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Sample records for karman-rostovstev plate equations

  1. Attractors for stochastic strongly damped plate equations with additive noise

    Directory of Open Access Journals (Sweden)

    Wenjun Ma

    2013-04-01

    Full Text Available We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.

  2. EQUIVALENCE BETWEEN EXACT INTERNAL CONTROLLABILITY OF THE KIRCHHOFF PLATE-LIKE EQUATION AND THE WAVE EQUATION

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    When the rotatory inertia is taken into account, vibrations of a linear plate can be described by the Kirchhoff plate equation. Consider this equation with locally distributed control forces and some boundary condition which is the simply supported boundary condition for a rectangular plate. In this paper, the authors establish exact controllability of the system in terms of the equivalence to exact internal controllability of the wave equation, by means of a frequency domain characterization of exact controllability introduced recently in [11].

  3. A Rigorous Derivation of the Equations for the Clamped Biot-Kirchhoff-Love Poroelastic plate

    CERN Document Server

    Marciniak-Czochra, Anna

    2012-01-01

    In this paper we investigate the limit behavior of the solution to quasi-static Biot's equations in thin poroelastic plates as the thickness tends to zero. We choose Terzaghi's time corresponding to the plate thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure and total poroelastic stress to the solution of the new class of plate equations. In the new equations the in-plane stretching is described by the 2D Navier's linear elasticity equations, with elastic moduli depending on Gassmann's and Biot's coefficients. The bending equation is coupled with the pressure equation and it contains the bending moment due to the variation in pore pressure across the plate thickness. The pressure equation is parabolic only in the vertical direction. As additional terms it contains the time derivative of the in-plane Laplacean of the vertical deflection of the plate and of the the elastic in-plane compression term.

  4. A unique continuation result for the plate equation and an application

    OpenAIRE

    Arat, Zehra; Khanmamedov, Azer; Simsek, Sema

    2014-01-01

    In this paper, we prove the unique continuation property for the weak solution of the plate equation with non-smooth coefficients. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping.

  5. Initial-boundary value problems for a class of nonlinear thermoelastic plate equations

    Institute of Scientific and Technical Information of China (English)

    Zhang Jian-Wen; Rong Xiao-Liang; Wu Run-Heng

    2009-01-01

    This paper studies initial-boundary value problems for a class of nonlinear thermoelastic plate equations. Under some certain initial data and boundary conditions,it obtains an existence and uniqueness theorem of global weak solutions of the nonlinear thermoelstic plate equations,by means of the Galerkin method. Moreover,it also proves the existence of strong and classical solutions.

  6. Analysis of Blasius Equation for Flat-Plate Flow with Infinite Boundary Value

    DEFF Research Database (Denmark)

    Miansari, M. O.; Miansari, M. E.; Barari, Amin;

    2010-01-01

    This paper applies the homotopy perturbation method (HPM) to determine the well-known Blasius equation with infinite boundary value for Flat-plate Flow. We study here the possibility of reducing the momentum and continuity equations to ordinary differential equations by a similarity transformatio...

  7. Interaction of surface water waves with a vertical elastic plate: a hypersingular integral equation approach

    Science.gov (United States)

    Chakraborty, Rumpa; Mondal, Arpita; Gayen, R.

    2016-10-01

    In this paper, we present an alternative method to investigate scattering of water waves by a submerged thin vertical elastic plate in the context of linear theory. The plate is submerged either in deep water or in the water of uniform finite depth. Using the condition on the plate, together with the end conditions, the derivative of the velocity potential in the direction of normal to the plate is expressed in terms of a Green's function. This expression is compared with that obtained by employing Green's integral theorem to the scattered velocity potential and the Green's function for the fluid region. This produces a hypersingular integral equation of the first kind in the difference in potential across the plate. The reflection coefficients are computed using the solution of the hypersingular integral equation. We find good agreement when the results for these quantities are compared with those for a vertical elastic plate and submerged and partially immersed rigid plates. New results for the hydrodynamic force on the plate, the shear stress and the shear strain of the vertical elastic plate are also evaluated and represented graphically.

  8. Solution of the two- dimensional heat equation for a rectangular plate

    Directory of Open Access Journals (Sweden)

    Nurcan BAYKUŞ SAVAŞANERİL

    2015-11-01

    Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.

  9. Numerical Solutions of the von Karman Equations for a Thin Plate

    OpenAIRE

    da Silva, Pedro Patricio; Krauth, Werner

    1996-01-01

    In this paper, we present an algorithm for the solution of the von Karman equations of elasticity theory and related problems. Our method of successive reconditioning is able to avoid convergence problems at any ratio of the nonlinear streching and the pure bending energies. We illustrate the power of the method by numerical calculations of pinched or compressed plates subject to fixed boundaries.

  10. Influence of conducting plate boundary conditions on the transverse envelope equations describing intense ion beam transport

    Directory of Open Access Journals (Sweden)

    Steven M. Lund

    2004-06-01

    Full Text Available In typical diagnostic applications, intense ion beams are intercepted by a conducting plate associated with devices used to measure beam phase-space projections. This results in the transverse space-charge field near the plate being shorted out, rendering simple envelope models with constant space-charge strength inaccurate. Here we develop corrected envelope models based on analytical calculations to account for this effect on the space-charge term of the envelope equations, thereby removing a systematic source of error in the equations and enabling more accurate comparisons with experiment. For common intense beam parameters, we find that the envelope correction occurs primarily in the envelope angles near the plate and that the effect can be large enough to degrade precision beam matching in periodic transport lattices. Results are verified with 3D self-consistent particle-in-cell simulations based on intense beam experiments associated with driver development for heavy-ion fusion.

  11. Influence of Roll Elastic Deformation on Gaugemeter Equation for Plate Rolling

    Institute of Scientific and Technical Information of China (English)

    HU Xian-lei; WANG Jun; WANG Zhao-dong; LIU Xiang-hua; WANG Guo-dong

    2004-01-01

    The error of gaugemeter equation decreases the gap setting precision. The precision of gaugemeter equation is strongly influenced by plate width, work roll radius, backup roll radius, work roll crown, backup roll crown and rolling force. And these influences are hard to measure. All these factors are converted to roll deflection deformation and roll flattening deformation for calculation. In order to calculate the deformation, the theory of influence function method was adopted. By using simulation program, the influence of these factors on deformation was obtained. Then a simple model can be built. With this model, it is convenient to analyze the influence of different factors on gaugemeter equation.

  12. A form of MHD universal equations of unsteady incompressible fluid flow with variable elctroconductivity on heated moving plate

    Directory of Open Access Journals (Sweden)

    Boričić Zoran

    2005-01-01

    Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.

  13. Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients

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    Eleni Bisognin

    2008-03-01

    Full Text Available In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.

  14. Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations

    CERN Document Server

    Loredo, Alexandre

    2013-01-01

    A multilayered plate theory which uses transverse shear warping functions issued from three-dimensional elasticity is presented. Two methods to obtain these transverse shear warping functions are detailed. The warping functions are issued from the variations of transverse shear stresses computed at special location points for a simply supported bending problem. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed by the integration of equilibrium equations. Hence, an iterative process is applied, the model being updated with the new warping functions, and so on. These two models are compared to other models and to analytical solutions for the bending of simply supported plates. Four different laminates and a sandwich are considered, length-to-thickness values varying from 2 to 100. An additional analytical solution that simulates the behavior of laminates under the plane stress hypothesis - ...

  15. Generalized equations of finite difference method in the problems of dynamic load calculation for thin bending plates

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    Gabbasov Radek Fatykhovich

    Full Text Available Bending plate is widely used in the construction of large-span structures. Its advantage is light weight, industrial production, low cost and easy installation. Implementing the algorithm for calculating bending plates in engineering practice is an important issue of the construction science. The generalized equations of finite difference method is a new trend in the calculation of building construction. FDM with generalized equation provides additional options for an engineer along with other methods (FEM. In the article the algorithm for dynamic calculation of thin bending plates basing on FDM was developed. The computer programs for dynamic calculation were created on the basis of the algorithm. The authors come to the conclusion that the more simple equations of FDM can be used in case of solving the impulse load problems in dynamic load calculation of thin bending plate.

  16. Extension of Golay's plate height equation from laminar to turbulent flow I - Theory.

    Science.gov (United States)

    Gritti, Fabrice

    2017-04-07

    The reduced plate height (RPH) equation of Golay derived in 1958 for open tubular columns (OTC) is extended from laminar to turbulent-like flow. The mass balance equation is solved under near-equilibrium conditions in the mobile phase for changing shapes of the velocity profile across the OTC diameter. The final expression of the general RPH equation is: [Formula: see text] where ν is the reduced linear velocity, k is the retention factor, Dm is the bulk diffusion coefficient in the mobile phase, Da¯ is the average axial dispersion coefficient, Dr¯ is the average radial dispersion coefficient, Ds is the diffusion coefficient of the analyte in the stationary film of thickness df, D is the OTC inner diameter, and n≥2 is a positive number controlling the shape of the flow profile (polynomial of degree n). The correctness of the derived RPH equation is verified for Poiseuille (n=2), turburlent-like (n=10), and uniformly flat (n→∞) flow profiles. The derived RPH equation is applied to predict the gain in speed-resolution of a 180μm i.d.×20m OTC (df=2μm) from laminar to turbulent flow in supercritical fluid chromatography. Using pure carbon dioxide as the mobile phase at 297K, k=1, and increasing the Reynolds number from 2000 (laminar) to 4000 (turbulent), the OTC efficiency is expected to increase from 125 to 670 (×5.4) while the hold-up time decreases from 19 to 9s (×0.5). Despite the stronger resistance to mass transfer in the stationary phase, the projected improvement of the column performance in turbulent flow is explained by the quasi-elimination of the resistance to mass transfer in the mobile phase while axial dispersion remains negligible. Copyright © 2017 Elsevier B.V. All rights reserved.

  17. RESEARCH ON THE COMPANION SOLUTION FOR A THIN PLATE IN THE MESHLESS LOCAL BOUNDARY INTEGRAL EQUATION METHOD

    Institute of Scientific and Technical Information of China (English)

    龙述尧; 熊渊博

    2004-01-01

    The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method(GFEM), boundary element method(BEM) and element free Galerkin method(EFGM), and is a truly meshless method possessing wide prospects in engineering applications.The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem.

  18. BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS

    Institute of Scientific and Technical Information of China (English)

    黄家寅

    2004-01-01

    Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction ( z-direction ), the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given; then introducing the dimensionless variables and three small parameters, the dimensionaless governing equations of the deflection function and stress function are given.

  19. Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Singhatanadgid, Pairod; Jommalai, Panupan [Chulalongkorn University, Bangkok (Thailand)

    2016-05-15

    The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.

  20. Boundary integral equation methods and numerical solutions thin plates on an elastic foundation

    CERN Document Server

    Constanda, Christian; Hamill, William

    2016-01-01

    This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...

  1. PLATE

    DEFF Research Database (Denmark)

    Kling, Joyce; Hjulmand, Lise-Lotte

    2008-01-01

    ’s level of English is sufficient for the increasing number of courses offered in English each semester. This paper addresses these concerns and describes a pilot project initiated in 2003 at CBS to gauge the overall English language proficiency of those teaching content courses in English. Through......Copenhagen Business School (CBS) finds itself needing to address the issue of English-medium instruction for its increasing number of foreign exchange and full degree students. With internationalisation as a main pillar of the institution’s agenda, there are concerns whether the teaching faculty...... the Project in Language Assessment for Teaching in English (PLATE) language professionals from CBS’s Language Center observe teachers and provide feedback using evaluation criteria from the Common European Framework for Reference (CEFR) supplemented by some additional criteria which take the LSP nature...

  2. PLATE

    DEFF Research Database (Denmark)

    Kling, Joyce; Hjulmand, Lise-Lotte

    2008-01-01

    Copenhagen Business School (CBS) finds itself needing to address the issue of English-medium instruction for its increasing number of foreign exchange and full degree students. With internationalisation as a main pillar of the institution’s agenda, there are concerns whether the teaching faculty......’s level of English is sufficient for the increasing number of courses offered in English each semester. This paper addresses these concerns and describes a pilot project initiated in 2003 at CBS to gauge the overall English language proficiency of those teaching content courses in English. Through...... the Project in Language Assessment for Teaching in English (PLATE) language professionals from CBS’s Language Center observe teachers and provide feedback using evaluation criteria from the Common European Framework for Reference (CEFR) supplemented by some additional criteria which take the LSP nature...

  3. INTEGRAL EQUATION METHOD'S APPLICATION IN HOLE-EDGE STRESS OF COMPOSITE MATERIAL PLATE WITH DIFFERENT SHAPED HOLES

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material. The holes will lead to mutations and discontinuity to the structure. So the hole-edge stress concentration is always a serious phenomenon. And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points. Most partial damage begins from these weak points. According to the complex variable functions theory, the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes. Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress function. The boundary integral equations are founded based on exact boundary conditions. Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved. Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed. And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made. It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient; and smaller angle of outer load and fiber can decrease the stress peak value.

  4. Asymptotic analysis of the equations and boundary conditions of thermoelasticity of micropolar thin plates

    Directory of Open Access Journals (Sweden)

    Vardanyan S. A.

    2007-09-01

    Full Text Available In the framework of the asymmetrical momental micropolar theory in the present work the boundary value problem of thermal stresses in a three-dimensional thin plate with independent fields of displacements and rotations is studied on the basis of asymptotic method. Depending on the values of physical dimensionless constants of the material three applied two-dimensional theories of thermoelasticity of micropolar thin plate are constructed (theories with independent rotations, with constrained rotations and with small shift rigidity.

  5. SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    LI Cheng; ZHENG Yanping; CHEN Zhongzhong

    2007-01-01

    Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

  6. Heat transfer in plate heat exchanger channels: Experimental validation of selected correlation equations

    Directory of Open Access Journals (Sweden)

    Cieśliński Janusz T.

    2016-09-01

    Full Text Available This study is focused on experimental investigation of selected type of brazed plate heat exchanger (PHEx. The Wilson plot approach was applied in order to estimate heat transfer coefficients for the PHEx passages. The main aim of the paper was to experimentally check ability of several correlations published in the literature to predict heat transfer coefficients by comparison experimentally obtained data with appropriate predictions. The results obtained revealed that Hausen and Dittus-Boelter correlations underestimated heat transfer coefficient for the tested PHEx by an order of magnitude. The Aspen Plate code overestimated heat transfer coefficient by about 50%, while Muley-Manglik correlation overestimated it from 1% to 25%, dependent on the value of Reynolds number and hot or cold liquid side.

  7. Heat transfer in plate heat exchanger channels: Experimental validation of selected correlation equations

    Science.gov (United States)

    Cieśliński, Janusz T.; Fiuk, Artur; Typiński, Krzysztof; Siemieńczuk, Bartłomiej

    2016-09-01

    This study is focused on experimental investigation of selected type of brazed plate heat exchanger (PHEx). The Wilson plot approach was applied in order to estimate heat transfer coefficients for the PHEx passages. The main aim of the paper was to experimentally check ability of several correlations published in the literature to predict heat transfer coefficients by comparison experimentally obtained data with appropriate predictions. The results obtained revealed that Hausen and Dittus-Boelter correlations underestimated heat transfer coefficient for the tested PHEx by an order of magnitude. The Aspen Plate code overestimated heat transfer coefficient by about 50%, while Muley-Manglik correlation overestimated it from 1% to 25%, dependent on the value of Reynolds number and hot or cold liquid side.

  8. Long-time dynamics of two classes of beam and plate equations

    OpenAIRE

    2016-01-01

    In this thesis we will discuss the well-posedness and long-time dynamics of curved beam and thermoelastic plates. First, we considered the Bresse system with nonlinear damping and forcing terms. For this model we show the Timoshenko system as a singular limit of the Bresse system as the arch curvature l goes to 0 and under suitable assumptions on the nonlinearity we prove the existence of a smooth global attractor with finite fractal dimension and exponential attractors as well. We also compa...

  9. Well-posedness and exponential stability for a plate equation with time-varying delay and past history

    Science.gov (United States)

    Feng, Baowei

    2017-02-01

    This paper is concerned with a class of plate equation with past history and time-varying delay in the internal feedback u_{tt}+α Δ ^2 u-int limits ^t_{-∞}g(t-s)Δ ^2 u(s)ds+μ _1u_t+μ _2u_t(t-τ (t))+f(u)=h(x), defined in a bounded domain of {R}^n (n≥1) with some suitable initial data and boundary conditions. For arbitrary real numbers μ _1 and μ _2, we proved the global well-posedness of the problem. Results on stability of energy are also proved under some restrictions on μ _1, μ _2 and h(x)=0.

  10. Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates

    CERN Document Server

    Kitahara, M

    1985-01-01

    The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro

  11. equations

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    1998-01-01

    Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.

  12. Sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation

    CERN Document Server

    Morassi, Antonino; Vessella, Sergio

    2010-01-01

    We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation for the anisotropic plate equation. Among these, we prove a stability estimate for the Cauchy problem for such an equation and we illustrate some applications to the size estimates of an unknown inclusion made of different material that might be present in the plate. The paper is self-contained and the Carleman estimate, from which the sharp three sphere inequality is derived, is proved in an elementary and direct way based on standard integration by parts.

  13. Decoupling of constitutive equations for multi-layered nano-plates embedded in elastic matrix based on non-local elasticity theory using first and higher-order shear deformation theories

    Energy Technology Data Exchange (ETDEWEB)

    Dastjerdi, Shahriar; Aliabadi, Sharifeh; Jabbarzadeh Mehrdad [Islamic Azad University, Tehran (Iran, Islamic Republic of)

    2016-03-15

    The constitutive equations of nano-plates embedded in elastic matrix are derived based on Eringen non-local elasticity theory. Considering the non-local differential constitutive relations of Eringen theory in Cartesian and cylindrical coordinates system based on the first and higher order shear deformation theories and using the Von Karman strain field, the equilibrium differential equations are derived in terms of generalized displacements and rotations. In addition, the obtained governing equations for single layer nano plates are developed for multi-layer nano-plates. Rectangular, annular/circular and sectorial nano-plates are considered. In the most of the investigations in non-local elasticity theory, the classical plate theory (CLPT) is used, however in this paper, the governing equations are derived based on both FSDT and HSDT theories because of obtaining more accurate results.

  14. The capacitance of the circular parallel plate capacitor obtained by solving the Love integral equation using an analytic expansion of the kernel

    CERN Document Server

    Norgren, Martin

    2009-01-01

    The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in accuracy problems at small plate separations. We show that this bottleneck can be alleviated, by calculating all expansion integrals analytically in terms of the Sine and Cosine integrals. Hence, we can, in the approximation of the kernel, use considerably larger matrices, resulting in improved numerical accuracy for the capacitance. In order to improve the accuracy at the smallest separations, we develop a heuristic extrapolation scheme that takes into account the convergence properties of the algorithm. Our results are compared with other numerical results from the literature and with the Kirchhoff result. Error estimates are presented, from which we conclude that our results is a substantial improvement compared with earlier numerical results.

  15. A numerical method for solving the boundary layer equations of laminar natural convention about a vertical plate

    Institute of Scientific and Technical Information of China (English)

    Liancun Zheng; Chen Liang; Xinxin Zhang

    2007-01-01

    An improved shooting method was presented for solving the natural convention boundary layer equations,with a coupling of the velocity field to the temperature field.The numerical results are consistent with the approximate solution obtained by former researchers.

  16. Bending and stretching of plates

    CERN Document Server

    Mansfield, E H; Hemp, W S

    1964-01-01

    The Bending and Stretching of Plates deals with elastic plate theory, particularly on small- and large-deflexion theory. Small-deflexion theory concerns derivation of basic equations, rectangular plates, plates of various shapes, plates whose boundaries are amenable to conformal transformation, plates with variable rigidity, and approximate methods. Large-deflexion theory includes general equations and some exact solutions, approximate methods in large-deflexion theory, asymptotic large-deflexion theories for very thin plates. Asymptotic theories covers membrane theory, tension field theory, a

  17. Linearized Euler Equations for the Determination of Scattering Matrices for Orifice and Perforated Plate Configurations in the High Mach Number Regime

    Directory of Open Access Journals (Sweden)

    Moritz Schulze

    2016-10-01

    Full Text Available The interaction of a plane acoustic wave and a sheared flow is numerically investigated for simple orifice and perforated plate configurations in an isolated, non-resonant environment for Mach numbers up to choked conditions in the holes. Analytical derivations found in the literature are not valid in this regime due to restrictions to low Mach numbers and incompressible conditions. To allow for a systematic and detailed parameter study, a low-cost hybrid Computational Fluid Dynamic/Computational Aeroacoustic (CFD/CAA methodology is used. For the CFD simulations, a standard k–ϵ Reynolds-Averaged Navier–Stokes (RANS model is employed, while the CAA simulations are based on frequency space transformed linearized Euler equations (LEE, which are discretized in a stabilized Finite Element method. Simulation times in the order of seconds per frequency allow for a detailed parameter study. From the application of the Multi Microphone Method together with the two-source location procedure, acoustic scattering matrices are calculated and compared to experimental findings showing very good agreement. The scattering properties are presented in the form of scattering matrices for a frequency range of 500–1500 Hz.

  18. Electronic Equipment Cold Plates

    Science.gov (United States)

    1976-04-01

    equations for such a flow regiae. For laainar flow and Moderate teaperature differwwe« between the well «nd coolant, a aodifled Sieder -Tate...con- figuration. The heat-transfer coefficients, therefore, were determined by using both the Sieder -Tate and McAdams equations and the coaputed...values used In the analytical predictions. As with th* previous cold Plates, the Sieder -Tate equation gave too low of values for the heat- transfer

  19. UNSYMMETRICAL LARGE DEFORMATION PROBLEM OF ORTHOTROPIC PLATES

    Institute of Scientific and Technical Information of China (English)

    王新志; 赵永刚; 叶开沅; 黄达文

    2002-01-01

    Based upon the theory of anisotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations. And the procedure to solve the problem using the iterative method is given.

  20. Modelling of CMUTs with Anisotropic Plates

    DEFF Research Database (Denmark)

    la Cour, Mette Funding; Christiansen, Thomas Lehrmann; Jensen, Jørgen Arendt

    2012-01-01

    Traditionally, CMUTs are modelled using the isotropic plate equation and this leads to deviations between analytical calculations and FEM simulations. In this paper, the deflection profile and material parameters are calculated using the anisotropic plate equation. It is shown that the anisotropic...

  1. Study on the influence of finite element formulation and equation of motion solution scheme on FEM analysis results based on the asymmetrically loaded plate problem

    Directory of Open Access Journals (Sweden)

    Marcin Krzeszowiec

    2015-03-01

    Full Text Available Computer simulations of physical phenomena are at the moment common both in science and industry. The possibility of finding approximate solutions for complicated systems of differential equations, mathematically describing issues in the fields of mechanics, physics or chemistry, allows for shorten design and research time, often significantly reducing the need for expensive experimental studies or costly production of prototypes. However, the mentioned prevalence of these methods, particularly the Finite Element Method, resulted in analysis outcomes to be often in advance regarded as accurate ones. The purpose of the article is to showcase, on a simple stress analysis problem, how parameters such as the density of the finite element mesh, finite element formulation or integration scheme significantly influence on the simulation results and how easy it is to end up with the results that do not hold any physical sense, despite the fact that all the basic assumptions of correct analysis (suitable boundary conditions, total system energy stored etc. have been met. The results of this study can serve as a warning against premature conclusion drawing from calculations carried out by means of FEM simulation.[b]Keywords[/b]: computational mechanics, finite element method, shell elements, numerical integration

  2. Strain resolving method of composite plane plates

    Directory of Open Access Journals (Sweden)

    Ion FUIOREA

    2011-06-01

    Full Text Available The paper deals with the extension of isotropic plates problem to the case of composite plates. In order to perform it, the Kirchhoff-Love hypotheses were “softened” by some additional ones. Considering the constitutive laws for composite materials the stress functions were eliminated by using Cauchy equations. As a result a partial derivative equation in displacements was obtained. Finally the boundary condition formulation was extended for the case of complex composite plates.

  3. Temperature field of steel plate cooling process after plate rolling

    Directory of Open Access Journals (Sweden)

    Huijun Feng, Lingen Chen, Fengrui Sun

    2015-01-01

    Full Text Available Based on numerical calculation with Matlab, the study on cooling process after plate rolling is carried out, and the temperature field distribution of the plate varying with the time is obtained. The effects of the plate thickness, final rolling temperature, cooling water temperature, average flow rate of the cooling water, carbon content of the plate and cooling method on the plate surface and central temperatures as well as final cooling temperature are discussed. For the same cooling time, the plate surface and central temperatures as well as their temperature difference increase; with the decrease in rolling temperature and the increase in average flow rate of the cooling water, the plate surface and central temperatures decrease. Compared with the single water cooling process, the temperature difference between the plate centre and surface based on intermittent cooling is lower. In this case, the temperature uniformity of the plate is better, and the corresponding thermal stress is lower. The fitting equation of the final cooling temperature with respect to plate thickness, final rolling temperature, cooling water temperature and average flow rate of the cooling water is obtained.

  4. 压电材料的K正则方程及其层合板的显式辛算法%SEPARABLE K-CANONICAL EQUATION OF PIEZOELECTRICITY AND EXPLICIT SYMPLECTIC METHOD FOR LAMINATED PLATES

    Institute of Scientific and Technical Information of China (English)

    卿光辉; 王亚辉; 李顶河

    2011-01-01

    In the application of symplectic numerical methods to Hamiltonian systems, it is important to recognize that a nearby Hamiltonian is approximately conserved for.exponentially long times. The numerical result of separable differential equation is very accurate by using the symplectic numerical methods. Based on the modified Hellinger-Reissner (H-R) variational principle of piezoelectricity, Hamiltonian four-node rectangular element matrix was constructed in this paper. Then the separable K-canonical formulation of the Hamiltonian element was derived by exchanging the row-column of Hamiltonian element formulation. Finally, the explicit symplectic schemes was employed to solve the static problem of piezoelectric material laminated plate. The numerical examples show that the explicit symplectic method can be applied to the large-scale differential equation.%显式辛数值算法有一个重要的特性,即在长时间内保存Hamilton函数的指数幂,用这种方法求解可分的微分方程所得到的解逼近精确解.该文基于压电材料修正后的H-R混合变分原理,首先推导了Hamiltonian四节点有限元列式,然后通过对该列式进行行列变换,得到了K正则方程.最后将显式辛数值算法用于求解压电材料层合板的静力学问题,数值算例说明显式辛数值算法完全可以应用到高维的微分方程中.

  5. Analytical solution for multilayer plates using general layerwise plate theory

    Directory of Open Access Journals (Sweden)

    Vuksanović Đorđe M.

    2005-01-01

    Full Text Available This paper deals with closed-form solution for static analysis of simply supported composite plate, based on generalized laminate plate theory (GLPT. The mathematical model assumes piece-wise linear variation of in-plane displacement components and a constant transverse displacement through the thickness. It also include discrete transverse shear effect into the assumed displacement field, thus providing accurate prediction of transverse shear stresses. Namely, transverse stresses satisfy Hook's law, 3D equilibrium equations and traction free boundary conditions. With assumed displacement field, linear strain-displacement relation, and constitutive equations of the lamina, equilibrium equations are derived using principle of virtual displacements. Navier-type closed form solution of GLPT, is derived for simply supported plate, made of orthotropic laminae, loaded by harmonic and uniform distribution of transverse pressure. Results are compared with 3D elasticity solutions and excellent agreement is found.

  6. On the Quintic Nonlinear Schrödinger Equation Created by the Vibrations of a Square Plate on a Weakly Nonlinear Elastic Foundation and the Stability of the Uniform Solution

    OpenAIRE

    Nohara, Ben T.; Arimoto, Akio

    2007-01-01

    Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this...

  7. Numerical Investigation on Submerged Horizontal Plate

    Institute of Scientific and Technical Information of China (English)

    康海贵; 王科

    2001-01-01

    Hydrodynamic characters on a horizontal, thin, rigid plate located beneath the free surface are numerically investigated. Assuming a linear, time-harmonic potential flow and utilizing Green identity, the governing Laplace equation can be simplified into Fredholm integral equation ofthe second kind. Supposing linear-order discontinuous elements along intersecting vertical boundaries, and by use of the boundary element method, numerical solution about source strength distribution on the plate can be changed into a series of algebraic equations. The 3D Green function is introduced to set up the integral equations, and the GMRES solver is performed for solving the large dense linear system of equations. The added-mass, damping force and exciting force are evaluated directly from the equations. It is found that the added-mass coefficient becomes negative for a range of frequencies when the plate is sufficiently close to the free surface.

  8. Amplification of acoustic waves in laminated piezoelectric semiconductor plates

    Energy Technology Data Exchange (ETDEWEB)

    Yang, J.S.; Yang, X.M.; Turner, J.A. [University of Nebraska, Department of Engineering Mechanics, Lincoln, NE (United States)

    2004-12-01

    Two-dimensional equations for coupled extensional, flexural and thickness-shear motions of laminated plates of piezoelectric semiconductors are obtained systematically from the three-dimensional equations by retaining lower order terms in power series expansions in the plate thickness coordinate. The equations are used to analyze extensional waves in a composite plate of piezoelectric ceramics and semiconductors. Dispersion and dissipation due to semiconduction as well as wave amplification by a dc electric field are discussed. (orig.)

  9. Coupling between plate vibration and acoustic radiation

    Science.gov (United States)

    Frendi, Abdelkader; Maestrello, Lucio; Bayliss, Alvin

    1993-01-01

    A detailed numerical investigation of the coupling between the vibration of a flexible plate and the acoustic radiation is performed. The nonlinear Euler equations are used to describe the acoustic fluid while the nonlinear plate equation is used to describe the plate vibration. Linear, nonlinear, and quasi-periodic or chaotic vibrations and the resultant acoustic radiation are analyzed. We find that for the linear plate response, acoustic coupling is negligible. However, for the nonlinear and chaotic responses, acoustic coupling has a significant effect on the vibration level as the loading increases. The radiated pressure from a plate undergoing nonlinear or chaotic vibrations is found to propagate nonlinearly into the far field. However, the nonlinearity due to wave propagation is much weaker than that due to the plate vibrations. As the acoustic wave propagates into the far field, the relative difference in level between the fundamental and its harmonics and subharmonics decreases with distance.

  10. Theories for Elastic Plates via Orthogonal Polynomials

    DEFF Research Database (Denmark)

    Krenk, Steen

    1981-01-01

    A complementary energy functional is used to derive an infinite system of two-dimensional differential equations and appropriate boundary conditions for stresses and displacements in homogeneous anisotropic elastic plates. Stress boundary conditions are imposed on the faces a priori...

  11. Dynamics of Tectonic Plates

    CERN Document Server

    Pechersky, E; Sadowski, G; Yambartsev, A

    2014-01-01

    We suggest a model that describes a mutual dynamic of tectonic plates. The dynamic is a sort of stick-slip one which is modeled by a Markov random process. The process defines a microlevel of the dynamic. A macrolevel is obtained by a scaling limit which leads to a system of integro-differential equations which determines a kind of mean field systems. Conditions when Gutenberg-Richter empirical law are presented on the mean field level. These conditions are rather universal and do not depend on features of resistant forces.

  12. Dynamics of Tectonic Plates

    OpenAIRE

    2014-01-01

    We suggest a model that describes a mutual dynamic of tectonic plates. The dynamic is a sort of stick-slip one which is modeled by a Markov random process. The process defines a microlevel of the dynamic. A macrolevel is obtained by a scaling limit which leads to a system of integro-differential equations which determines a kind of mean field systems. Conditions when Gutenberg-Richter empirical law are presented on the mean field level. These conditions are rather universal and do not depend ...

  13. Create Your Plate

    Medline Plus

    Full Text Available ... A A A Listen En Español Create Your Plate Create Your Plate is a simple and effective ... and that your options are endless. Create Your Plate! Click on the plate sections below to add ...

  14. ANALYTICAL RELATIONS BETWEEN EIGENVALUES OF CIRCULAR PLATE BASED ON VARIOUS PLATE THEORIES

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory(CPT), the first-order shear deformation plate theory(FPT) and the Reddy's third-order shear deformation plate theory(RPT), analytical relations between the eigenvalues of circular plate based on various plate theories are investigated. In the present paper, the eigenvalue problem is transformed to solve an algebra equation. Analytical relationships that are expressed explicitly between various theories are presented. Therefore, from these relationships one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequencyfor a circular plate with CPT solutions. The relationships are useful for engineering application, and can be used to check the validity, convergence and accuracy of numerical results for the eigenvalue problem of plates.

  15. Modeling and Measurements of CMUTs with Square Anisotropic Plates

    DEFF Research Database (Denmark)

    la Cour, Mette Funding; Christiansen, Thomas Lehrmann; Dahl-Petersen, Christian;

    2013-01-01

    The conventional method of modeling CMUTs use the isotropic plate equation to calculate the deflection, leading to deviations from FEM simulations including anisotropic effects of around 10% in center deflection. In this paper, the deflection is found for square plates using the full anisotropic...... plate equation and the Galerkin method. Utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is

  16. RAYLEIGH LAMB WAVES IN MICROPOLAR ISOTROPIC ELASTIC PLATE

    Institute of Scientific and Technical Information of China (English)

    Rajneesh Kumar; Geeta Partap

    2006-01-01

    The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit,the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.

  17. The postbuckling analysis of laminated circular plate with elliptic delamination

    Science.gov (United States)

    Chen, Deliang; Chen, Changping; Fu, Yiming

    2011-01-01

    Based on the Von Karman plate theory, considering the effect of transverse shear deformation, and using the method of the dissociated three regions, the postbuckling governing equations for the axisymmetric laminated circular plates with elliptical delamination are derived. By using the orthogonal point collocation method, the governing equations, boundary conditions and continuity conditions are transformed into a group of nonlinear algebraically equation and the equations are solved with the alternative method. In the numerical examples, the effects of various elliptical in shape, delamination depth and different material properties on buckling and postbuckling of the laminated circular plates are discussed and the numerical results are compared with available data.

  18. An Analysis of Elasto-Plastic Bending of Rectangular Plate

    OpenAIRE

    Matsuda, Hiroshi; Sakiyama, Takeshi

    1988-01-01

    In this paper, a discrete method for analyzing the problem of elasto-plastic bending of a rectangular plate is proposed. The solutions for partial differential equation of rectangular plate are obtained in discrete forms by applying numerical integnltion. An incremental variable elasticity procedure has been used for the clasta-plastic analysis of the rectangular plate. As the applications of the proposed method, clasta-plastic bending of rectangular plate with four types of boundary conditio...

  19. Mathematical methods for elastic plates

    CERN Document Server

    Constanda, Christian

    2014-01-01

    Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff’s classical one.   The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions.   The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex ana...

  20. A new refined theory of plates with transverse shear deformation for moderately thick and thick plates

    CERN Document Server

    Valle, Jose Miguel Martinez

    2015-01-01

    In this paper we propose a new refined shear deformation plate theory which possesses a series of desirable features, the most salient of which are as follows: (i) The loads, which are generally considered to be applied on the middle surface of the plate, act on the upper surface of the plate; (ii) The equations are applicable to the calculation of the stresses in isotropic plates and provide the same order of accuracy as several theories with second order shear deformation effects; (iii) It constitutes a theory, in the sense defined by Love, since it gives easy expressions for application to problems in different fields in architecture and civil engineering

  1. Chaotic Motion of Corrugated Circular Plates

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Large deflection theory of thin anisotropic circular plates was used to analyze the bifurcation behavior and chaotic phenomena of a corrugated thin circular plate with combined transverse periodic excitation and an in-plane static boundary load. The nonlinear dynamic equation for the corrugated plate was derived by employing Galerkin's technique. The critical conditions for occurrence of the homoclinic and subharmonic bifurcations as well as chaos were studied theoretically using the Melnikov function method. The chaotic motion was also simulated numerically using Maple, with the Poincaré map and phase curve used to evaluate when chaotic motion appears. The results indicate some chaotic motion in the corrugated plate. The method is directly applicable to chaotic analysis of an isotropic circular plate.

  2. FLEXURAL WAVE PROPAGATION IN NARROW MINDLIN'S PLATE

    Institute of Scientific and Technical Information of China (English)

    HU Chao; HAN Gang; FANG Xue-qian; HUANG Wen-hu

    2006-01-01

    Appling Mindlin's theory of thick plates and Hamilton system to propagation of elastic waves under free boundary condition, a solution of the problem was given.Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method. It was compared with the dispersion relation that was gained through solution of thick plate theory proposed by Mindlin. Based on the two kinds of theories,the dispersion curves show great difference in the region of short waves, and the cutoff frequencies are higher in Hamiltonian systems. However, the dispersion curves are almost the same in the region of long waves.

  3. GENERALIZED VARIATIONAL PRINCIPLESFOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

    Institute of Scientific and Technical Information of China (English)

    ShengDongfa; ChengChangjun

    2004-01-01

    From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.

  4. Modelling conjugation with stochastic differential equations

    DEFF Research Database (Denmark)

    Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

    2010-01-01

    Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...

  5. Processless offset printing plates

    Directory of Open Access Journals (Sweden)

    Sanja Mahović Poljaček

    2015-06-01

    Full Text Available With the implementation of platesetters in the offset printing plate making process, imaging of the printing plate became more stable and ensured increase of the printing plate quality. But as the chemical processing of the printing plates still highly influences the plate making process and the graphic reproduction workflow, development of printing plates that do not require chemical processing for offset printing technique has been one of the top interests in graphic technology in the last few years. The main reason for that came from the user experience, where majority of the problems with plate making process could be connected with the chemical processing of the printing plate. Furthermore, increased environmental standards lead to reducing of the chemicals used in the industrial processes. Considering these facts, different types of offset printing plates have been introduced to the market today. This paper presents some of the processless printing plates.

  6. Thermoelastic wave propagation in laminated composites plates

    Directory of Open Access Journals (Sweden)

    Verma K. L.

    2012-12-01

    Full Text Available The dispersion of thermoelastic waves propagation in an arbitrary direction in laminated composites plates is studied in the framework of generalized thermoelasticity in this article. Three dimensional field equations of thermoelasticity with relaxation times are considered. Characteristic equation is obtained on employing the continuity of displacements, temperature, stresses and thermal gradient at the layers’ interfaces. Some important particular cases such as of free waves on reducing plates to single layer and the surface waves when thickness tends to infinity are also discussed. Uncoupled and coupled thermoelasticity are the particular cases of the obtained results. Numerical results are also obtained and represented graphically.

  7. Hill's equation

    CERN Document Server

    Magnus, Wilhelm

    2004-01-01

    The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period

  8. Elasto-plastic postbuckling of damaged orthotropic plates

    Institute of Scientific and Technical Information of China (English)

    TIAN Yan-ping; FU Yi-ming

    2008-01-01

    Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.

  9. The problem of isotropic rectangular plate with four clamped edges

    Indian Academy of Sciences (India)

    C Erdem İmrak; Ismail Gerdemeli

    2007-06-01

    The examination of the exact solution of the governing equation of the rectangular plate is important for many reasons. This report discusses in exact solution of the governing equation of an isotropic rectangular plate with four clamped edges. A numerical method for clamped isotropic rectangular plate under distributed loads and an exact solution of the governing equation in terms of trigonometric and hyperbolic function are given. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

  10. Large Deflections of Elastic Rectangular Plates

    Science.gov (United States)

    Razdolsky, A. G.

    2015-11-01

    It is known that elastic large deflections of thin plates are governed by von Karman nonlinear equations. The analytical solution of these equations in the general case is unfeasible. Samuel Levy, in 1942, showed that large deflections of the rectangular plate can be expressed as a double series of sine-shaped harmonics (deflection harmonics). However, this method gave no way of creating the computer algorithm of solving the problem. The stress function expression taken in the Levy's method must be revised to find the approach that takes into account of all possible products of deflection coefficients. The algorithm of solving the problem for the rectangular plate with an arbitrary aspect ratio under the action of the lateral distributed load is reported in this paper. The approximation of the plate deflection is taken in the form of double series proposed by Samuel Levy. However, the expression for the stress function is presented in the form that incorporates products of deflection coefficients in the explicit form in distinction to the Levy's expression. The number of harmonics in the deflection expression may be arbitrary. The algorithm provides composing the system of governing cubic equations, which includes the deflection coefficients in the explicit form. Solving the equation system is based on using the principle of minimum potential energy. A method of the gradient descent is applied to find the equilibrium state of the plate as the minimum point of the potential energy. A computer program is developed on the basis of the present algorithm. Numerical examples carried out for the plate model with 16 deflection harmonics illustrate the potentialities of the program. The results of solving the examples are presented in the graphical form for the plates with a different aspect ratio and may be used under designing thin-walled elements of airplane and ship structures.

  11. Investigation of acoustic field near to elastic thin plate using integral method

    Directory of Open Access Journals (Sweden)

    В.І. Токарев

    2004-01-01

    Full Text Available  Investigation of acoustic field near to elastic thin plate using  integral method The influence of boundary conditions on sound wave propagation, radiation and transmission through thin elastic plate is investigated. Necessary for that numerical model was found using the Helmholtz equation and equation of oscilated plate by means of integral formulation of the solution for acoustic fields near to elastic thin plate and for bending waves of small amplitudes.

  12. Closed form solutions for free vibrations of rectangular Mindlin plates

    Institute of Scientific and Technical Information of China (English)

    Yufeng Xing; Bo Liu

    2009-01-01

    A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate.

  13. Modeling of plates with multiple anisotropic layers and residual stress

    DEFF Research Database (Denmark)

    Engholm, Mathias; Pedersen, Thomas; Thomsen, Erik Vilain

    2016-01-01

    Usually the analytical approach for modeling of plates uses the single layer plate equation to obtain the deflection and does not take anisotropy and residual stress into account. Based on the stress–strain relation of each layer and balancing stress resultants and bending moments, a general...... multilayered anisotropic plate equation is developed for plates with an arbitrary number of layers. The exact deflection profile is calculated for a circular clamped plate of anisotropic materials with residual bi-axial stress.From the deflection shape the critical stress for buckling is calculated......, and an excellent agreement between the two models is seen with a relative difference of less than 2% for all calculations. The model was also used to extract the cell capacitance, the parasitic capacitance and the residual stress of a pressure sensor composed of a multilayered plate of silicon and silicon oxide...

  14. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  15. Create Your Plate

    Medline Plus

    Full Text Available ... steps to get started: Using your dinner plate, put a line down the middle of the plate. ... vegetables . Now in one of the small sections, put grains and starchy foods. See this list of ...

  16. Create Your Plate

    Medline Plus

    Full Text Available ... Your Plate It's simple and effective for both managing diabetes and losing weight. Creating your plate lets ... 2016 Articles from Diabetes Forecast® magazine: wcie-meal-planning, In this section Food Planning Meals Diabetes Meal ...

  17. Create Your Plate

    Medline Plus

    Full Text Available ... Your Plate Gluten Free Diets Meal Planning for Vegetarian Diets Cook with Heart-Healthy Foods Holiday Meal ... Healthy Diet Create Your Plate Meal Planning for Vegetarian Diets Gluten Free Diets Holiday Meal Planning Cook ...

  18. Food guide plate

    Science.gov (United States)

    ... chips or cookies. VEGETABLES: MAKE HALF OF YOUR PLATE FRUITS AND VEGETABLES Vegetables can be raw, fresh, ... as a snack. FRUITS: MAKE HALF OF YOUR PLATE FRUITS AND VEGETABLES Fruits can be fresh, canned, ...

  19. Growth Plate Fractures

    Science.gov (United States)

    ... the most widely used by doctors is the Salter-Harris system, described below. Type I Fractures These ... incidence of growth plate fractures peaks in adolescence. Salter-Harris classification of growth plate fractures. AAOS does ...

  20. Create Your Plate

    Medline Plus

    Full Text Available ... Planning Meals Diabetes Meal Plans Create Your Plate Gluten Free Diets Meal Planning for Vegetarian Diets Cook ... Create Your Plate Meal Planning for Vegetarian Diets Gluten Free Diets Holiday Meal Planning Cook with Heart- ...

  1. Create Your Plate

    Medline Plus

    Full Text Available ... Planning Meals Diabetes Meal Plans Create Your Plate Gluten Free Diets Meal Planning for Vegetarian Diets Cook ... Create Your Plate Meal Planning for Vegetarian Diets Gluten Free Diets Holiday Meal Planning Cook with Heart- ...

  2. Create Your Plate

    Medline Plus

    Full Text Available ... Your Plate It's simple and effective for both managing diabetes and losing weight. Creating your plate lets you still choose the foods you want, but changes the portion sizes so you are getting larger ...

  3. Create Your Plate

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    Full Text Available ... Your Plate It's simple and effective for both managing diabetes and losing weight. Creating your plate lets ... Sleeve Custom jerseys for your Tour de Cure team benefits the cause. Ask the Experts: Learn to ...

  4. Numerical Wave Flume Study on Wave Motion Around Submerged Plates

    Institute of Scientific and Technical Information of China (English)

    齐鹏; 侯一筠

    2003-01-01

    Nonlinear interaction between surface waves and a submerged horizontal plate is investigated in the absorbed numerical wave flume developed based on the volume of fluid (VOF) method. The governing equations of the numerical model are the continuity equation and the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ε turbulence equations. Incident waves are generated by an absorbing wave-maker that eliminates the waves reflected from structures. Results are obtained for a range of parameters, with consideration of the condition under which the reflection coefficient becomes maximal and the transmission coefficient minimal. Wave breaking over the plate, vortex shedding downwave, and pulsating flow below the plate are observed. Time-averaged hydrodynamic force reveals a negative drift force. All these characteristics provide a reference for construction of submerged plate breakwaters.

  5. Null controllability of a thermoelastic plate

    Directory of Open Access Journals (Sweden)

    Assia Benabdallah

    2002-01-01

    Full Text Available Thermoelastic plate model with a control term in the thermal equation is considered. The main result in this paper is that with thermal control, locally distributed within the interior and square integrable in time and space, any finite energy solution can be driven to zero at the control time T.

  6. Accelerated plate tectonics.

    Science.gov (United States)

    Anderson, D L

    1975-03-21

    The concept of a stressed elastic lithospheric plate riding on a viscous asthenosphere is used to calculate the recurrence interval of great earthquakes at convergent plate boundaries, the separation of decoupling and lithospheric earthquakes, and the migration pattern of large earthquakes along an arc. It is proposed that plate motions accelerate after great decoupling earthquakes and that most of the observed plate motions occur during short periods of time, separated by periods of relative quiescence.

  7. Buckling and Multiple Equilibrium States of Viscoelastic Rectangular Plates

    Institute of Scientific and Technical Information of China (English)

    1999-01-01

    On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro-partial-differential equations is first presented by means of a structural function introduced in this paper. Then,by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro-partial-differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.

  8. The sound transmission of finite ribbed plates using a variational

    DEFF Research Database (Denmark)

    Brunskog, Jonas

    2012-01-01

    Many lightweight structures consist of plates being stiffened by ribs. The rib stiffeners can significantly change the vibration field and the radiation behavior of the structure. These type of structures has thus often been studied in the past. However, there is a lack of simplified expressions...... for the sound transmission of these structures. Therefore, simplified expressions for the sound transmission of finite single leaf ribbed plates are derived, using a variational technique based on integral equations of the fluid loaded plate....

  9. A New Approximate Fundamental Solution for Orthotropic Plate

    Institute of Scientific and Technical Information of China (English)

    WU Pei-liang; L(U) Yan-ping

    2002-01-01

    A weight double trigonometric series is presented as an approximate fundamental solution for orthotropic plate.Integral equation of orthotropic plate bending is solved by a new method, which only needs one basic boundary integral Eq., puts one fictitious boundary outside plate domain. Examples show that the approximate fundamental solution and solving method proposed in this paper are simple, reliable and quite precise. And they are applicable for various boundary conditions.

  10. Create Your Plate

    Medline Plus

    Full Text Available ... Reset Plate Share Create Your Plate ! Share: Seven Simple Steps to Create Your Plate It's simple and effective for both managing diabetes and losing ... en.html Have Type 2 Diabetes? Our free program will help you live well. More from diabetes. ...

  11. Obliquity along plate boundaries

    Science.gov (United States)

    Philippon, Mélody; Corti, Giacomo

    2016-12-01

    Most of the plate boundaries are activated obliquely with respect to the direction of far field stresses, as roughly only 8% of the plate boundaries total length shows a very low obliquity (ranging from 0 to 10°, sub-orthogonal to the plate displacement). The obliquity along plate boundaries is controlled by (i) lateral rheological variations within the lithosphere and (ii) consistency with the global plate circuit. Indeed, plate tectonics and magmatism drive rheological changes within the lithosphere and consequently influence strain localization. Geodynamical evolution controls large-scale mantle convection and plate formation, consumption, and re-organization, thus triggering plate kinematics variations, and the adjustment and re-orientation of far field stresses. These geological processes may thus result in plate boundaries that are not perpendicular but oblique to the direction of far field stresses. This paper reviews the global patterns of obliquity along plate boundaries. Using GPlate, we provide a statistical analysis of present-day obliquity along plate boundaries. Within this framework, by comparing natural examples and geological models, we discuss deformation patterns and kinematics recorded along oblique plate boundaries.

  12. Lateral heat transfer in conducting and mutually irradiating plates

    Energy Technology Data Exchange (ETDEWEB)

    Krishnaprakas, C.K.; Badari Narayana, K. [Thermal Systems Group, ISRO Satellite Centre, Bangalore 560 017 (India)

    2004-05-01

    Lateral heat transfer effect in conducting and mutually irradiating parallel plates has been investigated. The effect of reflection in the diffuse-specular regime has been included. The governing equation of this problem is a complicated integro-differential equation, and this has been solved using the accurate Gauss-Jacobi orthogonal collocation method. The effective thermal conductivity along the lateral direction increases with decreasing conduction-radiation number, increasing emittance of the plates and increasing spacing. Specular reflection effects are insignificant. (orig.)

  13. Riccati equations

    Directory of Open Access Journals (Sweden)

    Lloyd K. Williams

    1987-01-01

    Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.

  14. Closed-form solution for free vibration of piezoelectric coupled annular plates using Levinson plate theory

    Science.gov (United States)

    Hosseini Hashemi, Sh.; Es'haghi, M.; Karimi, M.

    2010-04-01

    Free vibration analysis of annular moderately thick plates integrated with piezoelectric layers is investigated in this study for different combinations of soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the Levinson plate theory (LPT). The distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the Maxwell static electricity equation is approximately satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. In this study the closed-form solution for characteristic equations, displacement components of the plate and electric potential are derived for the first time in the literature. To demonstrate the accuracy of the present solution, comparison studies is first carried out with the available data in the literature and then natural frequencies of the piezoelectric coupled annular plate are presented for different thickness-radius ratios, inner-outer radius ratios, thickness of piezoelectric, material of piezoelectric and boundary conditions. Present analytical model provides design reference for piezoelectric material application, such as sensors, actuators and ultrasonic motors.

  15. Equation poems

    Science.gov (United States)

    Prentis, Jeffrey J.

    1996-05-01

    One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.

  16. Penetration equations

    Energy Technology Data Exchange (ETDEWEB)

    Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)

    1997-10-01

    In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.

  17. Solution of non-rectangular plates with macroelement method

    Science.gov (United States)

    Delyavskyy, Mykhaylo; Rosinski, Krystian

    2017-03-01

    New approach to static analysis of thin non-rectangular arbitrarily loaded plates, called the macroelement method, has been developed in this paper. Macroelement is a rectangular plate which entirely contains real plate. The mathematical model of macroelement was built. The equilibrium equations are performed for macroelement and boundary conditions are written on the line corresponding to contour of real plate in the nodes which are zero points of trigonometric functions, included in the macroelement model. The load is applied only to separate nodes on the surface of real plate, whereas the complement of a plate to macroelement is unloaded. Analysis of construction is reduced to solving a system of linear algebraic equations. The method provides better accuracy compared to finite element method and requires less equations. There is trapeze plate clamped at inclined edge and simply supported at opposite one considered in this paper. The other edges of the plate are free. Uniformly distributed load on the surface of real plate is taken into account.

  18. Angular shear plate

    Science.gov (United States)

    Ruda, Mitchell C [Tucson, AZ; Greynolds, Alan W [Tucson, AZ; Stuhlinger, Tilman W [Tucson, AZ

    2009-07-14

    One or more disc-shaped angular shear plates each include a region thereon having a thickness that varies with a nonlinear function. For the case of two such shear plates, they are positioned in a facing relationship and rotated relative to each other. Light passing through the variable thickness regions in the angular plates is refracted. By properly timing the relative rotation of the plates and by the use of an appropriate polynomial function for the thickness of the shear plate, light passing therethrough can be focused at variable positions.

  19. Modelling conjugation with stochastic differential equations.

    Science.gov (United States)

    Philipsen, K R; Christiansen, L E; Hasman, H; Madsen, H

    2010-03-07

    Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.

  20. Bending and buckling behavior analysis of foamed metal circular plate.

    Science.gov (United States)

    Fan, Jian Ling; Ma, Lian Sheng; Zhang, Lu; De Su, Hou

    2016-07-04

    This paper establishes a density gradient model along the thickness direction of a circular plate made of foamed material. Based on the first shear deformation plate theory, the result is deduced that the foamed metal circular plate with graded density along thickness direction yields axisymmetric bending problem under the action of uniformly distributed load, and the analytical solution is obtained by solving the governing equation directly. The analyses on two constraint conditions of edge radial clamping and simply supported show that the density gradient index and external load may affect the axisymmetric bending behavior of the plate. Then, based on the classical plate theory, the paper analyzes the behavior of axisymmetric buckling under radial pressure applied on the circular plate. Shooting method is used to obtain the critical load, and the effects of gradient nature of material properties and boundary conditions on the critical load of the plate are analyzed.

  1. 1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES

    Institute of Scientific and Technical Information of China (English)

    李银山; 张年梅; 杨桂通

    2003-01-01

    The problem of nonlinear forced oscillations for elliptical sandwich plates is dealtwith. Based on the governing equations expressed in terms of five displacement components,the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force isderived. A superpositive-iterative harmonic balance ( SIHB ) method is presented for thesteady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodicsolutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus,an oscillation system which is described as a second order ordinary differential equation,can be expressed as fundamental differential equation with fundamental harmonics andincremental differential equation with derived harmonics. The 1/3 subharnonic solution ofan elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB methodis compared with the numerical integration method. Finally, asymptotical stability of the1/3 subharmonic oscillations is inspected.

  2. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  3. Exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (Ⅰ)——Exact solutions for piezoelectric circular plate

    Institute of Scientific and Technical Information of China (English)

    丁皓江; 徐荣桥; 国凤林

    1999-01-01

    Based on three-dimensional elastic equations for piezoelectric materials, the state equations for piezoelectric circular plate under axisymmetric deformation are derived. Applying Hankel transform to them and letting the free boundary terms resulting from Hankel transform be zero, a set of ordinary differential equations with constant coefficients and associated boundary conditions are obtained. Furthermore, two exact solutions corresponding to generalized rigid slipping and generalized elastic simple support are deduced. Then, the governing equations obtained reduce to equations for axisymmetric problem of transversely isotropic circular plate. Under the two types of boundary conditions of elastic simple support and rigid slipping, exact solutions are derived. Finally, numerical results are presented and applicability of the classical plate theory is discussed.

  4. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  5. Thermal Analysis of Thin Plates Using the Finite Element Method

    Science.gov (United States)

    Er, G. K.; Iu, V. P.; Liu, X. L.

    2010-05-01

    The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis.

  6. Transfer function modeling of damping mechanisms in viscoelastic plates

    Science.gov (United States)

    Slater, J. C.; Inman, D. J.

    1991-01-01

    This work formulates a method for the modeling of material damping characteristics in plates. The Sophie German equation of classical plate theory is modified to incorporate hysteresis effects represented by complex stiffness using the transfer function approach proposed by Golla and Hughes, (1985). However, this procedure is not limited to this representation. The governing characteristic equation is decoupled through separation of variables, yielding a solution similar to that of undamped classical plate theory, allowing solution of the steady state as well as the transient response problem.

  7. LARGE AMPLITUDE FREE VIBRATIONS OF LAMINATED COMPOSITE PLATES

    Institute of Scientific and Technical Information of China (English)

    Wang Haowen; Gao Zheng; Zheng Zhaochang

    2000-01-01

    This paper deals with large amplitude free flexural vibrations of laminated composite plates using a 9-node Heterosis degenerated isoparametric quadrilateral element, including the effects of transverse shear and rotary inertia. The nonlinear dynamic equations of the plates are formulated in von Karman's sense. Amplitude-frequemcy relationships are obtained through dynamic response history using the Newmark numerical integration scheme. Detailed numerical results based on various parameters are presented for orthotropic laminated plates with different boundary conditions. The rectangular anti-symmetric cross-ply plates show the softening type of nonlinearity for initial small amplitudes. The displacement amplitudes decrease and nonlinear frequencies increase with the increment of time.

  8. ANALYSIS OF GLOBAL DYNAMICS IN A PAIAMETIICALLY EXCITED THIN PLATE

    Institute of Scientific and Technical Information of China (English)

    张伟

    2001-01-01

    The global bifurcations and chaos of a simply supported rectangular thin plate with parametric excitation are analyzed. The formulas of the thin plate are derived by yon Karman type equation and Galerkin's approach. The method of multiple scales is used to obtain the averaged equations. Based on the averaged equations, the theory of the normal form is used to give the explicit expressions of the normal form associated with a double zero and a pair of pure imaginary eigenvalues by Maple program. On the basis of the normal form, a global bifurcation analysis of the parametrically excited recta ngular thin plate is given by the global perturbation method developed by Kovacic and Wiggins. The chaotic motion of thin plate is also found by numerical simulation.

  9. A Geometrically—Nonlinear Plate Theory 12

    Institute of Scientific and Technical Information of China (English)

    AlbertC.J.LUO

    1999-01-01

    An approximate plate theory developed in this paper is based on an assumed displacement field,the strains described by a Taylor series in the normal distance from the middle surface,the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface,In this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of the plate.Application of this theory does not depend on the constitutive law.THis theory can reduce to some existing nonlinear theories through imposition of constraints.

  10. Finite stretching of an annular plate.

    Science.gov (United States)

    Biricikoglu, V.; Kalnins, A.

    1971-01-01

    The problem of the finite stretching of an annular plate which is bonded to a rigid inclusion at its inner edge is considered. The material is assumed to be isotropic and incompressible with a Mooney-type constitutive law. It is shown that the inclusion of the effect of the transverse normal strain leads to a rapid variation in thickness which is confined to a narrow edge zone. The explicit solutions to the boundary layer equations, which govern the behavior of the plate near the edges, are presented.

  11. Generalized Fibonacci zone plates

    CERN Document Server

    Ke, Jie; Zhu, Jianqiang

    2015-01-01

    We propose a family of zone plates which are produced by the generalized Fibonacci sequences and their axial focusing properties are analyzed in detail. Compared with traditional Fresnel zone plates, the generalized Fibonacci zone plates present two axial foci with equal intensity. Besides, we propose an approach to adjust the axial locations of the two foci by means of different optical path difference, and further give the deterministic ratio of the two focal distances which attributes to their own generalized Fibonacci sequences. The generalized Fibonacci zone plates may allow for new applications in micro and nanophotonics.

  12. Solving the problem of elasticity for round thick plates at axially symmetric strain

    Directory of Open Access Journals (Sweden)

    Oleksiy Hvertsev

    2016-12-01

    Full Text Available An exact solution of the equations of elasticity for round plates loaded axially symmetric. The problem of bending round plates, which are under the influence of normal forces attached to any law to load any type of resistance. It is shown that pasture circular plate under axially symmetric load leads to appearance of temperature field.

  13. General Analytical Solution of Transverse Vibration For Orthotropic Rectangular Thin Plates

    Institute of Scientific and Technical Information of China (English)

    HUANG; Yan; ZHANG; Xiao-jin

    2002-01-01

    A general solution of differential equation for transverse displacement function of orthotropic rectangular thin plates in free vibration is established in this paper. It can be used to solve the vibration problem of plate with arbitrary boundaries. As an example, the frequencies of a composite laminated plate with four free edges have been solved. The result as compared with the experiment is satisfactory.

  14. Nonlinear dynamic buckling of stiffened plates under in-plane impact load

    Institute of Scientific and Technical Information of China (English)

    张涛; 刘土光; 赵耀; 罗家智

    2004-01-01

    This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Appling the Hamilton's principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained form Budiansky-Roth criterion.

  15. DYNAMIC BUCKLING OF STIFFENED PLATES UNDER FLUID-SOLID IMPACT LOAD

    Institute of Scientific and Technical Information of China (English)

    张涛; 刘土光; 熊有伦; 张维衡

    2004-01-01

    A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton' s principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method,the discrete equations can be deduced, which can be solved easily by Runge-Kutta method.The dynamic buckling loads of the stiffened plates are obtained from Budiansky-Roth ( B-R )curves.

  16. Blue Willow Story Plates

    Science.gov (United States)

    Fontes, Kris

    2009-01-01

    In the December 1997 issue of "SchoolArts" is a lesson titled "Blue Willow Story Plates" by Susan Striker. In this article, the author shares how she used this lesson with her middle-school students many times over the years. Here, she describes a Blue Willow plate painting project that her students made.

  17. Create Your Plate

    Medline Plus

    Full Text Available ... In Memory In Honor Become a Member En Español Type 1 Type 2 About Us Online Community ... Page Text Size: A A A Listen En Español Create Your Plate Create Your Plate is a ...

  18. Create Your Plate

    Medline Plus

    Full Text Available ... Diabetes Meal Plans Create Your Plate Gluten Free Diets Meal Planning for Vegetarian Diets Cook with Heart-Healthy Foods Holiday Meal Planning ... Planning Meals Diabetes Meal Plans and a Healthy Diet Create Your Plate Meal Planning for Vegetarian Diets ...

  19. Dynamic response of visco-elastic plates

    Science.gov (United States)

    Kadıoǧlu, Fethi; Tekin, Gülçin

    2016-12-01

    In this study, a comprehensive analysis about the dynamic response characteristics of visco-elastic plates is given. To construct the functional in the Laplace-Carson domain for the analysis of visco-elastic plates based on the Kirchhoff hypothesis, functional analysis method is employed. By using this new energy functional in the Laplace-Carson domain, moment values that are important for engineers can be obtained directly with excellent accuracy and element equations can be written explicitly. Three-element model is considered for modelling the visco-elastic material behavior. The solutions obtained in the Laplace-Carson domain by utilizing mixed finite element formulation are transformed to the time domain using the Durbin's inverse Laplace transform technique. The proposed mixed finite element formulation is shown to be simple to implement and gives satisfactory results for dynamic response of visco-elastic plates.

  20. Theoretical Modelling of Sound Radiation from Plate

    Science.gov (United States)

    Zaman, I.; Rozlan, S. A. M.; Yusoff, A.; Madlan, M. A.; Chan, S. W.

    2017-01-01

    Recently the development of aerospace, automotive and building industries demands the use of lightweight materials such as thin plates. However, the plates can possibly add to significant vibration and sound radiation, which eventually lead to increased noise in the community. So, in this study, the fundamental concept of sound pressure radiated from a simply-supported thin plate (SSP) was analyzed using the derivation of mathematical equations and numerical simulation of ANSYS®. The solution to mathematical equations of sound radiated from a SSP was visualized using MATLAB®. The responses of sound pressure level were measured at far field as well as near field in the frequency range of 0-200 Hz. Result shows that there are four resonance frequencies; 12 Hz, 60 Hz, 106 Hz and 158 Hz were identified which represented by the total number of the peaks in the frequency response function graph. The outcome also indicates that the mathematical derivation correlated well with the simulation model of ANSYS® in which the error found is less than 10%. It can be concluded that the obtained model is reliable and can be applied for further analysis such as to reduce noise emitted from a vibrating thin plate.

  1. Wave Interaction with Dual Circular Porous Plates

    Institute of Scientific and Technical Information of China (English)

    Arpita Mondal; R.Gayen

    2015-01-01

    In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green’s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cum-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.

  2. Wave interaction with dual circular porous plates

    Science.gov (United States)

    Mondal, Arpita; Gayen, R.

    2015-12-01

    In this paper we investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green's integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cum-collocation method using the behaviour of the potential functions at the tips of the plates. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.

  3. Space-time as strongly bent plate

    CERN Document Server

    Kokarev, S S

    1999-01-01

    Futher development is made of a consept of space-time as multidimensional elastic plate, proposed earlier in [20,21]. General equilibrium equations, including 4-dimensional tangent stress tensor - energy-momentum tensor of matter - are derived. Comparative analysis of multidimensional elasticity theory (MET) and GR is given. Variational principle, boundary conditions, energy-momentum tensor, matter and space-time signature are reviewed within the context of MET.

  4. Pixelated neutron image plates

    Science.gov (United States)

    Schlapp, M.; Conrad, H.; von Seggern, H.

    2004-09-01

    Neutron image plates (NIPs) have found widespread application as neutron detectors for single-crystal and powder diffraction, small-angle scattering and tomography. After neutron exposure, the image plate can be read out by scanning with a laser. Commercially available NIPs consist of a powder mixture of BaFBr : Eu2+ and Gd2O3 dispersed in a polymer matrix and supported by a flexible polymer sheet. Since BaFBr : Eu2+ is an excellent x-ray storage phosphor, these NIPs are particularly sensitive to ggr-radiation, which is always present as a background radiation in neutron experiments. In this work we present results on NIPs consisting of KCl : Eu2+ and LiF that were fabricated into ceramic image plates in which the alkali halides act as a self-supporting matrix without the necessity for using a polymeric binder. An advantage of this type of NIP is the significantly reduced ggr-sensitivity. However, the much lower neutron absorption cross section of LiF compared with Gd2O3 demands a thicker image plate for obtaining comparable neutron absorption. The greater thickness of the NIP inevitably leads to a loss in spatial resolution of the image plate. However, this reduction in resolution can be restricted by a novel image plate concept in which a ceramic structure with square cells (referred to as a 'honeycomb') is embedded in the NIP, resulting in a pixelated image plate. In such a NIP the read-out light is confined to the particular illuminated pixel, decoupling the spatial resolution from the optical properties of the image plate material and morphology. In this work, a comparison of experimentally determined and simulated spatial resolutions of pixelated and unstructured image plates for a fixed read-out laser intensity is presented, as well as simulations of the properties of these NIPs at higher laser powers.

  5. Plate removal following orthognathic surgery.

    Science.gov (United States)

    Little, Mhairi; Langford, Richard Julian; Bhanji, Adam; Farr, David

    2015-11-01

    The objectives of this study are to determine the removal rates of orthognathic plates used during orthognathic surgery at James Cook University Hospital and describe the reasons for plate removal. 202 consecutive orthognathic cases were identified between July 2004 and July 2012. Demographics and procedure details were collected for these patients. Patients from this group who returned to theatre for plate removal between July 2004 and November 2012 were identified and their notes were analysed for data including reason for plate removal, age, smoking status, sex and time to plate removal. 3.2% of plates were removed with proportionally more plates removed from the mandible than the maxilla. 10.4% of patients required removal of one or more plate. Most plates were removed within the first post-operative year. The commonest reasons for plate removal were plate exposure and infection. The plate removal rates in our study are comparable to those seen in the literature.

  6. NATURAL TRANSVERSE VIBRATIONS OF A PRESTRESSED ORTHOTROPIC PLATE-STRIPE

    Directory of Open Access Journals (Sweden)

    Egorychev Oleