a Nonlinear Four-Point Singular Boundary Value Problem with a p-Laplacian Operator on Time Scales

    Directory of Open Access Journals (Sweden)

    Shihuang Hong

    2009-01-01

    Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.

  13. Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow

    International Nuclear Information System (INIS)

    Knoll, D.A.

    1998-01-01

    The authors study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. They use Newton's method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. They investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, mesh sequencing, and a pseudotransient continuation technique is used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with incomplete lower-upper (ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a mesh sequencing implementation provides significant CPU savings for fine grid calculations. Performance comparisons of modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented

  14. Regularity of the solutions to a nonlinear boundary problem with indefinite weight

    Directory of Open Access Journals (Sweden)

    Aomar Anane

    2011-01-01

    Full Text Available In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p−2}u in the bounded smooth domainOmega ⊂ R^N,with|∇u|^{p−2} partial_{nu} u = lambda V (x|u|^{p−2}u + h as a nonlinear boundary condition, where partial Omega is C^{2,beta}, with beta ∈]0, 1[, and V is a weight in L^s(partial Omega and h ∈ L^s(partial Omega for some s ≥ 1. We prove that all solutions are in L^{infty}(Omega cap L^{infty}(Omega, and using the D.Debenedetto’s theorem of regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega} for some alpha ∈ ]0, 1[.

  15. Boundary-value problems with free boundaries for elliptic systems of equations

    CERN Document Server

    Monakhov, V N

    1983-01-01

    This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.

  16. Chaotic saddles in nonlinear modulational interactions in a plasma

    International Nuclear Information System (INIS)

    Miranda, Rodrigo A.; Rempel, Erico L.; Chian, Abraham C.-L.

    2012-01-01

    A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.

  17. Chaotic saddles in nonlinear modulational interactions in a plasma

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)

    2012-11-15

    A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.

  18. Validity of Miles Equation in Predicting Propellant Slosh Damping in Baffled Tanks at Variable Slosh Amplitude

    Science.gov (United States)

    Yang, H. Q.; West, Jeff

    2018-01-01

    Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

  19. Nonlinear theory of surface-wave--particle interactions in a cylindrical plasma

    International Nuclear Information System (INIS)

    Dengra, A.; Palop, J.I.F.

    1994-01-01

    This work is an application of the specular reflection hypothesis to the study of the nonlinear surface-wave--particle interactions in a cylindrical plasma. The model is based on nonlinear resolution of the Vlasov equation by the method of characteristics. The expression obtained for the rate of increase of kinetic energy per electron has permitted us to investigate the temporal behavior of nonlinear collisionless damping for different situations as a function of the critical parameters

  20. The damped wave equation with unbounded damping

    Czech Academy of Sciences Publication Activity Database

    Freitas, P.; Siegl, Petr; Tretter, C.

    2018-01-01

    Roč. 264, č. 12 (2018), s. 7023-7054 ISSN 0022-0396 Institutional support: RVO:61389005 Keywords : damped wave equation * unbounded damping * essential spectrum * quadratic operator funciton with unbounded coefficients * Schrodinger operators with complex potentials Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016

  1. Evolution Of Nonlinear Waves in Compressing Plasma

    International Nuclear Information System (INIS)

    Schmit, P.F.; Dodin, I.Y.; Fisch, N.J.

    2011-01-01

    Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size Δ during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches Δ. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.

  2. Evolution Of Nonlinear Waves in Compressing Plasma

    Energy Technology Data Exchange (ETDEWEB)

    P.F. Schmit, I.Y. Dodin, and N.J. Fisch

    2011-05-27

    Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.

  3. Numerical studies of shear damped composite beams using a constrained damping layer

    DEFF Research Database (Denmark)

    Kristensen, R.F.; Nielsen, Kim Lau; Mikkelsen, Lars Pilgaard

    2008-01-01

    Composite beams containing one or more damping layers are studied numerically. The work is based on a semi-analytical model using a Timoshenko beam theory and a full 2D finite element model. The material system analysed, is inspired by a train wagon suspension system used in a EUREKA project Sigma......!1841. For the material system, the study shows that the effect of the damping layer is strongly influenced by the presence of a stiff constraining layer, that enforces large shear strain amplitudes. The thickness of the damping rubber layer itself has only a minor influence on the overall damping....... In addition, a large influence of ill positioned cuts in the damping layer is observed....

  4. Beam Stability and Nonlinear Dynamics. Proceedings

    International Nuclear Information System (INIS)

    Parsa, Z.

    1997-01-01

    These proceedings represent papers presented at the Beam Stability and Nonlinear Dynamics symposium held in Santa Barbara in December 1996. The symposium was sponsored by the National Science Foundation as part of the United States long term accelerator research. The focus of this symposium was on nonlinear dynamics and beam stability. The topics included single-particle and many-particle dynamics, and stability in large circular accelerators such as the Large Hadron Collider(LHC). Other subjects covered were spin dynamics, nonlinear aberration correction, collective effects in the LHC, sawtooth instability and Landau damping in the presence of strong nonlinearity. There were presentations concerning plasma physics including the effect of beam echo. There are 17 papers altogether in these proceedings and 8 of them have been abstracted for the Energy Science and Technology database

  5. Nonlinear wavenumber of an electron plasma wave

    International Nuclear Information System (INIS)

    Vidmar, P.J.; Malmberg, J.H.; Starke, T.P.

    1976-01-01

    The wavenumber of a large-amplitude electron plasma wave propagating on a collisionless plasma column is measured. The wavenumber is shifted from that of a small-amplitude wave of the same frequency. This nonlinear wavenumber shift, deltak/subr/, depends on position, frequency, and initial wave amplitude, Phi. The observed spatial oscillations of deltak/subr/ agree qualitatively with recent theories. Experimentally deltak/subr/proportionalk/subi/S (Phi) rootPhi where k/subi/ is the linear Landau damping coefficient, S (Phi) equivalentk/subi/(Phi)/k/subi/, and k/subi/(Phi) is the initial damping coefficient which depends on Phi

  6. problem for the damped Boussinesq equation

    Directory of Open Access Journals (Sweden)

    Vladimir V. Varlamov

    1997-01-01

    Full Text Available For the damped Boussinesq equation utt−2butxx=−αuxxxx+uxx+β(u2xx,x∈(0,π,t>0;α,b=const>0,β=const∈R1, the second initial-boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long-time asymptotics is obtained in the explicit form and the question of the blow up of the solution in a certain case is examined. The possibility of passing to the limit b→+0 in the constructed solution is investigated.

  7. Viscous damping of solitary waves in the mud banks of Kerala, West coast of India

    Digital Repository Service at National Institute of Oceanography (India)

    Shenoi, S.S.C.; Murty, C.S.

    Analysis of wave damping in mud bank region following the process of transfer of wave energy to the interior of fluid column through the boundary layer and the energy loss computations owing to viscous shear beneath the solitary wave over a smooth...

  8. Suppression of Instabilities Generated by an Anti-Damper with a Nonlinear Magnetic Element in IOTA

    Energy Technology Data Exchange (ETDEWEB)

    Stern, E. [Fermilab

    2018-04-01

    The Integrable Optics Test Accelerator (IOTA) storage ring is being constructed at Fermilab as a testbed for new accelerator concepts. One important series of experiments tests the use of a novel nonlinear magnetic insert to damp coherent instabilities. To test the damping power of the element, an instability of desired strength may be intentionally excited with an anti-damper. We report on simulations of beam stabilization using the Synergia modeling framework over ranges of driving and damping strengths.

  9. Pipe damping studies

    International Nuclear Information System (INIS)

    Ware, A.G.

    1986-01-01

    The Idaho National Engineering Laboratory (INEL) is conducting a research program to assist the United States Nuclear Regulatory Commission (USNRC) in determining best-estimate damping values for use in the dynamic analysis of nuclear power plant piping systems. This paper describes four tasks in the program that were undertaken in FY-86. In the first task, tests were conducted on a 5-in. INEL laboratory piping system and data were analyzed from a 6-in. laboratory system at the ANCO Engineers facility to investigate the parameters influencing damping in the seismic frequency range. Further tests were conducted on 3- and 5-in. INEL laboratory piping systems as the second task to determine damping values representative of vibrations in the 33 to 100 Hz range, typical of hydrodynamic transients. In the third task a statistical evaluation of the available damping data was conduted to determine probability distributions suitable for use in probabilistic risk assessments (PRAs), and the final task evaluated damping data at high strain levels

  10. Identifying the nonlinear mechanical behaviour of micro-speakers from their quasi-linear electrical response

    Science.gov (United States)

    Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith

    2017-05-01

    In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.

  11. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain

    Science.gov (United States)

    Ikehata, Ryo

    We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2Japon. 55 (2002) 33) plays an effective role.

  12. Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials

    Science.gov (United States)

    Shiroky, I. B.; Gendelman, O. V.

    2018-02-01

    We address the problem of transition front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of the front propagation, and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to the fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its velocity, as well as the frequency and the amplitude of the oscillatory tail. Numerical results are in good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load, the next-nearest-neighbor coupling and the on-site damping. When the damping is moderate, it is possible to consider the shock propagation in the damped chain as a perturbation of the undamped dynamics. This approach yields reasonable predictions. When the damping is high, the transition front enters a completely different asymptotic regime of a subsonic kink. The gradient nonlinearity generically turns negligible, and the propagating front converges to the regime described by a simple exact solution for a continuous model with linear coupling.

  13. Progress on low emittance tuning for the CLIC Damping Rings

    CERN Document Server

    Alabau-Gonzalvo, J; Papaphilippou, Y

    2014-01-01

    In the frame of the CLIC main Damping Ring a study on the sensitivity of the lattice to different sources of misalignment is presented. The minimum equilibrium emittance is simulated and analytically estimated under dipole and quadrupole rolls, and quadrupole and sextupole vertical offsets. The result of this study establishes alignment tolerances to preserve the vertical emittance below the design value (1 pmrad). Non-linear dynamics studies have been done to determine the dynamic aperture in the presence of misalignments.

  14. Transition from weak to strong measurements by nonlinear quantum feedback control

    International Nuclear Information System (INIS)

    Zhang Jing; Liu Yuxi; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

    2010-01-01

    We find that feedback control may induce 'pseudo'-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

  15. Propagation of flexural waves in inhomogeneous plates exhibiting hysteretic nonlinearity: Nonlinear acoustic black holes.

    Science.gov (United States)

    Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua

    2015-08-01

    Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.

  16. Enhanced nonlinear iterative techniques applied to a non-equilibrium plasma flow

    Energy Technology Data Exchange (ETDEWEB)

    Knoll, D.A.; McHugh, P.R. [Idaho National Engineering Lab., Idaho Falls, ID (United States)

    1996-12-31

    We study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially-ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales, and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton`s method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. We investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, one-way multigrid and a pseudo-transient continuation technique are used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with Incomplete Lower-Upper(ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a one-way multigrid implementation provides significant CPU savings for fine grid calculations. Performance comparisons of the modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented.

  17. Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities

    Directory of Open Access Journals (Sweden)

    Idris Addou

    2000-01-01

    Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.

  18. Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

    Science.gov (United States)

    Fang, Fei; Xia, Guanghui; Wang, Jianguo

    2018-02-01

    The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

  19. Power oscillation damping controller

    DEFF Research Database (Denmark)

    2012-01-01

    A power oscillation damping controller is provided for a power generation device such as a wind turbine device. The power oscillation damping controller receives an oscillation indicating signal indicative of a power oscillation in an electricity network and provides an oscillation damping control...

  20. Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

    Science.gov (United States)

    Yang, H. Q.; West, Jeff

    2016-01-01

    Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

  1. Soil-structure interaction including nonlinear soil

    OpenAIRE

    Gicev, Vlado

    2008-01-01

    There are two types of models of soil-structure system depending upon the rigidity of foundation: models with rigid and models with flexible foundation. Main features of the soil-structure interaction phenomenon: -wave scattering, -radiation damping, -reduction of the system frequencies. In this presentation, the influence of interaction on the development of nonlinear zones in the soil is studied.

  2. A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

    Science.gov (United States)

    Macías-Díaz, J. E.

    2017-12-01

    In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

  3. Sub-synchronous resonance damping using high penetration PV plant

    Science.gov (United States)

    Khayyatzadeh, M.; Kazemzadeh, R.

    2017-02-01

    The growing need to the clean and renewable energy has led to the fast development of transmission voltage-level photovoltaic (PV) plants all over the world. These large scale PV plants are going to be connected to power systems and one of the important subjects that should be investigated is the impact of these plants on the power system stability. Can large scale PV plants help to damp sub-synchronous resonance (SSR) and how? In this paper, this capability of a large scale PV plant is investigated. The IEEE Second Benchmark Model aggregated with a PV plant is utilized as the case study. A Wide Area Measurement System (WAMS) based conventional damping controller is designed and added to the main control loop of PV plant in order to damp the SSR and also investigation of the destructive effect of time delay in remote feedback signal. A new optimization algorithm called teaching-learning-based-optimization (TLBO) algorithm has been used for managing the optimization problems. Fast Furrier Transformer (FFT) analysis and also transient simulations of detailed nonlinear system are considered to investigate the performance of the controller. Robustness of the proposed system has been analyzed by facing the system with disturbances leading to significant changes in generator and power system operating point, fault duration time and PV plant generated power. All the simulations are carried out in MATLAB/SIMULINK environment.

  4. Coulomb Damping

    Science.gov (United States)

    Fay, Temple H.

    2012-01-01

    Viscous damping is commonly discussed in beginning differential equations and physics texts but dry friction or Coulomb friction is not despite dry friction being encountered in many physical applications. One reason for avoiding this topic is that the equations involve a jump discontinuity in the damping term. In this article, we adopt an energy…

  5. Magnetic Damping For Maglev

    Directory of Open Access Journals (Sweden)

    S. Zhu

    1998-01-01

    Full Text Available Magnetic damping is one of the important parameters that control the response and stability of maglev systems. An experimental study to measure magnetic damping directly is presented. A plate attached to a permanent magnet levitated on a rotating drum was tested to investigate the effect of various parameters, such as conductivity, gap, excitation frequency, and oscillation amplitude, on magnetic damping. The experimental technique is capable of measuring all of the magnetic damping coefficients, some of which cannot be measured indirectly.

  6. ENERGY DISSIPATION AND LANDAU DAMPING IN TWO- AND THREE-DIMENSIONAL PLASMA TURBULENCE

    Energy Technology Data Exchange (ETDEWEB)

    Li, Tak Chu; Howes, Gregory G. [Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242 (United States); Klein, Kristopher G. [Space Science Center, University of New Hampshire, Durham, NH 03824 (United States); TenBarge, Jason M. [IREAP, University of Maryland, College Park, MD 20742 (United States)

    2016-12-01

    Plasma turbulence is ubiquitous in space and astrophysical plasmas, playing an important role in plasma energization, but the physical mechanisms leading to dissipation of the turbulent energy remain to be definitively identified. Kinetic simulations in two dimensions (2D) have been extensively used to study the dissipation process. How the limitation to 2D affects energy dissipation remains unclear. This work provides a model of comparison between two- and three-dimensional (3D) plasma turbulence using gyrokinetic simulations; it also explores the dynamics of distribution functions during the dissipation process. It is found that both 2D and 3D nonlinear gyrokinetic simulations of a low-beta plasma generate electron velocity-space structures with the same characteristics as that of the linear Landau damping of Alfvén waves in a 3D linear simulation. The continual occurrence of the velocity-space structures throughout the turbulence simulations suggests that the action of Landau damping may be responsible for the turbulent energy transfer to electrons in both 2D and 3D, and makes possible the subsequent irreversible heating of the plasma through collisional smoothing of the velocity-space fluctuations. Although, in the 2D case where variation along the equilibrium magnetic field is absent, it may be expected that Landau damping is not possible, a common trigonometric factor appears in the 2D resonant denominator, leaving the resonance condition unchanged from the 3D case. The evolution of the 2D and 3D cases is qualitatively similar. However, quantitatively, the nonlinear energy cascade and subsequent dissipation is significantly slower in the 2D case.

  7. Passive acoustic radiation control for a vibrating panel with piezoelectric shunt damping circuit using particle swarm optimization algorithm

    International Nuclear Information System (INIS)

    Jeon, Jin Young

    2009-01-01

    This paper presents a new acoustic radiation optimization method for a vibrating panel-like structure with a passive piezoelectric shunt damping system in order to minimize well-radiating modes generated from the panel. The optimization method is based on an idea of using the p-version finite element method(p-version FEM), the boundary element method(BEM), and the particle swarm optimization algorithm(PSOA). Optimum embossment design for the vibrating panel using the PSOA is first investigated in order to minimize noise radiation over a frequency range of interest. The optimum embossment design works as a kind of stiffener so that well-radiating natural modes are shifted up with some degrees. The optimized panel, however, may still require additional damping for attenuating the peak acoustic amplitudes. A passive shunt damping system is thus employed to additionally damp the well-radiating modes from the optimized panel. To numerically evaluate the acoustic multiple-mode damping capability by a shunt damping system, the integrated p-version FEM/BEM for the panel with the shunt damping system is modeled and developed by MATLAB. Using the PSOA, the optimization technique for the optimal multiple-mode shunt damper is investigated in order to achieve the optimum damping performance for the well-radiating modes simultaneously. Also, the acoustic damping performance of the shunt damping circuit in the acoustic environment is demonstrated numerically and experimentally with respect to the realistically sized panel. The simulated result shows a good agreement with that of the experimental result

  8. Second-mode control in hypersonic boundary layers over assigned complex wall impedance

    Science.gov (United States)

    Sousa, Victor; Patel, Danish; Chapelier, Jean-Baptiste; Scalo, Carlo

    2017-11-01

    The durability and aerodynamic performance of hypersonic vehicles greatly relies on the ability to delay transition to turbulence. Passive aerodynamic flow control devices such as porous acoustic absorbers are a very attractive means to damp ultrasonic second-mode waves, which govern transition in hypersonic boundary layers under idealized flow conditions (smooth walls, slender geometries, small angles of attack). The talk will discuss numerical simulations modeling such absorbers via the time-domain impedance boundary condition (TD-IBC) approach by Scalo et al. in a hypersonic boundary layer flow over a 7-degree wedge at freestream Mach numbers M∞ = 7.3 and Reynolds numbers Rem = 1.46 .106 . A three-parameter impedance model tuned to the second-mode waves is tested first with varying resistance, R, and damping ratio, ζ, revealing complete mode attenuation for R workers at DLR-Göttingen.

  9. Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface

    International Nuclear Information System (INIS)

    Lasiecka, I.; Lebiedzik, C.

    2000-01-01

    We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω coupled with a thermoelastic plate equation defined on Γ 0 -a flat surface of the boundary Ω. Thus, the coupling between the wave and the plate takes place on the interface Γ 0 . The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the 'minimal amount' of dissipation necessary to obtain uniform decay rates for the energy of the overall system? Our main result states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary which is complementary to Γ 0 , suffices for the stabilization of the entire structure. This result is new with respect to the literature on several accounts: (i) thermoelasticity is accounted for in the plate model; (ii) the plate model does not account for any type of mechanical damping, including the structural damping most often considered in the literature; (iii) there is no mechanical damping placed on the interface Γ 0 ; (iv) the boundary damping is nonlinear without a prescribed growth rate at the origin; (v) the undamped portions of the boundary partial Ω are subject to Neumann (rather than Dirichlet) boundary conditions, which is a recognized difficulty in the context of stabilization of wave equations, due to the fact that the strong Lopatinski condition does not hold. The main mathematical challenge is to show how the thermal energy is propagated onto the hyperbolic component of the structure. This is achieved by using a recently developed sharp theory of boundary traces corresponding to wave and plate equations, along with the analytic

  10. boundary dissipation

    Directory of Open Access Journals (Sweden)

    Mehmet Camurdan

    1998-01-01

    are coupled by appropriate trace operators. This overall model differs from those previously studied in the literature in that the elastic chamber floor is here more realistically modeled by a hyperbolic Kirchoff equation, rather than by a parabolic Euler-Bernoulli equation with Kelvin-Voight structural damping, as in past literature. Thus, the hyperbolic/parabolic coupled system of past literature is replaced here by a hyperbolic/hyperbolic coupled model. The main result of this paper is a uniform stabilization of the coupled PDE system by a (physically appealing boundary dissipation.

  11. 4th International Conference on Structural Nonlinear Dynamics and Diagnosis

    CERN Document Server

    2018-01-01

    This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...

  12. Landau damping: the mechanics model and its ultimate entropy gain

    International Nuclear Information System (INIS)

    Hannay, J H; Kluge, Michel

    2011-01-01

    Classical mechanics has only been invoked to account for Landau damping in a rather half-hearted way, alongside plasma perturbation theory. In particular this invocation is essential for the study of the saturation, or post-linear (or 'nonlinear') regime of the damping initiated by Dawson and O'Neill. By embracing mechanics wholeheartedly here, with its attendant phase space, one can access results, old and new, cleanly and directly, and with one fewer numerical integration for the post-linear regime. By using a summation technique familiar in semiclassical quantum mechanics (Poisson summation), the one remaining numerical integration can be much improved in accuracy. Also accessible from mechanics is the ultimate entropy gain. Though zero for any finite time (in the absence of coarse graining), the entropy gain is ultimately non-zero (at infinite time the required coarse graining is zero). It is calculated analytically by using the appropriate asymptotics, hitherto not fully exploited.

  13. Wigglers and single-particle dynamics in the NLC damping rings

    International Nuclear Information System (INIS)

    Venturini, Marco; Wolski, Andrzej; Dragt, Alex

    2003-01-01

    Wiggler insertions are expected to occupy a significant portion of the lattice of the Next Linear Collider (NLC) Main Damping Rings (MDR) and have a noticeable impact on the single-particle beam dynamics. Starting from a realistic 3D representation of the magnetic fields we calculate the transfer maps for the wigglers, accounting for linear and nonlinear effects, and we study the beam dynamics with particular attention paid to the Dynamic Aperture(DA). A DA reduction is observed but appears to remain within acceptable limits

  14. Sublayer of Prandtl Boundary Layers

    Science.gov (United States)

    Grenier, Emmanuel; Nguyen, Toan T.

    2018-03-01

    The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit {ν \\to 0} . In Grenier (Commun Pure Appl Math 53(9):1067-1091, 2000), one of the authors proved that there exists no asymptotic expansion involving one of Prandtl's boundary layer, with thickness of order {√{ν}} , which describes the inviscid limit of Navier-Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order {ν^{3/4}} . In this paper, we point out how the stability of the classical Prandtl's layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in L^∞. That is, either the Prandtl's layer or the boundary sublayer is nonlinearly unstable in the sup norm.

  15. Combination tones along the basilar membrane in a 3D finite element model of the cochlea with acoustic boundary layer attenuation

    Science.gov (United States)

    Böhnke, Frank; Scheunemann, Christian; Semmelbauer, Sebastian

    2018-05-01

    The propagation of traveling waves along the basilar membrane is studied in a 3D finite element model of the cochlea using single and two-tone stimulation. The advantage over former approaches is the consideration of viscous-thermal boundary layer damping which makes the usual but physically unjustified assumption of Rayleigh damping obsolete. The energy loss by viscous boundary layer damping is 70 dB lower than the actually assumed power generation by outer hair cells. The space-time course with two-tone stimulation shows the traveling waves and the periodicity of the beat frequency f2 - f1.

  16. Mimicking the cochlear amplifier in a cantilever beam using nonlinear velocity feedback control

    International Nuclear Information System (INIS)

    Joyce, Bryan S; Tarazaga, Pablo A

    2014-01-01

    The mammalian cochlea exhibits a nonlinear amplification which allows mammals to detect a large range of sound pressure levels while maintaining high frequency sensitivity. This work seeks to mimic the cochlea’s nonlinear amplification in a mechanical system. A nonlinear, velocity-based feedback control law is applied to a cantilever beam with piezoelectric actuators. The control law reduces the linear viscous damping of the system while introducing a cubic damping term. The result is a system which is positioned close to a Hopf bifurcation. Modelling and experimental results show that the beam with this control law undergoes a one-third amplitude scaling near the resonance frequency and an amplitude-dependent bandwidth. Both behaviors are characteristic of data obtained from the mammalian cochlea. This work could provide insight on the biological cochlea while producing bio-inspired sensors with a large dynamic range and sharp frequency sensitivity. (papers)

  17. Mimicking the cochlear amplifier in a cantilever beam using nonlinear velocity feedback control

    Science.gov (United States)

    Joyce, Bryan S.; Tarazaga, Pablo A.

    2014-07-01

    The mammalian cochlea exhibits a nonlinear amplification which allows mammals to detect a large range of sound pressure levels while maintaining high frequency sensitivity. This work seeks to mimic the cochlea’s nonlinear amplification in a mechanical system. A nonlinear, velocity-based feedback control law is applied to a cantilever beam with piezoelectric actuators. The control law reduces the linear viscous damping of the system while introducing a cubic damping term. The result is a system which is positioned close to a Hopf bifurcation. Modelling and experimental results show that the beam with this control law undergoes a one-third amplitude scaling near the resonance frequency and an amplitude-dependent bandwidth. Both behaviors are characteristic of data obtained from the mammalian cochlea. This work could provide insight on the biological cochlea while producing bio-inspired sensors with a large dynamic range and sharp frequency sensitivity.

  18. Analysis and design of robust decentralized controllers for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Schoenwald, D.A.

    1993-07-01

    Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.

  19. Nonlinear analysis and analog simulation of a piezoelectric buckled beam with fractional derivative

    Science.gov (United States)

    Mokem Fokou, I. S.; Buckjohn, C. Nono Dueyou; Siewe Siewe, M.; Tchawoua, C.

    2017-08-01

    In this article, an analog circuit for implementing fractional-order derivative and a harmonic balance method for a vibration energy harvesting system under pure sinusoidal vibration source is proposed in order to predict the system response. The objective of this paper is to discuss the performance of the system with fractional derivative and nonlinear damping (μb). Bifurcation diagram, phase portrait and power spectral density (PSD) are provided to deeply characterize the dynamics of the system. These results are corroborated by the 0-1 test. The appearance of the chaotic vibrations reduces the instantaneous voltage. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim). The corresponding electronic circuit is designed, exhibiting periodic and chaotic behavior, in accord with numerical simulations. The impact of fractional derivative and nonlinear damping is presented with detail on the output voltage and power of the system. The agreement between numerical and analytical results justifies the efficiency of the analytical technique used. In addition, by combining the harmonic excitation with the random force, the stochastic resonance phenomenon occurs and improves the harvested energy. It emerges from these results that the order of fractional derivative μ and nonlinear damping μb play an important role in the response of the system.

  20. Nonlinear Modeling and Simulation of Thermal Effects in Microcantilever Resonators Dynamic

    International Nuclear Information System (INIS)

    Tadayon, M A; Sayyaadi, H; Jazar, G Nakhaie

    2006-01-01

    Thermal dependency of material characteristics in micro electromechanical systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulus temperature relation. Based on some reported theoretical and experimental results, we model the thermal phenomena and use two Lorentzian functions to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, by considering capacitor nonlinearity, have been used. The response of the system is developed by employing multiple time scales perturbation method on nondimensionalized form of equations. Frequency response, resonant frequency and peak amplitude are examined for variation of dynamic parameters involved

  1. A universal nonlinear relation among boundary states in closed string field theory

    International Nuclear Information System (INIS)

    Kishimoto, Isao; Matsuo, Yutaka; Watanabe, Eitoku

    2004-01-01

    We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis [hep-th/0306189] in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the α parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation. (author)

  2. Variational approaches to conservation laws for a nonlinear ...

    African Journals Online (AJOL)

    The conservation laws of a nonlinear evolution equation of time dependent variable coefficients of damping and dispersion is studied. The equation under consideration is not derivable from a variational principle which means that one cannot appeal to the Noether theorem to determine the conservation laws. We utilize the ...

  3. Non-linear vibrations induced by fluidelastic forces in tube bundles

    International Nuclear Information System (INIS)

    Langre, E. de; Hadj-Sadok, C.; Beaufils, B.

    1992-01-01

    We present in this paper computations of the response of a loosely supported tube to fluid elastic forces. Several models of forces are considered, including negative damping, coupling forces and Price and Paidoussis' model. Unidirectional and bidirectional motions are studied, special attention being paid to the evolution of dynamic parameters influencing wear and to the changes in the dynamic regimes. The influence of the coefficient of friction is also analysed. A corrective methodology is proposed for the use of the negative damping model in non-linear computations

  4. Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

    Science.gov (United States)

    Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.

    2015-04-01

    by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system's robustness to parasitic damping.

  5. Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities

    NARCIS (Netherlands)

    van Rooij, A.C.L.M.

    2017-01-01

    Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities

  6. Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

    International Nuclear Information System (INIS)

    Lai, S K; Chow, K W

    2012-01-01

    Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

  7. Landau Damping Revisited

    International Nuclear Information System (INIS)

    Rees, John; Chao, Alexander

    2008-01-01

    Landau damping, as the term is used in accelerator science, is a physical process in which an ensemble of harmonic oscillators--an accelerator beam, for example--that would otherwise be unstable is stabilized by a spread in the natural frequencies of the oscillators. This is a study of the most basic aspects of that process. It has two main goals: to gain a deeper insight into the mechanism of Landau damping and to find the coherent motion of the ensemble and thus the dependence of the total damping rate on the frequency spread

  8. Earthquake analysis with nonlinear soil-structure interaction and nonlinear supports of components

    International Nuclear Information System (INIS)

    Hansson, V.

    1990-01-01

    For the determination of the seismic response of a structure the soil-structure interaction in most cases is modelled by a mass-spring-damper-system. Normally design concepts for components and piping are based on linear calculations and stress limitations. A concept for a reactor building for the HTR 100 consisted of a relatively high structure compared with the dimensions of the foundation. The structure was comparatively deep embedded in the soil, so here the embedment influences significantly the soil-structure interaction. The assembly of reactor vessel, heat exchanger and circulators has a height of about 37 m. Supports are arranged at different levels. Due to temperature deformations of the vessel and of the support constructions small gaps at the supports may only be avoided by complicated constructions of the supports. Nonlinear analyses were performed for soil, building and component with all supports. The finite element analyses used time histories. In order to describe the radiation damping the hysteresis of the soil with 1 percent material damping was considered. Nonlinearities in the interface of soil and foundation and due to gaps and friction at the supports were taken into account. The stiffness of the support constructions influences reactions and accelerations to a high extent. Properly chosen stiffnesses of the support constructions lead to a behaviour similar to linear elastic behaviour. 13 figs

  9. Damping in LMFBR pipe systems

    International Nuclear Information System (INIS)

    Anderson, M.J.; Barta, D.A.; Lindquist, M.R.; Renkey, E.J.; Ryan, J.A.

    1983-06-01

    LMFBR pipe systems typically utilize a thicker insulation package than that used on water plant pipe systems. They are supported with special insulated pipe clamps. Mechanical snubbers are employed to resist seismic loads. Recent laboratory testing has indicated that these features provide significantly more damping than presently allowed by Regulatory Guide 1.61 for water plant pipe systems. This paper presents results of additional in-situ vibration tests conducted on FFTF pipe systems. Pipe damping values obtained at various excitation levels are presented. Effects of filtering data to provide damping values at discrete frequencies and the alternate use of a single equivalent modal damping value are discussed. These tests further confirm that damping in typical LMFBR pipe systems is larger than presently used in pipe design. Although some increase in damping occurred with increased excitation amplitude, the effect was not significant. Recommendations are made to use an increased damping value for both the OBE and DBE seismic events in design of LMFBR pipe systems

  10. Seismic Response and Evaluation of SDOF Self-Centering Friction Damping Braces Subjected to Several Earthquake Ground Motions

    Directory of Open Access Journals (Sweden)

    Jong Wan Hu

    2015-01-01

    Full Text Available This paper mainly deals with seismic response and performance for self-centering friction damping braces (SFDBs subjected to several maximum- or design-leveled earthquake ground motions. The self-centering friction damping brace members consist of core recentering components fabricated with superelastic shape memory alloy wires and energy dissipation devices achieved through shear friction mechanism. As compared to the conventional brace members for use in the steel concentrically braced frame structure, these self-centering friction damping brace members make the best use of their representative characteristics to minimize residual deformations and to withstand earthquake loads without member replacement. The configuration and response mechanism of self-centering friction damping brace systems are firstly described in this study, and then parametric investigations are conducted through nonlinear time-history analyses performed on numerical single degree-of-freedom spring models. After observing analysis results, adequate design methodologies that optimally account for recentering capability and energy dissipation according to their comparative parameters are intended to be suggested in order to take advantage of energy capacity and to minimize residual deformation simultaneously.

  11. PSS and TCSC damping controller coordinated design using PSO in multi-machine power system

    Energy Technology Data Exchange (ETDEWEB)

    Shayeghi, H., E-mail: hshayeghi@gmail.co [Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil (Iran, Islamic Republic of); Safari, A.; Shayanfar, H.A. [Center of Excellence for Power System Automation and Operation, Electrical Engineering Department, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)

    2010-12-15

    The paper develops a new design procedure for simultaneous coordinated designing of the thyristor controlled series capacitor (TCSC) damping controller and power system stabilizer (PSS) in multi-machine power system. The coordinated design problem of PSS and TCSC damping controllers over a wide range of loading conditions is converted to an optimization problem with the time domain-based objective function that is solved by a particle swarm optimization (PSO) technique which has a strong ability to find the most optimistic results. By minimizing the proposed fitness function in which oscillatory characteristics between areas are included and thus the interactions among the TCSC controller and PSS under transient conditions in the multi-machine power system are improved. To ensure the robustness of the proposed stabilizers, the design process takes a wide range of operating conditions into account. The effectiveness of the proposed controller is demonstrated through the nonlinear time-domain simulation and some performance indices studies. The results of these studies show that the proposed coordinated controllers have an excellent capability in damping power system inter-area oscillations and enhance greatly the dynamic stability of the power system. Moreover, it is superior to both the uncoordinated designed stabilizers of the PSS and the TCSC damping controller.

  12. Reflectivity of stimulated back scattering in a homogeneous-slab medium in the case of negligible pump-wave damping

    International Nuclear Information System (INIS)

    Cho, G.S.; Cho, B.H.

    1981-01-01

    As to the backscatter instability which is one of nonlinear three-wave resonant interactions, the reflectivity(r) in the case of homogeneous-slab medium is calculated, assuming all the three wavepackets negligible damping caused by medium. The expression has turned out such that r = tanh 2 KAsub(p)L, where K, Asub(p), and L are the constant coupling coefficient, the constant pump-wave amplitude, and the thickness of the medium engaged in the interaction each. When this result is interpreted in terms of the stimulated Brillouin back-scattering in a so-called underdense plasma in controlled fusion, we find the reflectivity twice as large as that by others in the limit of large pump-wave damping, and unfitting to former experiments in the independence on the incident laser-light intensity. We see the incompatibility rise chiefly from neglecting the damping of pump-wave in the plasma. In contrast to the former results by others in the limit of large pump-wave damping, our result might be regarded as that for cases of negligible pump-wave damping, in general stimulated back-scattering phenomena. (author)

  13. The Stiffness and Damping Characteristics of a Dual-Chamber Air Spring Device Applied to Motion Suppression of Marine Structures

    Directory of Open Access Journals (Sweden)

    Xiaohui Zeng

    2016-03-01

    Full Text Available Dual-chamber air springs are used as a key component for vibration isolation in some industrial applications. The working principle of the dual-chamber air spring device as applied to motion suppression of marine structures is similar to that of the traditional air spring, but they differ in their specific characteristics. The stiffness and damping of the dual-chamber air spring device determine the extent of motion suppression. In this article, we investigate the stiffness and damping characteristics of a dual-chamber air spring device applied to marine structure motion suppression using orthogonal analysis and an experimental method. We measure the effects of volume ratio, orifice ratio, excitation amplitude, and frequency on the stiffness and damping of the dual-chamber vibration absorber. Based on the experimental results, a higher-order non-linear regression method is obtained. We achieve a rapid calculation model for dual-chamber air spring stiffness and damping, which can provide guidance to project design.

  14. Transition to chaos in the damped and forced non-lnear oscillator

    International Nuclear Information System (INIS)

    Montenegro Joo, J.; Universidad Nacional Mayor de San Marcos, Lima

    2009-01-01

    A Virtual Lab to study the Transition to Chaos in second order non-linear differential equations has been developed and successfully applied to the search for chaotic behavior in the damped and forced non-linear oscillator. This simulation and visualization software evaluates the equation under investigation at up to one million time-steps, generating in real-time and on the screen, plots like amplitude of oscillation, phase diagram, amplitude oscillation peaks and an animation of an oscillator governed by the problem equation. In this way the investigator not only gets important behavior graphs but he or she also gets a physical visualization of the system under investigation. Visualizing an animation of the system under study is an enormous help because it is not always easy to interpret behavior graphs. (author).

  15. Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Sté phane; Said-Houari, Belkacem

    2013-01-01

    The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.

  16. Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Stéphane

    2013-01-15

    The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.

  17. Nonlinear dynamic analysis and state space representation of a manipulator under viscoelastic material conditions

    Directory of Open Access Journals (Sweden)

    Esfandiar, H.

    2013-05-01

    Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.

  18. Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation

    International Nuclear Information System (INIS)

    Vasileva, D.P.

    1993-01-01

    Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u t = Δ u σ+1 + u β are found in the case β = σ + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case β>σ + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs

  19. On Coulomb and Viscosity damped single-degree-of-freedom vibrating systems

    DEFF Research Database (Denmark)

    Jakobsen, J.; Sivebæk, Ion Marius

    2016-01-01

    influence. The amount of analyses of friction damped system is comparatively more limited. The periodic square wave is a frequently occurring type of friction in this type of analyses. This periodic square wave is often named Coulomb friction. It can be resolved in an infinite series of harmonic components...... with frequencies 1, 3, 5, … times the basic frequency of the square wave and with respective amplitudes: (4/π)∗(1, 1/3, 1/5... )∗Fμ(ωt). Fμ(ωt): the square wave amplitude. The governing equation for the sequence of a free vibration with Coulomb friction damping is nonlinear, but is linear within each ½ period....... A complete solution can therefore be made up compounding solutions from ½ periods by inserting end conditions from one ½ period as initial conditions for the following ½ period. – Only spring and Coulomb forces act together. As a Coulomb force is conceivable as an infinite series of harmonic components...

  20. Critical density for Landau damping in a two-electron-component plasma

    Energy Technology Data Exchange (ETDEWEB)

    Rupp, Constantin F.; López, Rodrigo A.; Araneda, Jaime A. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción (Chile)

    2015-10-15

    The asymptotic evolution of an initial perturbation in a collisionless two-electron-component plasma with different temperatures is studied numerically. The transition between linear and nonlinear damping regimes is determined by slowly varying the density of the secondary electron-component using high-resolution Vlasov-Poisson simulations. It is shown that, for fixed amplitude perturbations, this transition behaves as a critical phenomenon with time scales and field amplitudes exhibiting power-law dependencies on the threshold density, similar to the critical amplitude behavior in a single-component plasma.

  1. Nuclear piping system damping data studies

    International Nuclear Information System (INIS)

    Ware, A.G.; Arendts, J.G.

    1985-01-01

    A programm has been conducted at the Idaho National Engineering Laboratory to study structural damping data for nuclear piping systems and to evaluate if changes in allowable damping values for structural seismic analyses are justified. The existing pipe damping data base was examined, from which a conclusion was made that there were several sets of data to support higher allowable values. The parameters which most influence pipe damping were identified and an analytical investigation demonstrated that increased damping would reduce the required number of seismic supports. A series of tests on several laboratory piping systems was used to determine the effect of various parameters such as types of supports, amplitude of vibration, frequency, insulation, and pressure on damping. A multiple regression analysis was used to statistically assess the influence of the various parameters on damping, and an international pipe damping data bank has been formed. (orig.)

  2. Direct approach for solving nonlinear evolution and two-point

    Indian Academy of Sciences (India)

    Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

  3. Damping measurements in flowing water

    Science.gov (United States)

    Coutu, A.; Seeley, C.; Monette, C.; Nennemann, B.; Marmont, H.

    2012-11-01

    Fluid-structure interaction (FSI), in the form of mass loading and damping, governs the dynamic response of water turbines, such as Francis turbines. Water added mass and damping are both critical quantities in evaluating the dynamic response of the turbine component. Although the effect of fluid added mass is well documented, fluid damping, a critical quantity to limit vibration amplitudes during service, and therefore to help avoiding possible failure of the turbines, has received much less attention in the literature. This paper presents an experimental investigation of damping due to FSI. The experimental setup, designed to create dynamic characteristics similar to the ones of Francis turbine blades is discussed, together with the experimental protocol and examples of measurements obtained. The paper concludes with the calculated damping values and a discussion on the impact of the observed damping behaviour on the response of hydraulic turbine blades to FSI.

  4. Damping measurements in flowing water

    International Nuclear Information System (INIS)

    Coutu, A; Monette, C; Nennemann, B; Marmont, H; Seeley, C

    2012-01-01

    Fluid-structure interaction (FSI), in the form of mass loading and damping, governs the dynamic response of water turbines, such as Francis turbines. Water added mass and damping are both critical quantities in evaluating the dynamic response of the turbine component. Although the effect of fluid added mass is well documented, fluid damping, a critical quantity to limit vibration amplitudes during service, and therefore to help avoiding possible failure of the turbines, has received much less attention in the literature. This paper presents an experimental investigation of damping due to FSI. The experimental setup, designed to create dynamic characteristics similar to the ones of Francis turbine blades is discussed, together with the experimental protocol and examples of measurements obtained. The paper concludes with the calculated damping values and a discussion on the impact of the observed damping behaviour on the response of hydraulic turbine blades to FSI.

  5. Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

    Science.gov (United States)

    Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

    2016-01-01

    Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

  6. Developing an active artificial hair cell using nonlinear feedback control

    Science.gov (United States)

    Joyce, Bryan S.; Tarazaga, Pablo A.

    2015-09-01

    The hair cells in the mammalian cochlea convert sound-induced vibrations into electrical signals. These cells have inspired a variety of artificial hair cells (AHCs) to serve as biologically inspired sound, fluid flow, and acceleration sensors and could one day replace damaged hair cells in humans. Most of these AHCs rely on passive transduction of stimulus while it is known that the biological cochlea employs active processes to amplify sound-induced vibrations and improve sound detection. In this work, an active AHC mimics the active, nonlinear behavior of the cochlea. The AHC consists of a piezoelectric bimorph beam subjected to a base excitation. A feedback control law is used to reduce the linear damping of the beam and introduce a cubic damping term which gives the AHC the desired nonlinear behavior. Model and experimental results show the AHC amplifies the response due to small base accelerations, has a higher frequency sensitivity than the passive system, and exhibits a compressive nonlinearity like that of the mammalian cochlea. This bio-inspired accelerometer could lead to new sensors with lower thresholds of detection, improved frequency sensitivities, and wider dynamic ranges.

  7. Optimization of damping in the passive automotive suspension system with using two quarter-car models

    Science.gov (United States)

    Lozia, Z.; Zdanowicz, P.

    2016-09-01

    The paper presents the optimization of damping in the passive suspension system of a motor vehicle moving rectilinearly with a constant speed on a road with rough surface of random irregularities, described according to the ISO classification. Two quarter-car 2DoF models, linear and non-linear, were used; in the latter, nonlinearities of spring characteristics of the suspension system and pneumatic tyres, sliding friction in the suspension system, and wheel lift-off were taken into account. The smoothing properties of vehicle tyres were represented in both models. The calculations were carried out for three roads of different quality, with simulating four vehicle speeds. Statistical measures of vertical vehicle body vibrations and of changes in the vertical tyre/road contact force were used as the criteria of system optimization and model comparison. The design suspension displacement limit was also taken into account. The optimum suspension damping coefficient was determined and the impact of undesirable sliding friction in the suspension system on the calculation results was estimated. The results obtained make it possible to evaluate the impact of the structure and complexity of the model used on the results of the optimization.

  8. Nonlinear analysis on power reactor dynamics

    International Nuclear Information System (INIS)

    Konno, H.; Hayashi, K.

    1997-01-01

    We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)

  9. Nonlinear modeling of tuned liquid dampers (TLDs) in rotating wind turbine blades for damping edgewise vibrations

    DEFF Research Database (Denmark)

    Zhang, Zili; Nielsen, Søren R. K.; Basu, Biswajit

    2015-01-01

    Tuned liquid dampers (TLDs) utilize the sloshing motion of the fluid to suppress structural vibrations and become a natural candidate for damping vibrations in rotating wind turbine blades. The centrifugal acceleration at the tip of a wind turbine blade can reach a magnitude of 7–8g. This facilit......Tuned liquid dampers (TLDs) utilize the sloshing motion of the fluid to suppress structural vibrations and become a natural candidate for damping vibrations in rotating wind turbine blades. The centrifugal acceleration at the tip of a wind turbine blade can reach a magnitude of 7–8g...... free-surface elevation equally well, the one-mode model can still be utilized for the design of TLD. Parametric optimization of the TLD is carried out based on the one-mode model, and the optimized damper effectively improves the dynamic response of wind turbine blades....

  10. Transit-Time Damping, Landau Damping, and Perturbed Orbits

    Science.gov (United States)

    Simon, A.; Short, R. W.

    1997-11-01

    Transit-time damping(G.J. Morales and Y.C. Lee, Phys. Rev. Lett. 33), 1534 (1974).*^,*(P.A. Robinson, Phys. Fluids B 3), 545 (1991).** has traditionally been obtained by calculating the net energy gain of transiting electrons, of velocity v, to order E^2* in the amplitude of a localized electric field. This necessarily requires inclusion of the perturbed orbits in the equation of motion. A similar method has been used by others(D.R. Nicholson, Introduction to Plasma Theory) (Wiley, 1983).*^,*(E.M. Lifshitz and L.P. Pitaevskifi, Physical Kinetics) (Pergamon, 1981).** to obtain a ``physical'' picture of Landau damping in a nonlocalized field. The use of perturbed orbits seems odd since the original derivation of Landau (and that of Dawson) never went beyond a linear picture of the dynamics. We introduce a novel method that takes advantage of the time-reversal invariance of the Vlasov equation and requires only the unperturbed orbits to obtain the result. Obviously, there is much reduction in complexity. Application to finite slab geometry yields a simple expression for the damping rate. Equivalence to much more complicated results^2* is demonstrated. This method allows us to calculate damping in more complicated geometries and more complex electric fields, such as occur in SRS in filaments. See accompanying talk.(R.W. Short and A. Simon, this conference.) This work was supported by the U.S. DOE Office of Inertial Confinement Fusion under Co-op Agreement No. DE-FC03-92SF19460.

  11. Damping in Timber Structures

    OpenAIRE

    Labonnote, Nathalie

    2012-01-01

    Key point to development of environmentally friendly timber structures, appropriate to urban ways of living, is the development of high-rise timber buildings. Comfort properties are nowadays one of the main limitations to tall timber buildings, and an enhanced knowledge on damping phenomena is therefore required, as well as improved prediction models for damping. The aim of this work has consequently been to estimate various damping quantities in timber structures. In particular, models h...

  12. Vibration and Damping Analysis of Composite Fiber Reinforced Wind Blade with Viscoelastic Damping Control

    Directory of Open Access Journals (Sweden)

    Tai-Hong Cheng

    2015-01-01

    Full Text Available Composite materials are increasingly used in wind blade because of their superior mechanical properties such as high strength-to-weight and stiffness-to-weight ratio. This paper presents vibration and damping analysis of fiberreinforced composite wind turbine blade with viscoelastic damping treatment. The finite element method based on full layerwise displacement theory was employed to analyze the damping, natural frequency, and modal loss factor of composite shell structure. The lamination angle was considered in mathematical modeling. The curved geometry, transverse shear, and normal strains were exactly considered in present layerwise shell model, which can depict the zig-zag in-plane and out-of-plane displacements. The frequency response functions of curved composite shell structure and wind blade were calculated. The results show that the damping ratio of viscoelastic layer is found to be very sensitive to determination of magnitude of composite structures. The frequency response functions with variety of thickness of damping layer were investigated. Moreover, the natural frequency, modal loss factor, and mode shapes of composite fiber reinforced wind blade with viscoelastic damping control were calculated.

  13. Controller Design of Complex System Based on Nonlinear Strength

    Directory of Open Access Journals (Sweden)

    Rongjun Mu

    2015-01-01

    Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

  14. Seismic damping factors of small bore piping as influenced by insulation and support elements

    International Nuclear Information System (INIS)

    Severud, L.K.; Anderson, M.J.; Barta, D.A.

    1985-01-01

    Seismic damping tests of a prototypical Liquid Metal Fast Breeder Reactor (LMFBR) small bore piping system is described, and measured transient responses to pulse excitations are reported. The test specimen was representative of a typical LMFBR insulated small bore piping system, and it was supported from a rigid test frame by prototypic dead weight supports, mechanical snubbers, and pipe clamps. Various support configurations were tested to assess the response sensitivity to insulation and other nonlinear support characteristics. Damping factors increased significantly due to the insulation and use of mechanical snubbers. Factors much higher than the magnitudes currently allowed in design by the USNRC Regulatory Guide 1.61, were found. This verified the design values, and it also pointed out the possibility of undue conservatism and costly overdesign resulting from use of the present design values

  15. Seismic damping factors of small bore piping as influenced by insulation and support elements

    International Nuclear Information System (INIS)

    Severud, L.K.; Barta, D.A.

    1983-01-01

    Seismic damping tests of a prototypical Liquid Metal Fast Breeder Reactor (LMFBR) small bore piping system is described, and measured transient responses to pulse excitations are reported. The test specimen was representative of a typical LMFBR insulated small bore piping system, and it was supported from a rigid test frame by prototypic dead weight supports, mechanical snubbers, and pipe clamps. Various support configurations were tested to assess the response sensitivity to insulation and other nonlinear support characteristics. Damping factors increased significantly due to the insulation and use of mechanical snubbers. Factors much higher than the magnitudes currently allowed in design, by the USNRC Regulatory Guide 1.61, were found. This verified the design values but also pointed out the possibility of undue conservatism and costly overdesign resulting from use of the present design values

  16. Classically integrable boundary conditions for symmetric-space sigma models

    International Nuclear Information System (INIS)

    MacKay, N.J.; Young, C.A.S.

    2004-01-01

    We investigate boundary conditions for the non-linear sigma model on the compact symmetric space G/H. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions which correspond to involutions which commute with the involution defining H. Applied to SO(3)/SO(2), the non-linear sigma model on S 2 , these yield the great circles as boundary submanifolds. Applied to GxG/G, they reproduce known results for the principal chiral model

  17. Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

    OpenAIRE

    Choe, Hui-Chol; Kang, Yong-Suk

    2013-01-01

    We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...

  18. Determining the boundary of inclusions with known conductivities using a Levenberg–Marquardt algorithm by electrical resistance tomography

    International Nuclear Information System (INIS)

    Tan, Chao; Xu, Yaoyuan; Dong, Feng

    2011-01-01

    Electrical resistance tomography (ERT) is a non-intrusive technique to image the electrical conductivity distribution of a closed vessel by injecting exciting current into the vessel and measuring the boundary voltages induced. ERT image reconstruction is characterized as a severely nonlinear and ill-posed inverse problem with many unknowns. In recent years, a growing number of papers have been published which aim to determine the locations and shapes of inclusions by assuming that their conductivities are piecewise constant and isotropic. In this work, the boundary of inclusions is reconstructed by ERT with a boundary element method. The Jacobian matrix of the forward problem is first calculated with a direct linearization method based on the boundary element, and validated through comparison with that determined by the finite element method and analytical method. A boundary reconstruction algorithm is later presented based on the Levenberg–Marquardt (L-M) method. Several numerical simulations and static experiments were conducted to study the reconstruction quality, where much importance was given to the smoothness of boundaries in the reconstruction; thus, a restriction of the curve radius is introduced to adjust the damping parameter for the L-M algorithm. Analytical results on the stability and precision of the boundary reconstruction demonstrate that stable reconstruction can be achieved when the conductivity of the objects differs much from that of the background medium, and convex boundaries can also be precisely reconstructed. Contrarily, the reconstructions for inclusions with similar conductivities to the background medium are not stable. The situation of an incorrect initial estimation of the inclusions' number is numerically studied and the results show that the boundary of inclusions could be correctly reconstructed with a splitting/merging function under the aforementioned proper operation condition of the present algorithm

  19. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  20. Renormgroup symmetries in problems of nonlinear geometrical optics

    International Nuclear Information System (INIS)

    Kovalev, V.F.

    1996-01-01

    Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)

  1. Method of Obtaining High Resolution Intrinsic Wire Boom Damping Parameters for Multi-Body Dynamics Simulations

    Science.gov (United States)

    Yew, Alvin G.; Chai, Dean J.; Olney, David J.

    2010-01-01

    The goal of NASA's Magnetospheric MultiScale (MMS) mission is to understand magnetic reconnection with sensor measurements from four spinning satellites flown in a tight tetrahedron formation. Four of the six electric field sensors on each satellite are located at the end of 60- meter wire booms to increase measurement sensitivity in the spin plane and to minimize motion coupling from perturbations on the main body. A propulsion burn however, might induce boom oscillations that could impact science measurements if oscillations do not damp to values on the order of 0.1 degree in a timely fashion. Large damping time constants could also adversely affect flight dynamics and attitude control performance. In this paper, we will discuss the implementation of a high resolution method for calculating the boom's intrinsic damping, which was used in multi-body dynamics simulations. In summary, experimental data was obtained with a scaled-down boom, which was suspended as a pendulum in vacuum. Optical techniques were designed to accurately measure the natural decay of angular position and subsequently, data processing algorithms resulted in excellent spatial and temporal resolutions. This method was repeated in a parametric study for various lengths, root tensions and vacuum levels. For all data sets, regression models for damping were applied, including: nonlinear viscous, frequency-independent hysteretic, coulomb and some combination of them. Our data analysis and dynamics models have shown that the intrinsic damping for the baseline boom is insufficient, thereby forcing project management to explore mitigation strategies.

  2. The importance of non-linearities in modern proton synchrotrons

    International Nuclear Information System (INIS)

    Wilson, E.J.N.

    1977-01-01

    The paper outlines the physics and mathematics of non-linear field errors in the quide fields of accelerators, with particular reference to large accelerators such as the SPS. These non-linearities give rise to closed orbital distortions and non-linear resonances or stopbands. Both of these effects are briefly discussed and the use of resonances for slow beam extraction is also described. Another problem considered is that of chromaticity of the particle beam. The use of sextupoles to correct chromaticity and the Landau damping of beam instabilities using octupoles are also discussed. In the final section the application of Hamiltonian mechanics to non-linearities is demonstrated. The author concludes that the effect of non-linearities on particle dynamics may place a more severe limit on intensity and storage time in large rings than any other effect in transverse phase space. (B.D.)

  3. Frequency Response Analysis of Hydroelectric Power Plants with Influence From a Non-Linearized Frictional Damping and the Turbine Characteristics

    Directory of Open Access Journals (Sweden)

    H. Brekke

    1985-01-01

    Full Text Available The main purpose of the dissertation has been to establish a complete stability analysis of a hydroelectric power plant. The most important part in this study has been to establish a theory for the damping of oscillatory flow in tunnels and pipes. The influence of the turbine characteristics is also important and has been included by differentiation of the turbine equation. The partial derivative values can be found by means of the characteristic diagram of the turbine. Special attention is paid to establishing an empirical friction function for tunnels with rough walls. The author has based his theory on experimental tests carried out for damping of sea waves on rough beds, and the friction factor is a function of both frequency, amplitudes, cross section area and roughness of the wall (Jonsson 1978. Further, the damping of oscillations in shafts leading to tunnels taking into account the mean velocity in the tunnel has been established.

  4. Capacitor Current Feedback-Based Active Resonance Damping Strategies for Digitally-Controlled Inductive-Capacitive-Inductive-Filtered Grid-Connected Inverters

    DEFF Research Database (Denmark)

    Lorzadeh, Iman; Askarian Abyaneh, Hossein; Savaghebi, Mehdi

    2016-01-01

    Inductive-capacitive-inductive (LCL)-type line filters are widely used in grid-connected voltage source inverters (VSIs), since they can provide substantially improved attenuation of switching harmonics in currents injected into the grid with lower cost, weight and power losses than their L......-type counterparts. However, the inclusion of third order LCL network complicates the current control design regarding the system stability issues because of an inherent resonance peak which appears in the open-loop transfer function of the inverter control system near the control stability boundary. To avoid...... passive (resistive) resonance damping solutions, due to their additional power losses, active damping (AD) techniques are often applied with proper control algorithms in order to damp the LCL filter resonance and stabilize the system. Among these techniques, the capacitor current feedback (CCF) AD has...

  5. Boundary fluxes for nonlocal diffusion

    Science.gov (United States)

    Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi

    We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.

  6. Improved algorithm for solving nonlinear parabolized stability equations

    International Nuclear Information System (INIS)

    Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

    2016-01-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

  7. Process Damping Parameters

    International Nuclear Information System (INIS)

    Turner, Sam

    2011-01-01

    The phenomenon of process damping as a stabilising effect in milling has been encountered by machinists since milling and turning began. It is of great importance when milling aerospace alloys where maximum surface speed is limited by excessive tool wear and high speed stability lobes cannot be attained. Much of the established research into regenerative chatter and chatter avoidance has focussed on stability lobe theory with different analytical and time domain models developed to expand on the theory first developed by Trusty and Tobias. Process damping is a stabilising effect that occurs when the surface speed is low relative to the dominant natural frequency of the system and has been less successfully modelled and understood. Process damping is believed to be influenced by the interference of the relief face of the cutting tool with the waveform traced on the cut surface, with material properties and the relief geometry of the tool believed to be key factors governing performance. This study combines experimental trials with Finite Element (FE) simulation in an attempt to identify and understand the key factors influencing process damping performance in titanium milling. Rake angle, relief angle and chip thickness are the variables considered experimentally with the FE study looking at average radial and tangential forces and surface compressive stress. For the experimental study a technique is developed to identify the critical process damping wavelength as a means of measuring process damping performance. For the range of parameters studied, chip thickness is found to be the dominant factor with maximum stable parameters increased by a factor of 17 in the best case. Within the range studied, relief angle was found to have a lesser effect than expected whilst rake angle had an influence.

  8. A Marker Method for the Solution of the Damped Burgers' Equation

    International Nuclear Information System (INIS)

    Jerome L.V. Lewandowski

    2005-01-01

    A new method for the solution of the damped Burgers equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations

  9. Pressure Feedback in Fluid Power Systems--Active Damping Explained and Exemplified

    DEFF Research Database (Denmark)

    Pedersen, Henrik Clemmensen; Andersen, Torben O.

    2018-01-01

    Fluid power systems are inherently nonlinear and typically suffer from very poor damping. Despite these characteristics, it is not uncommon that traditional linear type controllers are applied. This typically results in conservative adjustment of the controllers, or when more advanced controllers...... a given system, and how to adjust the parameters of the pressure feedback to obtain the best results. This is done for both a traditional symmetric cylinder servo system and a system with a differential cylinder using both pressure and nonpressure compensated proportional valves. Based on the presented...

  10. Experimental verification of a bridge-shaped, nonlinear vibration energy harvester

    Energy Technology Data Exchange (ETDEWEB)

    Gafforelli, Giacomo, E-mail: giacomo.gafforelli@polimi.it; Corigliano, Alberto [Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, 20133 (Italy); Xu, Ruize; Kim, Sang-Gook [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

    2014-11-17

    This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.

  11. Anisotropic damping of Timoshenko beam elements

    Energy Technology Data Exchange (ETDEWEB)

    Hansen, M.H.

    2001-05-01

    This report contains a description of a structural damping model for Timoshenko beam elements used in the aeroelastic code HawC developed at Risoe for modeling wind turbines. The model has been developed to enable modeling of turbine blades which often have different damping characteristics for flapwise, edgewise and torsional vibrations. The structural damping forces acting on the beam element are modeled by viscous damping described by an element damping matrix. The composition of this matrix is based on the element mass and stiffness matrices. It is shown how the coefficients for the mass and stiffness contributions can be calibrated to give the desired modal damping in the complete model of a blade. (au)

  12. Comparative Research on Characteristics of the Isolation Systems with Dry Friction Damping and with Vicious Damping under Base Excitation

    Science.gov (United States)

    Hou, Junfang; jing, Min; Zhang, Weihua; Lu, Yahui; He, Haiwen

    2017-12-01

    As for the isolation problem of electronic equipments on vehicle, the vibration response characteristics of dry friction damping isolation system under base displacement excitation was analyzed in theory by harmonic balance method, and the displacement response was compared between the isolation systems with dry friction damping and vicious damping separately. The results show that the isolation system with small dry friction damping can’t meet the demands of displacement reduction close to the natural frequency, and it can realize full-frequency vibration isolation by improving dry friction damping when the lock frequency passes beyond the resonance frequency band. The results imply that the damping mechanism of dry friction isolator can’t be described only by dry friction damping, and the composite damping with dry friction and vicious damping is more appropriate.

  13. Simulation of the injection damping and resonance correction systems for the HEB of the SSC

    Energy Technology Data Exchange (ETDEWEB)

    Li, M.; Zhang, P.; Machida, S.

    1993-02-01

    An injection damping and resonance correction system for the High Energy Booster (HEB) of the Superconducting Super Collider (SSC) was investigated by means of multiparticle tracking. For an injection damping study, the code Simpsons is modified to utilize two Beam Position Monitors (BPM) and two dampers. ne particles of 200 Gev/c, numbered 1024 or more, with Gaussian distribution in 6-D phase space are injected into the HEB with certain injection offsets. The whole bunch of particles is then kicked in proportion to the BPM signals with some upper limit. Tracking these particles up to several hundred turn while the damping system is acting shows the turn-by-turn emittance growth, which is caused by the tune spread due to nonlinearity of the lattice and residual chromaticity with synchrotron oscillations. For a resonance correction study, the operating tune is scanned as a function of time so that a bunch goes through a resonance. The performance of the resonance correction system is demonstrated. We optimize the system parameters which satisfy the emittance budget of the HEB, taking into account the realistic hardware requirement.

  14. Simulation of the injection damping and resonance correction systems for the HEB of the SSC

    Energy Technology Data Exchange (ETDEWEB)

    Li, M.; Zhang, P.; Machida, S. (Superconducting Super Collider Laboratory, Dallas, Texas 75237 (United States))

    1993-12-25

    An injection damping and resonance correction system for the High Energy Booster (HEB) of the Superconducting Super Collider (SSC) was investigated by means of multiparticle tracking. For an injection damping study, the code Simpsons is modified to utilize two Beam Position Monitors (BPM) and two dampers. The particles of 200 Gev/c, numbered 1024 or more, with Gaussian distribution in 6-D phase space are injected into the HEB with certain injection offsets. The whole bunch of particles is then kicked in proportion to the BPM signals with some upper limit. Tracking these particles up to several hundred turns while the damping system is acting shows the turn-by-turn emittance growth, which is caused by the tune spread due to nonlinearity of the lattice and residual chromaticity with synchrotron oscillations. For a resonance correction study, the operating tune is scanned as a function of time so that a bunch goes through a resonance. The performance of the resonance correction system is demonstrated. We optimize the system parameters which satisfy the emittance budget of the HEB, taking into account the realistic hardware requirement.

  15. Dampness in buildings and health. Building characteristics as predictors for dampness in 8681 Swedish dwellings

    DEFF Research Database (Denmark)

    Hagerhed, L.; Bornehag, Carl-Gustaf; Sundell, Jan

    2002-01-01

    Questionnaire data on 8681 dwellings included in the Swedish study "Dampness in Buildings and Health" have been analysed for associations between dampness indicators, perceptions of indoor air quality and building characteristics such as time of construction, type of ventilation and type of found......Questionnaire data on 8681 dwellings included in the Swedish study "Dampness in Buildings and Health" have been analysed for associations between dampness indicators, perceptions of indoor air quality and building characteristics such as time of construction, type of ventilation and type...... of "Dry air" in 17.3 and 33.7% respectively. Older buildings and the use of natural ventilation were associated with increased frequency of dampness indicators as well as to increased frequencies of complaints on bad indoor air quality....

  16. Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

    Science.gov (United States)

    Markou, A. A.; Manolis, G. D.

    2018-03-01

    Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

  17. Global dynamics and control of a comprehensive nonlinear beam equation

    International Nuclear Information System (INIS)

    You Yuncheng; Taboada, M.

    1994-01-01

    A nonlinear hinged extensible elastic beam equation with the structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures. It is proved that there exists an absorbing set in the energy space and that there exist inertial manifolds whose exponential attracting rates however are nonuniform. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite-dimensional feedback control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to uncertainty in the structural parameters. (author). 5 refs

  18. Elliptical Leaf Spring Shock and Vibration Mounts with Enhanced Damping and Energy Dissipation Capabilities Using Lead Spring

    Directory of Open Access Journals (Sweden)

    Moussa Leblouba

    2015-01-01

    Full Text Available We present an enhancement to the existing elliptical leaf spring (ELS for improved damping and energy dissipation capabilities. The ELS consists of a high tensile stainless steel elliptical leaf spring with polymer or rubber compound. This device is conceived as a shock and vibration isolator for equipment and lightweight structures. The enhancement to the ELS consists of a lead spring plugged vertically between the leaves (referred to as lead-rubber elliptical leaf spring (LRELS. The lead is shown to produce hysteretic damping under plastic deformations. The LRELS isolator is shown to exhibit nonlinear hysteretic behavior. In both horizontal directions, the LRELS showed symmetrical rate independent behavior but undergoes stiffening behavior under large displacements. However, in the vertical direction, the LRELS behavior is asymmetric, exhibiting softening behavior in compression and stiffening behavior in tension. Mathematical models based on the Bouc-Wen model, describing the hysteretic behavior of the proposed isolator, are developed and numerically calibrated using a series of finite element analyses. The LRELS is found to be effective in the in-plane and vertical directions. The improved damping and energy dissipation of the LRELS is provided from the hysteretic damping of the lead spring.

  19. Towards a Reactive Power Oscillation Damping Controller for Wind Power Plant Based on Full Converter Wind Turbines

    DEFF Research Database (Denmark)

    Knüppel, Thyge; Kumar, Sathess; Thuring, Patrik

    2012-01-01

    In this paper a power oscillation damping controller (POD) based on modulation of reactive power (Q POD) is analyzed where the modular and distributed characteristics of the wind power plant (WPP) are considered. For a Q POD it is essential that the phase of the modulated output is tightly...... contributes to a collective response. This ability is shown with a 150 wind turbine (WT) WPP with all WTs represented, and it is demonstrated that the WPP contributes to the inter-area damping. The work is based on a nonlinear, dynamic model of the 3.6 MW Siemens Wind Power WT....... controlled to achieve a positive damping contribution. It is investigated how a park level voltage, reactive power, and power factor control at different grid strengths interact with the Q POD in terms of a resulting phase shift. A WPP is modular and distributed and a WPP Q POD necessitate that each WT...

  20. Dynamic relaxation method for nonlinear buckling analysis of moderately thick FG cylindrical panels with various boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Golmakani, M. E.; Far, M. N. Sadraee; Moravej, M. [Dept. of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad (Iran, Islamic Republic of)

    2016-12-15

    Using new approach proposed by Dynamic relaxation (DR) method, buckling analysis of moderately thick Functionally graded (FG) cylindrical panels subjected to axial compression is investigated for various boundary conditions. The mechanical properties of FG panel are assumed to vary continuously along the thickness direction by the simple rule of mixture and Mori-Tanaka model. The incremental form of nonlinear formulations are derived based on First-order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the incremental form of equilibrium equations. The critical mechanical buckling load is determined based on compressive load-displacement curve by adding the incremental displacements in each load step to the displacements obtained from the previous ones. A detailed parametric study is carried out to investigate the influences of the boundary conditions, rule of mixture, grading index, radius-to-thickness ratio, length-to-radius ratio and panel angle on the mechanical buckling load. The results reveal that with increase of grading index the effect of radius-to-thickness ratio on the buckling load decreases. It is also observed that effect of distribution rules on the buckling load is dependent to the type of boundary conditions.

  1. Helmholtz bright and boundary solitons

    International Nuclear Information System (INIS)

    Christian, J M; McDonald, G S; Chamorro-Posada, P

    2007-01-01

    We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts

  2. Approximation of the modal damping coefficients equivalent to material damping by harmonic excitation with ASKA

    International Nuclear Information System (INIS)

    Edme, R.

    1983-01-01

    If a dynamic response analysis (harmonic excitation) is carried out with the modal method, the modal damping coefficients must be approximated to match the structural damping. The program ASKA-Damping, which also supplies an error assessment of the approximation, was developed for this purpose. The modal method and the direct method are applied to a test example and their results compared. It is suggested that the ASKA manufacturers extend the spectral earthquake response analysis to take these modal damping coefficients into account so that the results become less conservative. (orig.) [de

  3. The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

    Energy Technology Data Exchange (ETDEWEB)

    Smith, Scott A [Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Catalfamo, Simone [Univ. of Stuttgart (Germany); Brake, Matthew R. W. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rice Univ., Houston, TX (United States); Schwingshackl, Christoph W. [Imperial College, London (United Kingdom); Reusb, Pascal [Daimler AG, Stuttgart (Germany)

    2017-01-01

    In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratio variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.

  4. Boundary stabilization of memory-type thermoelasticity with second sound

    Science.gov (United States)

    Mustafa, Muhammad I.

    2012-08-01

    In this paper, we consider an n-dimensional thermoelastic system of second sound with a viscoelastic damping localized on a part of the boundary. We establish an explicit and general decay rate result that allows a wider class of relaxation functions and generalizes previous results existing in the literature.

  5. Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

    International Nuclear Information System (INIS)

    Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo; Martinet, Philippe

    2008-01-01

    Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot

  6. Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

    Energy Technology Data Exchange (ETDEWEB)

    Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo [Sungkyunkwan University, Suwon (Korea, Republic of); Martinet, Philippe [Blaise Pascal University, Clermont-Ferrand Cedex (France)

    2008-07-15

    Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot

  7. Recent topics in nonlinear PDE

    International Nuclear Information System (INIS)

    Mimura, Masayasu; Nishida, Takaaki

    1984-01-01

    The meeting on the subject of nonlinear partial differential equations was held at Hiroshima University in February, 1983. Leading and active mathematicians were invited to talk on their current research interests in nonlinear pdes occuring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. This volume contains the theory of nonlinear pdes and the related topics which have been recently developed in Japan. (Auth.)

  8. Group invariance in engineering boundary value problems

    CERN Document Server

    Seshadri, R

    1985-01-01

    REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Inte...

  9. Spread F bubbles - Nonlinear Rayleigh-Taylor mode in two dimensions

    Science.gov (United States)

    Hudson, M. K.

    1978-01-01

    The paper discusses long-wavelength developed bottomside spread F which has been attributed to the Rayleigh-Taylor instability. The nonlinear saturation amplitude and the k spectrum of the inertia-dominated Rayleigh-Taylor instability is found in two directions: east-west and vertical. As in the collisional case (Chaturvedi and Ossakow, 1977), the dominant nonlinearity is found to be two-dimensional. It is found that the linearly most unstable modes, which are primarily horizontal, saturate by the nonlinear generation of vertical spatial harmonics. The harmonics are damped by diffusion or recombination. The resulting amplitude spectrum indicates that bubbles are vertically elongated in both inertial and collisional regimes.

  10. Decreasing the LHC impedance with a nonlinear collimation system

    CERN Document Server

    Resta-López, J; Zimmermann, F

    2007-01-01

    A two-stage nonlinear collimation system based on a pair of skew sextupoles is presented for the LHC.We show the details of the optics design and study the halo cleaning efficiency of such a system. This nonlinear collimation system would allow opening up collimator gaps, and thereby reduce the collimator impedance, which presently limits the LHC beam intensity. Assuming the nominal LHC beam at 7 TeV, the transverse coherent tune shifts of rigid-dipole coupled-bunch modes are computed for both the baseline linear collimation system and the proposed nonlinear one. In either case, the tune shifts of the most unstable modes are compared with the stability diagrams for Landau damping.

  11. Modeling and Analysis of Static and Dynamic Characteristics of Nonlinear Seat Suspension for Off-Road Vehicles

    Directory of Open Access Journals (Sweden)

    Zhenhua Yan

    2015-01-01

    Full Text Available Low-frequency vibrations (0.5–5 Hz that harm drivers occur in off-road vehicles. Thus, researchers have focused on finding methods to effectively isolate or control low-frequency vibrations. A novel nonlinear seat suspension structure for off-road vehicles is designed, whose static characteristics and seat-human system dynamic response are modeled and analyzed, and experiments are conducted to verify the theoretical solutions. Results show that the stiffness of this nonlinear seat suspension could achieve real zero stiffness through well-matched parameters, and precompression of the main spring could change the nonlinear seat suspension performance when a driver’s weight changes. The displacement transmissibility curve corresponds with the static characteristic curve of nonlinear suspension, where the middle part of the static characteristic curve is gentler and the resonance frequency of the displacement transmissibility curve and the isolation minimum frequency are lower. Damping should correspond with static characteristics, in which the corresponding suspension damping value should be smaller given a flatter static characteristic curve to prevent vibration isolation performance reduction.

  12. Grain size effects on stability of nonlinear vibration with nanocrystalline NiTi shape memory alloy

    Science.gov (United States)

    Xia, Minglu; Sun, Qingping

    2017-10-01

    Grain size effects on stability of thermomechanical responses for a nonlinear torsional vibration system with nanocrystalline superelastic NiTi bar are investigated in the frequency and amplitude domains. NiTi bars with average grain size from 10 nm to 100 nm are fabricated through cold-rolling and subsequent annealing. Thermomechanical responses of the NiTi bar as a softening nonlinear damping spring in the torsional vibration system are obtained by synchronised acquisition of rotational angle and temperature under external sinusoidal excitation. It is shown that nonlinearity and damping capacity of the NiTi bar decrease as average grain size of the material is reduced below 100 nm. Therefore jump phenomena of thermomechanical responses become less significant or even vanish and the vibration system becomes more stable. The work in this paper provides a solid experimental base for manipulating the undesired jump phenomena of thermomechanical responses and stabilising the mechanical vibration system through grain refinement of NiTi SMA.

  13. Nonlinear modeling of a rotational MR damper via an enhanced Bouc–Wen model

    International Nuclear Information System (INIS)

    Miah, Mohammad S; Chatzi, Eleni N; Dertimanis, Vasilis K; Weber, Felix

    2015-01-01

    The coupling of magnetorheological (MR) dampers with semi-active control schemes has proven to be an effective and failsafe approach for vibration mitigation of low-damped structures. However, due to the nonlinearities inherently relating to such damping devices, the characterization of the associated nonlinear phenomena is still a challenging task. Herein, an enhanced phenomenological modeling approach is proposed for the description of a rotational-type MR damper, which comprises a modified Bouc–Wen model coupled with an appropriately selected sigmoid function. In a first step, parameter optimization is performed on the basis of individual models in an effort to approximate the experimentally observed response for varying current levels and actuator force characteristics. In a second step, based on the previously identified parameters, a generalized best-fit model is proposed by performing a regression analysis. Finally, model validation is carried out via implementation on different sets of experimental data. The proposed model indeed renders an improved representation of the actually observed nonlinear behavior of the tested rotational MR damper. (paper)

  14. Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

    Science.gov (United States)

    Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

    2014-11-21

    Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

  15. Non-Linear Dynamics of Saturn's Rings

    Science.gov (United States)

    Esposito, L. W.

    2016-12-01

    Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries

  16. Exact solutions of a nonpolynomially nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Parwani, R.; Tan, H.S.

    2007-01-01

    A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

  17. Linear and nonlinear resonance features of an erbium-doped fibre ...

    Indian Academy of Sciences (India)

    2014-07-01

    Jul 1, 2014 ... Abstract. The continuous-wave output of a single-mode erbium-doped fibre ring laser when sub- jected to cavity-loss modulation is found to exhibit linear as well as nonlinear resonances. At sufficiently low driving amplitude, the system resembles a linear damped oscillator. At higher amplitudes, the ...

  18. Combined algorithms in nonlinear problems of magnetostatics

    International Nuclear Information System (INIS)

    Gregus, M.; Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

    1988-01-01

    To solve boundary problems of magnetostatics in unbounded two- and three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method of nonlinear magnetostatic problem without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in non-linear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given too. 14 refs.; 2 figs.; 1 tab

  19. Forced convective heat transfer in boundary layer flow of Sisko fluid over a nonlinear stretching sheet.

    Science.gov (United States)

    Munir, Asif; Shahzad, Azeem; Khan, Masood

    2014-01-01

    The major focus of this article is to analyze the forced convective heat transfer in a steady boundary layer flow of Sisko fluid over a nonlinear stretching sheet. Two cases are studied, namely (i) the sheet with variable temperature (PST case) and (ii) the sheet with variable heat flux (PHF case). The heat transfer aspects are investigated for both integer and non-integer values of the power-law index. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically. The numerical results are obtained by the shooting method using adaptive Runge Kutta method with Broyden's method in the domain[Formula: see text]. The numerical results for the temperature field are found to be strongly dependent upon the power-law index, stretching parameter, wall temperature parameter, material parameter of the Sisko fluid and Prandtl number. In addition, the local Nusselt number versus wall temperature parameter is also graphed and tabulated for different values of pertaining parameters. Further, numerical results are validated by comparison with exact solutions as well as previously published results in the literature.

  20. Twin Positive Solutions of a Nonlinear m-Point Boundary Value Problem for Third-Order p-Laplacian Dynamic Equations on Time Scales

    Directory of Open Access Journals (Sweden)

    Wei Han

    2008-01-01

    Full Text Available Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.

  1. Improved algorithm for solving nonlinear parabolized stability equations

    Science.gov (United States)

    Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

    2016-08-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

  2. A numerical solution of a singular boundary value problem arising in boundary layer theory.

    Science.gov (United States)

    Hu, Jiancheng

    2016-01-01

    In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

  3. Application of polynomial control to design a robust oscillation-damping controller in a multimachine power system.

    Science.gov (United States)

    Hasanvand, Hamed; Mozafari, Babak; Arvan, Mohammad R; Amraee, Turaj

    2015-11-01

    This paper addresses the application of a static Var compensator (SVC) to improve the damping of interarea oscillations. Optimal location and size of SVC are defined using bifurcation and modal analysis to satisfy its primary application. Furthermore, the best-input signal for damping controller is selected using Hankel singular values and right half plane-zeros. The proposed approach is aimed to design a robust PI controller based on interval plants and Kharitonov's theorem. The objective here is to determine the stability region to attain robust stability, the desired phase margin, gain margin, and bandwidth. The intersection of the resulting stability regions yields the set of kp-ki parameters. In addition, optimal multiobjective design of PI controller using particle swarm optimization (PSO) algorithm is presented. The effectiveness of the suggested controllers in damping of local and interarea oscillation modes of a multimachine power system, over a wide range of loading conditions and system configurations, is confirmed through eigenvalue analysis and nonlinear time domain simulation. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  4. Nonlinear oscillation regime of electromagnetic disturbances in the equatorial F region

    International Nuclear Information System (INIS)

    Sazonov, S.V.

    1990-01-01

    Nonlinear oscillation regime of electromagnetic dicturbances within equatorial ionosphere F-region resulted from Rayleigh-Taylor instability, gradient-drift instability and recombination processes is investigated on the basis of two-liquid quasihydrodynamics equations. It is shown, that at positive linear increment the oscillations are developing in regime with aggregation and are terminated by increment the effect of threshold destabilization, when under certain initial conditions underlgoes oscillation nonlinear swinging, resulting, as well, in bubble formation in contrast to small damping oscillations, is detected

  5. Damping in heat exchanger tube bundles. A review

    International Nuclear Information System (INIS)

    Iqbal, Qamar; Khushnood, Shahab; Ghalban, Ali Roheim El; Sheikh, Nadeem Ahmed; Malik, Muhammad Afzaal; Arastu, Asif

    2007-01-01

    Damping is a major concern in the design and operation of tube bundles with loosely supported tubes in baffles for process shell and tube heat exchangers and steam generators which are used in nuclear, process and power generation industries. System damping has a strong influence on the amplitude of vibration. Damping depends upon the mechanical properties of the tube material, geometry of intermediate supports and the physical properties of shell-side fluid. Type of tube motion, number of supports, tube frequency, vibration amplitude, tube mass or diameter, side loads, support thickness, higher modes, shell-side temperature etc., affect damping in tube bundles. The importance of damping is further highlighted due to current trend of larger exchangers with increased shell-side velocities in modern units. Various damping mechanisms have been identified (Friction damping, Viscous damping, Squeeze film damping, Support damping. Two-Phase damping, and very recent-Thermal damping), which affect the performance of process exchangers and steam generators with respect to flow induced vibration design, including standard design guidelines. Damping in two-phase flow is very complex and highly void fraction, and flow-regime dependent. The current paper focuses on the various known damping mechanisms subjected to both single and two-phase cross-flow in process heat exchangers and steam generators and formulates the design guidelines for safer design. (author)

  6. Design of output feedback UPFC controller for damping of electromechanical oscillations using PSO

    Energy Technology Data Exchange (ETDEWEB)

    Shayeghi, H. [Technical Engineering Dept., Univ. of Mohaghegh Ardabili, Ardabil (Iran); Shayanfar, H.A. [Center of Excellence for Power Automation and Operation, Electrical Engineering Dept., Iran Univ. of Science and Technology, Tehran (Iran); Jalilzadeh, S.; Safari, A. [Technical Engineering Dept., Zanjan Univ., Zanjan (Iran)

    2009-10-15

    In this paper, a novel method for the design of output feedback controller for unified power flow controller (UPFC) is developed. The selection of the output feedback gains for the UPFC controllers is converted to an optimization problem with the time domain-based objective function which is solved by a particle swarm optimization technique (PSO) that has a strong ability to find the most optimistic results. Only local and available state variables are adopted as the input signals of each controller for the decentralized design. Thus, structure of the designed UPFC controller is simple and easy to implement. To ensure the robustness of the proposed stabilizers, the design process takes into account a wide range of operating conditions and system configurations. The effectiveness of the proposed controller for damping low frequency oscillations is tested and demonstrated through nonlinear time-domain simulation and some performance indices studies. The results analysis reveals that the designed PSO-based output feedback UPFC damping controller has an excellent capability in damping power system low frequency oscillations and enhance greatly the dynamic stability of the power systems. Moreover, the system performance analysis under different operating conditions show that the {delta}{sub E} based controller is superior to both the m{sub B} based controller and conventional power system stablizer. (author)

  7. DAMPs, ageing, and cancer: The 'DAMP Hypothesis'.

    Science.gov (United States)

    Huang, Jin; Xie, Yangchun; Sun, Xiaofang; Zeh, Herbert J; Kang, Rui; Lotze, Michael T; Tang, Daolin

    2015-11-01

    Ageing is a complex and multifactorial process characterized by the accumulation of many forms of damage at the molecular, cellular, and tissue level with advancing age. Ageing increases the risk of the onset of chronic inflammation-associated diseases such as cancer, diabetes, stroke, and neurodegenerative disease. In particular, ageing and cancer share some common origins and hallmarks such as genomic instability, epigenetic alteration, aberrant telomeres, inflammation and immune injury, reprogrammed metabolism, and degradation system impairment (including within the ubiquitin-proteasome system and the autophagic machinery). Recent advances indicate that damage-associated molecular pattern molecules (DAMPs) such as high mobility group box 1, histones, S100, and heat shock proteins play location-dependent roles inside and outside the cell. These provide interaction platforms at molecular levels linked to common hallmarks of ageing and cancer. They can act as inducers, sensors, and mediators of stress through individual plasma membrane receptors, intracellular recognition receptors (e.g., advanced glycosylation end product-specific receptors, AIM2-like receptors, RIG-I-like receptors, and NOD1-like receptors, and toll-like receptors), or following endocytic uptake. Thus, the DAMP Hypothesis is novel and complements other theories that explain the features of ageing. DAMPs represent ideal biomarkers of ageing and provide an attractive target for interventions in ageing and age-associated diseases. Copyright © 2014 Elsevier B.V. All rights reserved.

  8. Helmholtz bright and boundary solitons

    Energy Technology Data Exchange (ETDEWEB)

    Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

    2007-02-16

    We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts.

  9. Pipe damping

    International Nuclear Information System (INIS)

    Ware, A.G.; Arendts, J.G.

    1984-01-01

    A program has been developed to assess the available piping damping data, to generate additional data and conduct seperate effects tests, and to establish a plan for reporting and storing future test results into a data bank. This effort is providing some of the basis for developing higher allowable damping values for piping seismic analyses, which will potentially permit removal of a considerable number of piping supports, particularly snubbers. This in turn will lead to more flexible piping systems which will be less susceptible to thermal cracking, will be easier to maintain and inspect, as well as less costly

  10. Boundary fluxes for non-local diffusion

    OpenAIRE

    Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.

    2006-01-01

    We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.

  11. Nonlinear second-order multivalued boundary value problems

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Department of Mathematics, National Technical University, Zografou Campus,. Athens 15780 ... incorporates gradient systems, evolutionary variational inequalities and the classical boundary value ... We are led to an eventual application.

  12. Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria

    International Nuclear Information System (INIS)

    Frieman, E.A.; Chen, L.

    1981-10-01

    A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magentic field geometries. The specific case of axisymmetric tokamaks is then considered, and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfven wave heating sceme, it is found that nonlinear ion Landau damping of kinetic shear-Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency

  13. Nonlinear modeling of magnetorheological energy absorbers under impact conditions

    Science.gov (United States)

    Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M.; Browne, Alan L.; Ulicny, John; Johnson, Nancy

    2013-11-01

    Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s-1. Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R&D Center for nominal drop speeds of up to 6 m s-1.

  14. Nonlinear analysis of shock absorbers with amplitude-dependent damping

    Science.gov (United States)

    Łuczko, Jan; Ferdek, Urszula; Łatas, Waldemar

    2018-01-01

    This paper contains an analysis of a quarter-car model representing a vehicle equipped with a hydraulic damper whose characteristics are dependent on the piston stroke. The damper, compared to a classical mono-tube damper, has additional internal chambers. Oil flow in those chambers is controlled by relative piston displacement. The proposed nonlinear model of the system is aimed to test the effect of key design parameters of the damper on the quality indices representing ride comfort and driving safety. Numerical methods were used to determine the characteristic curves of the damper and responses of the system to harmonic excitations with their amplitude decreasing as the values of frequency increase.

  15. Optimal boundary control and boundary stabilization of hyperbolic systems

    CERN Document Server

    Gugat, Martin

    2015-01-01

    This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.  The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization.  Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples.  To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled.  Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.

  16. Modeling and non-linear responses of MEMS capacitive accelerometer

    Directory of Open Access Journals (Sweden)

    Sri Harsha C.

    2014-01-01

    Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.

  17. Feedback options in nonlinear numerical finance

    DEFF Research Database (Denmark)

    Hugger, Jens; Mashayekhi, Sima

    2012-01-01

    on an infinite slab is presented and boundary values on a bounded domain are derived. This bounded, nonlinear, 2 dimensional initial-boundary value problem is solved numerically using a number of standard finite difference schemes and the methods incorporated in the symbolic software Maple™....

  18. ANFIS based UPFC supplementary controller for damping low frequency oscillations in power systems

    Directory of Open Access Journals (Sweden)

    M. Sobha

    2007-12-01

    Full Text Available An adaptive neuro- fuzzy inference system (ANFIS based supplementary Unified Power Flow Controller (UPFC to superimpose the damping function on the control signal of UPFC is proposed. By using a hybrid learning procedure, the proposed ANFIS construct an input –output mapping based on stipulated input-output data pairs. The linguistic rules, considering the dependence of the plant output on the controlling signal are used to build the initial fuzzy inference structure. On the basis of linearized Philips-Hefron model of power system installed with UPFC, the damping function of the UPFC with various alternative UPFC control signals are investigated. In the simulations under widely varying operating conditions and system parameters, ANFIS based controller yields improved performance when compared with constant gain controller, based on phase compensation technique. To validate the robustness of the proposed technique, the approach is integrated to a multi-machine power system and the nonlinear simulation results are presented

  19. Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane

    Science.gov (United States)

    Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.

    2018-01-01

    We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that

  20. Uncertainty in microscale gas damping: Implications on dynamics of capacitive MEMS switches

    International Nuclear Information System (INIS)

    Alexeenko, Alina; Chigullapalli, Sruti; Zeng Juan; Guo Xiaohui; Kovacs, Andrew; Peroulis, Dimitrios

    2011-01-01

    Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150 V), i.e. the voltage required to actuate 90% of the sample, is about 129 cm/s and increases to 173 cm/s for the 99%-actuation voltage (of about 173 V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness. - Highlights: → We examine stochastic non-linear response of a microsystem switch subject to multiple input uncertainties. → Sample devices have been fabricated and device

  1. Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

    Directory of Open Access Journals (Sweden)

    Zulqurnain Sabir

    2014-06-01

    Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

  2. Surge-damping vacuum valve

    International Nuclear Information System (INIS)

    Bullock, J.C.; Kelley, B.E.

    1977-01-01

    A valve for damping out flow surges in a vacuum system is described. The surge-damping mechanism consists of a slotted, spring-loaded disk adjacent to the valve's vacuum port (the flow passage to the vacuum roughing pump). Under flow surge conditions, the differential pressure forces the disk into a sealing engagement with the vacuum port, thereby restricting the gas flow path to narrow slots in the disk's periphery. The increased flow damps out the flow surge. When pressure is equalized on both sides of the valve, the spring load moves the disk away from the port to restore full flow conductance through the valve

  3. Reflection of equatorial Kelvin waves at eastern ocean boundaries Part I: hypothetical boundaries

    Directory of Open Access Journals (Sweden)

    J. Soares

    1999-06-01

    Full Text Available A baroclinic shallow-water model is developed to investigate the effect of the orientation of the eastern ocean boundary on the behavior of equatorial Kelvin waves. The model is formulated in a spherical polar coordinate system and includes dissipation and non-linear terms, effects which have not been previously included in analytical approaches to the problem. Both equatorial and middle latitude response are considered given the large latitudinal extent used in the model. Baroclinic equatorial Kelvin waves of intraseasonal, seasonal and annual periods are introduced into the domain as pulses of finite width. Their subsequent reflection, transmission and dissipation are investigated. It is found that dissipation is very important for the transmission of wave energy along the boundary and for reflections from the boundary. The dissipation was found to be dependent not only on the presence of the coastal Kelvin waves in the domain, but also on the period of these coastal waves. In particular the dissipation increases with wave period. It is also shown that the equatorial β-plane approximation can allow an anomalous generation of Rossby waves at higher latitudes. Nonlinearities generally have a small effect on the solutions, within the confines of this model.Key words. Oceanography: general (equatorial oceanography; numerical modeling · Oceanography: physical (eastern boundary currents

  4. Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark’s Method with Netwon-Raphson Iteration Revisited

    Directory of Open Access Journals (Sweden)

    Markou A.A.

    2018-03-01

    Full Text Available Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

  5. Damping in aerospace composite materials

    Science.gov (United States)

    Agneni, A.; Balis Crema, L.; Castellani, A.

    Experimental results are presented on specimens of carbon and Kevlar fibers in epoxy resin, materials used in many aerospace structures (control surfaces and wings in aircraft, large antennas in spacecraft, etc.). Some experimental methods of estimating damping ratios are first reviewed, either in the time domain or in the frequency domain. Some damping factor estimates from experimental tests are then shown; in order to evaluate the effects of the aerospace environment, damping factors have been obtained in a typical range of temperature, namely between +120 C and -120 C, and in the pressure range from room pressure to 10 exp -6 torr. Finally, a theoretical approach for predicting the bounds of the damping coefficients is shown, and prediction data are compared with experimental results.

  6. Coherent Nonlinear Longitudinal Phenomena in Unbunched Synchrotron Beams

    Energy Technology Data Exchange (ETDEWEB)

    Spentzouris, Linda Klamp [Northwestern U.

    1996-12-01

    Coherent nonlinear longitudinal phenomena are studied in proton and antiproton synchrotron beams. Theoretical development done in the eld of plasma physics for resonant wave-wave coupling is applied to the case of a particle beam. Results are given from experiments done to investigate the nature of the weakly nonlinear three-wave coupling processes known as parametric coupling and echoes. Storage ring impedances are shown to amplify the parametric coupling process, underlining the possibility that machine impedances might be extracted from coupling events instigated by external excitation. Echo amplitudes are demonstrated to be sensitive to diusion processes, such as intrabeam scattering, which degrade a beam. The result of a fast diusion rate measurement using echo amplitudes is presented. In addition to the wave-wave interactions, observations of moderately nonlinear waveparticle interactions are also included. The manifestations of these interactions that are documented include nonlinear Landau damping, higher harmonic generation, and signs of the possible formation of solitons.

  7. The periodic structure of the natural record, and nonlinear dynamics.

    Science.gov (United States)

    Shaw, H.R.

    1987-01-01

    This paper addresses how nonlinear dynamics can contribute to interpretations of the geologic record and evolutionary processes. Background is given to explain why nonlinear concepts are important. A resume of personal research is offered to illustrate why I think nonlinear processes fit with observations on geological and cosmological time series data. The fabric of universal periodicity arrays generated by nonlinear processes is illustrated by means of a simple computer mode. I conclude with implications concerning patterns of evolution, stratigraphic boundary events, and close correlations of major geologically instantaneous events (such as impacts or massive volcanic episodes) with any sharply defined boundary in the geologic column. - from Author

  8. Damping rates of the SRRC storage ring

    International Nuclear Information System (INIS)

    Hsu, K.T.; Kuo, C.C.; Lau, W.K.; Weng, W.T.

    1995-01-01

    The SRRC storage ring is a low emittance synchrotron radiation machine with nominal operation energy 1.3 GeV. The design damping time due to synchrotron radiation is 10.7, 14.4, 8.7 ms for the horizontal, vertical and longitudinal plane, respectively. The authors measured the real machine damping time as a function of bunch current, chromaticity, etc. To damp the transverse beam instability, especially in the vertical plane, they need to increase chromaticity to large positive value. The damping rates are much larger than the design values. Landau damping contribution in the longitudinal plane is quite large, especially in the multibunch mode. The estimated synchrotron tune spread from the Landau damping is in agreement with the measured coherent longitudinal coupled bunch oscillation amplitude

  9. Preliminary Study on the Damping Effect of a Lateral Damping Buffer under a Debris Flow Load

    Directory of Open Access Journals (Sweden)

    Zheng Lu

    2017-02-01

    Full Text Available Simulating the impact of debris flows on structures and exploring the feasibility of applying energy dissipation devices or shock isolators to reduce the damage caused by debris flows can make great contribution to the design of disaster prevention structures. In this paper, we propose a new type of device, a lateral damping buffer, to reduce the vulnerability of building structures to debris flows. This lateral damping buffer has two mechanisms of damage mitigation: when debris flows impact on a building, it acts as a buffer, and when the structure vibrates due to the impact, it acts as a shock absorber, which can reduce the maximum acceleration response and subsequent vibration respectively. To study the effectiveness of such a lateral damping buffer, an impact test is conducted, which mainly involves a lateral damping buffer attached to a two-degree-of-freedom structure under a simulated debris flow load. To enable the numerical study, the equation of motion of the structure along with the lateral damping buffer is derived. A subsequent parametric study is performed to optimize the lateral damping buffer. Finally, a practical design procedure is also provided.

  10. Non-Linear Dynamics of Saturn’s Rings

    Science.gov (United States)

    Esposito, Larry W.

    2015-11-01

    Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects

  11. Research on low strain magnetic mechanical hysteresis damping performance of Fe-15Cr-3Mo-0.5Si alloy

    International Nuclear Information System (INIS)

    Wang, Hui; Huang, Huawei; Hong, Xiaofeng; Yin, Changgeng; Huang, Zhaohua; Chen, Le

    2015-01-01

    Highlights: • Heat treatment system has a great effect on the alloy damping performance. • Damping performance does not improve monotonously with temperature. • Furnace cooling is higher than that of alloy after air cooling. • There is an optimum annealing temperature and grain size to obtain high damping. - Abstract: This paper studies the preparation of Fe-15Cr-3Mo-0.5Si alloy by using vacuum induction melting furnace and vacuum annealing furnace, the damping performance of which in different heat treatment states is tested with dynamic mechanical thermal analyzer (DMA). Through microstructure observation with metallographic microscope (OM), grain boundary observation with scanning electron microscopy (SEM), phase structure analysis with X-ray diffraction (XRD) and internal stress of S-B model analysis, the effect law of annealing temperature, types of cooling, holding time and grain sizes on the damping performance of alloy and the related mechanism can be concluded as follows. The annealing temperature and grain sizes have a significant impact on the damping strain amplitude as well as the magnetic and mechanical damping performance of this ferromagnetic alloy. Proper annealing temperature and grain size is the necessary condition to get high damping performance of the alloy. It is not conducive to improvement of the damping performance if the annealing temperature is too high or too low and the grain size is too small or too large. For Fe-15Cr-3Mo-0.5Si alloy, within the range of the low strain amplitude, alloy damping performance does not improve monotonously with the increase of the annealing temperature and grain size. The maximum value appears at the annealing temperature of 1100 °C/1 h with the grain size of about 300 μm. At high annealing temperature of 1100 °C, the damping performance of alloy in the slow cooling furnace is higher than that with air cooling treatment. The extension or shortening of the holding time, to a certain extent

  12. Research on low strain magnetic mechanical hysteresis damping performance of Fe-15Cr-3Mo-0.5Si alloy

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Hui, E-mail: qinghe5525@163.com; Huang, Huawei; Hong, Xiaofeng; Yin, Changgeng; Huang, Zhaohua; Chen, Le

    2015-02-15

    Highlights: • Heat treatment system has a great effect on the alloy damping performance. • Damping performance does not improve monotonously with temperature. • Furnace cooling is higher than that of alloy after air cooling. • There is an optimum annealing temperature and grain size to obtain high damping. - Abstract: This paper studies the preparation of Fe-15Cr-3Mo-0.5Si alloy by using vacuum induction melting furnace and vacuum annealing furnace, the damping performance of which in different heat treatment states is tested with dynamic mechanical thermal analyzer (DMA). Through microstructure observation with metallographic microscope (OM), grain boundary observation with scanning electron microscopy (SEM), phase structure analysis with X-ray diffraction (XRD) and internal stress of S-B model analysis, the effect law of annealing temperature, types of cooling, holding time and grain sizes on the damping performance of alloy and the related mechanism can be concluded as follows. The annealing temperature and grain sizes have a significant impact on the damping strain amplitude as well as the magnetic and mechanical damping performance of this ferromagnetic alloy. Proper annealing temperature and grain size is the necessary condition to get high damping performance of the alloy. It is not conducive to improvement of the damping performance if the annealing temperature is too high or too low and the grain size is too small or too large. For Fe-15Cr-3Mo-0.5Si alloy, within the range of the low strain amplitude, alloy damping performance does not improve monotonously with the increase of the annealing temperature and grain size. The maximum value appears at the annealing temperature of 1100 °C/1 h with the grain size of about 300 μm. At high annealing temperature of 1100 °C, the damping performance of alloy in the slow cooling furnace is higher than that with air cooling treatment. The extension or shortening of the holding time, to a certain extent

  13. On nonlinear statistical thermodynamics of boundary plasma with postactions

    International Nuclear Information System (INIS)

    Temko, S.W.; Temko, K.W.; Kuz'min, S.K.

    1992-01-01

    The authors use the statistical thermodynamics of small systems proposed before their publications for boundary weakly ionized plasma with postaction. Boundary properties of the plasma is taken into account by two ways: (1) suppose that only small number of very quick particles are able to leave the cloud having done entrance into outer medium work; (2) take into account the interaction between particles and inner surface of the cloud. Interactions in the boundary plasma are described by corresponding potential functions. The potential functions are mathematical models of real interactions in boundary plasma. Choosing of potential functions, their numerical parameters, geometrical form and dimensions of the cloud is made by using the methods of optimal experiment planning, maximum likelihood and computer experiment. Free energy of the cloud is a likelihood function. State of boundary plasma with admixtures is described by vector-density of particles distribution. Term ''distribution'' is used here in Sobolev-Schwartc sense. The authors obtain the vector-density of particles distribution in cloud which gives the condition minimum of free energy for every time moment under quasistatistical equilibrium. The system of conditions for free energy conditional minimizing for every time moment includes integral equilibrium equations, ''non-hard normalization'' and additional conditions taken as a result of analyzing physical and physical-chemical nature of boundary plasma. To obtain conditional minimum of free energy it is necessary to solve the system of conditions. First of all they solve equilibrium problem by the authors method. They obtain vector-density of particles distribution in the cloud. Then using method of random walk with postaction between sets of random walk process they build distribution function of random vector-density

  14. Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

    Science.gov (United States)

    Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

    2016-01-01

    Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

  15. On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Guotao Wang

    2012-01-01

    Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

  16. Importance of structural damping in the dynamic analysis of compliant deployable structures

    Science.gov (United States)

    Dewalque, Florence; Rochus, Pierre; Brüls, Olivier

    2015-06-01

    Compliant mechanisms such as tape springs are often used on satellites to deploy appendices, e.g. solar panels, antennas, telescopes and solar sails. Their main advantage comes from the fact that their motion results from the elastic deformation of structural components and the absence of actuators or external energy sources. The mechanical behaviour of a tape spring is intrinsically complex and nonlinear involving buckling, hysteresis and self-locking phenomena. In the majority of the previous works, dynamic simulations were performed without any physical representation of the structural damping. These simulations could be successfully achieved because of the presence of numerical damping in the transient solver. However, in this case, the dynamic response turns out to be quite sensitive to the amount of numerical dissipation, so that the predictive capabilities of the model are questionable. In this work based on numerical case studies, we show that the dynamic simulation of a tape spring can be made less sensitive to numerical parameters when the structural dissipation is taken into account.

  17. Bounce-harmonic Landau Damping of Plasma Waves

    Science.gov (United States)

    Anderegg, Francois

    2015-11-01

    We present measurement of plasma wave damping, spanning the temperature regimes of direct Landau damping, bounce-harmonic Landau damping, inter-species drag damping, and viscous damping. Direct Landau damping is dominant at high temperatures, but becomes negligible as v vph / 5 . The measurements are conducted in trapped pure ion plasmas contained in Penning-Malmberg trap, with wave-coherent LIF diagnostics of particle velocities. Our focus is on bounce harmonics damping, controlled by an applied ``squeeze'' potential, which generates harmonics in the wave potential and in the particle dynamics. A particle moving in z experiences a non-sinusoidal mode potential caused by the squeeze, producing high spatial harmonics with lower phase velocity. These harmonics are Landau damped even when the mode phase velocity vph is large compared to the thermal velocity v , since the nth harmonic is resonant with a particle bouncing at velocity vb =vph / n . Here we increase the bounce harmonics through applied squeeze potential; but some harmonics are always present in finite length systems. For our centered squeeze geometry, theory shows that only odd harmonics are generated, and predicts the Landau damping rate from vph / n . Experimentally, the squeeze potential increases the wave damping and reduces its frequency. The frequency shift occurs because the squeeze potential reduces the number of particle where the mode velocity is the largest, therefore reducing the mode frequency. We observe an increase in the damping proportional to Vs2,and a frequency reduction proportional to Vs , in quantitative agreement with theory. Wave-coherent laser induced fluorescence allows direct observation of bounce resonances on the particle distribution, here predominantly at vph / 3 . A clear increase of the bounce harmonics is visible on the particle distribution when the squeeze potential is applied. Supported by NSF Grant PHY-1414570, and DOE Grants DE-SC0002451 and DE-SC0008693.

  18. Next generation HOM-damping

    Science.gov (United States)

    Marhauser, Frank

    2017-06-01

    Research and development for superconducting radio-frequency cavities has made enormous progress over the last decades from the understanding of theoretical limitations to the industrial mass fabrication of cavities for large-scale particle accelerators. Key technologies remain hot topics due to continuously growing demands on cavity performance, particularly when in pursuit of high quality beams at higher beam currents or higher luminosities than currently achievable. This relates to higher order mode (HOM) damping requirements. Meeting the desired beam properties implies avoiding coupled multi-bunch or beam break-up instabilities depending on the machine and beam parameters that will set the acceptable cavity impedance thresholds. The use of cavity HOM-dampers is crucial to absorb the wakefields, comprised by all beam-induced cavity Eigenmodes, to beam-dynamically safe levels and to reduce the heat load at cryogenic temperature. Cavity damping concepts may vary, but are principally based on coaxial and waveguide couplers as well as beam line absorbers or any combination. Next generation energy recovery linacs and circular colliders call for cavities with strong HOM-damping that can exceed the state-of-the-art, while the operating mode efficiency shall not be significantly compromised concurrently. This imposes major challenges given the rather limited damping concepts. A detailed survey of established cavities is provided scrutinizing the achieved damping performance, shortcomings, and potential improvements. The scaling of the highest passband mode impedances is numerically evaluated in dependence on the number of cells for a single-cell up to a nine-cell cavity, which reveals the increased probability of trapped modes. This is followed by simulations for single-cell and five-cell cavities, which incorporate multiple damping schemes to assess the most efficient concepts. The usage and viability of on-cell dampers is elucidated for the single-cell cavity since it

  19. Towards realistic molecular dynamics simulations of grain boundary mobility

    International Nuclear Information System (INIS)

    Zhou, J.; Mohles, V.

    2011-01-01

    In order to investigate grain boundary migration by molecular dynamics (MD) simulations a new approach involving a crystal orientation-dependent driving force has been developed by imposing an appropriate driving force on grain boundary atoms and enlarging the effective range of driving force. The new approach has been validated by the work of the driving force associated with the motion of grain boundaries. With the new approach the relation between boundary migration velocity and driving force is found to be nonlinear, as was expected from rate theory for large driving forces applied in MD simulations. By evaluating grain boundary mobility nonlinearly for a set of symmetrical tilt boundaries in aluminum at high temperature, high-angle grain boundaries were shown to move much faster than low-angle grain boundaries. This agrees well with experimental findings for recrystallization and grain growth. In comparison with the available data the simulated mobility of a 38.21 o Σ7 boundary was found to be significantly lower than other MD simulation results and comparable with the experimental values. Furthermore, the average volume involved during atomic jumps for boundary migration is determined in MD simulations for the first time. The large magnitude of the volume indicates that grain boundary migration is accomplished by the correlated motion of atom groups.

  20. Test and evaluation about damping characteristics of hanger supports for nuclear power plant piping systems (Seismic Damping Ratio Evaluation Program)

    International Nuclear Information System (INIS)

    Shibata, H.; Ito, A.; Tanaka, K.; Niino, T.; Gotoh, N.

    1981-01-01

    Generally, damping phenomena of structures and equipments is caused by very complex energy dissipation. Especially, as piping systems are composed of many components, it is very difficult to evaluate damping characteristics of its system theoretically. On the other hand, the damping value for aseismic design of nuclear power plants is very important design factor to decide seismic response loads of structures, equipments and piping systems. The very extensive studies titled SDREP (Seismic Damping Ratio Evaluation Program) were performed to establish proper damping values for seismic design of piping as a joint work among a university, electric companies and plant makers. In SDREP, various systematic vibration tests were conducted to investigate factors which may contribute to damping characteristics of piping systems and to supplement the data of the pre-operating tests. This study is related to the component damping characteristics tests of that program. The object of this study is to clarify damping characteristics and mechanism of hanger supports used in piping systems, and to establish the evaluation technique of dispersing energy at hanger support points and its effect to the total damping ability of piping system. (orig./WL)

  1. Identification of Damping from Structural Vibrations

    DEFF Research Database (Denmark)

    Bajric, Anela

    Reliable predictions of the dynamic loads and the lifetime of structures are influenced by the limited accuracy concerning the level of structural damping. The mechanisms of damping cannot be derived analytically from first principles, and in the design of structures the damping is therefore based...... on experience or estimated from measurements. This thesis consists of an extended summary and three papers which focus on enhanced methods for identification of damping from random struc-tural vibrations. The developed methods are validated by stochastic simulations, experimental data and full-scale measurements...... which are representative of the vibrations in small and large-scale structures. The first part of the thesis presents an automated procedure which is suitable for estimation of the natural frequencies and the modal damping ratios from random response of structures. The method can be incorporated within...

  2. Nonlinear singular elliptic equations

    International Nuclear Information System (INIS)

    Dong Minh Duc.

    1988-09-01

    We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs

  3. Shape memory alloys as damping materials

    International Nuclear Information System (INIS)

    Humbeeck, J. van

    2000-01-01

    Shape memory alloys are gaining an increased interest as passive as well as active damping materials. This damping ability when applied in structural elements can lead to a better noise control, improved life time and even better performance of the envisaged tools. By passive damping, it is understood that the material converts a significant part of unwanted mechanical energy into heat. This mechanical energy can be a (resonance) vibration, impact loading or shock waves. This high damping capacity finds its origin in the thermoelastic martensitic phase due to the hysteretic mobility of martensite-variants or different phase interfaces. The damping capacity increases with increasing amplitude of the applied vibration or impact and is almost frequency independent. Special interest exists moreover for damping extreme large displacements by applying the mechanical hysteresis performed during pseudoelastic loading. This aspect is nowadays very strongly studied as a tool for protecting buildings against earthquakes in seismic active regions. Active damping can be obtained in hybrid composites by controlling the recovery stresses or strains of embedded shape memory alloy wires. This controls the internal energy fo a structure which allows controlled modal modification and tuning of the dynamical properties of structural elements. But also impact damage, acoustic radiation, dynamic shape control can be actively controlled. As a consequence improved fatigue-resistance, better performance and a longer lifetime of the structural elements can be obtained. (orig.)

  4. Homoclinic and quasi-homoclinic solutions for damped differential equations

    Directory of Open Access Journals (Sweden)

    Chuan-Fang Zhang

    2015-01-01

    Full Text Available We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \\ddot{u}+c\\dot{u}-L(tu+W_u(t,u=0, $$ where L(t and W(t,u are neither autonomous nor periodic in t. Under certain assumptions on L and W, we obtain infinitely many homoclinic solutions when the nonlinearity W(t,u is sub-quadratic or super-quadratic by using critical point theorems. Some recent results in the literature are generalized, and the open problem proposed by Zhang and Yuan is solved. In addition, with the help of the Nehari manifold, we consider the case where W(t,u is indefinite and prove the existence of at least one nontrivial quasi-homoclinic solution.

  5. Fully nonlinear phenomenology of the Berk-Breizman augmentation of the Vlasov-Maxwell system

    International Nuclear Information System (INIS)

    Vann, R.G.L.; Dendy, R.O.; Rowlands, G.; Arber, T.D.; D'Ambrumenil, N.

    2003-01-01

    The Berk-Breizman augmentation of the Vlasov-Maxwell system is widely used to model self-consistent resonant excitation and damping of wave fields by evolving energetic particle populations in magnetic fusion plasmas. The key model parameters are the particle annihilation rate ν a , which drives bump-on-tail structure, and the linear wave damping rate γ d . A code, based on the piecewise parabolic method, is used to integrate the fully nonlinear Berk-Breizman system of equations across the whole (ν a ,γ d ) parameter space. The results of this code show that the system's behavior can be classified into one of four types, each of which occurs in a well-defined region of parameter space: chaotic, periodic, steady state, and damped. The corresponding evolution in (x,v) phase space is also examined

  6. Nonlinear discrete-time multirate adaptive control of non-linear vibrations of smart beams

    Science.gov (United States)

    Georgiou, Georgios; Foutsitzi, Georgia A.; Stavroulakis, Georgios E.

    2018-06-01

    The nonlinear adaptive digital control of a smart piezoelectric beam is considered. It is shown that in the case of a sampled-data context, a multirate control strategy provides an appropriate framework in order to achieve vibration regulation, ensuring the stability of the whole control system. Under parametric uncertainties in the model parameters (damping ratios, frequencies, levels of non linearities and cross coupling, control input parameters), the scheme is completed with an adaptation law deduced from hyperstability concepts. This results in the asymptotic satisfaction of the control objectives at the sampling instants. Simulation results are presented.

  7. High Enthalpy Effects on Two Boundary Layer Disturbances in Supersonic and Hypersonic Flow

    Science.gov (United States)

    2012-05-01

    of damping rate per wavelength require a degeneracy of seven ( red ). . . . . . . . . . 78 5.3 Chemical damping processes examples...diameter, over the boundary layer displacement thickness versus the Reynolds number based on element diameter, ReD = UDν . Figure 2.5: This plot shows...3.22) Substituting these relationships into Equations 3.18 and 3.19, we have (ıωIji + Aji ) fi = Aji ( ρ0ω 2g ∂q∗i ∂p ∣∣∣∣ p0 − ρ0 ∂2g ∂x2 ∂q∗i ∂ρ

  8. A Numerical Study of 2-D Surface Roughness Effects on the Growth of Wave Modes in Hypersonic Boundary Layers

    Science.gov (United States)

    Fong, Kahei Danny

    The current understanding and research efforts on surface roughness effects in hypersonic boundary-layer flows focus, almost exclusively, on how roughness elements trip a hypersonic boundary layer to turbulence. However, there were a few reports in the literature suggesting that roughness elements in hypersonic boundary-layer flows could sometimes suppress the transition process and delay the formation of turbulent flow. These reports were not common and had not attracted much attention from the research community. Furthermore, the mechanisms of how the delay and stabilization happened were unknown. A recent study by Duan et al. showed that when 2-D roughness elements were placed downstream of the so-called synchronization point, the unstable second-mode wave in a hypersonic boundary layer was damped. Since the second-mode wave is typically the most dangerous and dominant unstable mode in a hypersonic boundary layer for sharp geometries at a zero angle of attack, this result has pointed to an explanation on how roughness elements delay transition in a hypersonic boundary layer. Such an understanding can potentially have significant practical applications for the development of passive flow control techniques to suppress hypersonic boundary-layer transition, for the purpose of aero-heating reduction. Nevertheless, the previous study was preliminary because only one particular flow condition with one fixed roughness parameter was considered. The study also lacked an examination on the mechanism of the damping effect of the second mode by roughness. Hence, the objective of the current research is to conduct an extensive investigation of the effects of 2-D roughness elements on the growth of instability waves in a hypersonic boundary layer. The goal is to provide a full physical picture of how and when 2-D roughness elements stabilize a hypersonic boundary layer. Rigorous parametric studies using numerical simulation, linear stability theory (LST), and parabolized

  9. Effect of second-order and fully nonlinear wave kinematics on a tension-leg-platform wind turbine in extreme wave conditions

    DEFF Research Database (Denmark)

    Pegalajar Jurado, Antonio Manuel; Borg, Michael; Robertson, Amy

    2017-01-01

    In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equa...... damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping....

  10. Global Format for Conservative Time Integration in Nonlinear Dynamics

    DEFF Research Database (Denmark)

    Krenk, Steen

    2014-01-01

    The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc. generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with essentially nonlinear structures. These problems are overcome....... In the present paper a conservative time integration algorithm is developed in a format using only the internal forces and the associated tangent stiffness at the specific time integration points. Thus, the procedure is computationally very similar to a collocation method, consisting of a series of nonlinear...... equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects: representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping with the purpose of extracting energy from undesirable high...

  11. A non-reflecting boundary for use in a finite element beam model of a railway track

    Science.gov (United States)

    Yang, Jiannan; Thompson, David J.

    2015-02-01

    Some beam-like structures such as a railway track are effectively infinite in nature. Analytical solutions exist for simple structures but numerical methods like the finite element (FE) method are often employed to study more complicated problems. However, when the FE method is used for structures of infinite extent it is essential to introduce artificial boundaries to limit the area of computation. Here, a non-reflecting boundary is developed using a damped tapered tip for application in a finite element model representing an infinite supported beam. The FE model of the tapered tip is validated against an analytical model based on Bessel functions. The reflection characteristics of the FE tapered tip are quantified using a wave/FE superposition method. It is shown that the damped tapered tip is much more effective than its constant counterpart and achieves reduction of the model size. The damped tapered tip is applied to a simple FE railway track model and good agreement is found when its point mobility is compared with an analytical infinite track model.

  12. A perturbation expansion for the nonlinear Schroedinger equation with application to the influence of nonlinear Landau damping

    International Nuclear Information System (INIS)

    Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.

    1977-12-01

    The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)

  13. Development of new damping devices for piping

    International Nuclear Information System (INIS)

    Kobayashi, Hiroe

    1991-01-01

    An increase of the damping ratio is known to be very effective for the seismic design of a piping system. Increasing the damping ratio and reducing the seismic response of the piping system, the following three types of damping devices for piping systems are introduced: (1) visco-elastic damper, (2) elasto-plastic damper and (3) compact dynamic damper. The dynamic characteristics of these damping devices were investigated by the component test and the applicability of them to the piping system was confirmed by the vibration test using a three dimensional piping model. These damping devices are more effective than mechanical snubbers to reduce the vibration of the piping system. (author)

  14. Modelling the nonlinear behaviour of double walled carbon nanotube based resonator with curvature factors

    Science.gov (United States)

    Patel, Ajay M.; Joshi, Anand Y.

    2016-10-01

    This paper deals with the nonlinear vibration analysis of a double walled carbon nanotube based mass sensor with curvature factor or waviness, which is doubly clamped at a source and a drain. Nonlinear vibrational behaviour of a double-walled carbon nanotube excited harmonically near its primary resonance is considered. The double walled carbon nanotube is harmonically excited by the addition of an excitation force. The modelling involves stretching of the mid plane and damping as per phenomenon. The equation of motion involves four nonlinear terms for inner and outer tubes of DWCNT due to the curved geometry and the stretching of the central plane due to the boundary conditions. The vibrational behaviour of the double walled carbon nanotube with different surface deviations along its axis is analyzed in the context of the time response, Poincaré maps and Fast Fourier Transformation diagrams. The appearance of instability and chaos in the dynamic response is observed as the curvature factor on double walled carbon nanotube is changed. The phenomenon of Periodic doubling and intermittency are observed as the pathway to chaos. The regions of periodic, sub-harmonic and chaotic behaviour are clearly seen to be dependent on added mass and the curvature factors in the double walled carbon nanotube. Poincaré maps and frequency spectra are used to explicate and to demonstrate the miscellany of the system behaviour. With the increase in the curvature factor system excitations increases and results in an increase of the vibration amplitude with reduction in excitation frequency.

  15. A review of experimental soil-structure interaction damping

    International Nuclear Information System (INIS)

    Tsai, N.C.

    1981-01-01

    In soil-structure interaction analysis, the foundation soil is usually represented by impedance springs and dampers. The impedance damping includes the effect of both the material damping and the radiation damping. Because the impedance theory normally assumes a rigid structural base and an elastic bond between the soil and structure, it is generally held that the radiation damping has been overestimated by the theory. There are some published information on the dynamic tests of footings and structures that allow direct or indirect assessments of the validity of the analytical radiation damping. An overview of such information is presented here. Based on these limited test data, it is concluded that for horizontal soil-structure interaction analysis the analytical radiation damping alone is sufficient to represent the combined material and radiation damping in the field. On the other hand, for vertical analysis it appears that the theory may have overestimated the radiation damping and certain reduction is recommended. (orig.)

  16. Nonlinear modeling of magnetorheological energy absorbers under impact conditions

    International Nuclear Information System (INIS)

    Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M; Browne, Alan L; Ulicny, John; Johnson, Nancy

    2013-01-01

    Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s −1 . Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R and D Center for nominal drop speeds of up to 6 m s −1 . (paper)

  17. Sturm-Liouville BVPs with Caratheodory nonlinearities

    Directory of Open Access Journals (Sweden)

    Abdelhamid Benmezai

    2016-11-01

    Full Text Available In this article we study the existence and multiplicity of solutions for several classes of Sturm-Liouville boundary value problems having Caratheodory nonlinearities. Many results existing in the literature for such boundary value problems in the continuous framework will find in this work their extensions to the Caratheodory setting.

  18. CORONAL HEATING BY SURFACE ALFVEN WAVE DAMPING: IMPLEMENTATION IN A GLOBAL MAGNETOHYDRODYNAMICS MODEL OF THE SOLAR WIND

    Energy Technology Data Exchange (ETDEWEB)

    Evans, R. M. [NASA Goddard Space Flight Center, Space Weather Lab, Greenbelt, MD 20771 (United States); Opher, M. [Astronomy Department, Boston University, 675 Commonwealth Avenue, Boston, MA 02215 (United States); Oran, R.; Van der Holst, B.; Sokolov, I. V.; Frazin, R.; Gombosi, T. I. [Center for Space Environment Modeling, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109 (United States); Vasquez, A., E-mail: Rebekah.e.frolov@nasa.gov [Instituto de Astronomia y Fisica del Espacio (CONICET-UBA) and FCEN (UBA), CC 67, Suc 28, Ciudad de Buenos Aires (Argentina)

    2012-09-10

    The heating and acceleration of the solar wind is an active area of research. Alfven waves, because of their ability to accelerate and heat the plasma, are a likely candidate in both processes. Many models have explored wave dissipation mechanisms which act either in closed or open magnetic field regions. In this work, we emphasize the boundary between these regions, drawing on observations which indicate unique heating is present there. We utilize a new solar corona component of the Space Weather Modeling Framework, in which Alfven wave energy transport is self-consistently coupled to the magnetohydrodynamic equations. In this solar wind model, the wave pressure gradient accelerates and wave dissipation heats the plasma. Kolmogorov-like wave dissipation as expressed by Hollweg along open magnetic field lines was presented in van der Holst et al. Here, we introduce an additional dissipation mechanism: surface Alfven wave (SAW) damping, which occurs in regions with transverse (with respect to the magnetic field) gradients in the local Alfven speed. For solar minimum conditions, we find that SAW dissipation is weak in the polar regions (where Hollweg dissipation is strong), and strong in subpolar latitudes and the boundaries of open and closed magnetic fields (where Hollweg dissipation is weak). We show that SAW damping reproduces regions of enhanced temperature at the boundaries of open and closed magnetic fields seen in tomographic reconstructions in the low corona. Also, we argue that Ulysses data in the heliosphere show enhanced temperatures at the boundaries of fast and slow solar wind, which is reproduced by SAW dissipation. Therefore, the model's temperature distribution shows best agreement with these observations when both dissipation mechanisms are considered. Lastly, we use observational constraints of shock formation in the low corona to assess the Alfven speed profile in the model. We find that, compared to a polytropic solar wind model, the wave

  19. An Energy Decaying Scheme for Nonlinear Dynamics of Shells

    Science.gov (United States)

    Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

    2000-01-01

    A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

  20. Stability and boundary stabilization of 1-D hyperbolic systems

    CERN Document Server

    Bastin, Georges

    2016-01-01

    This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary...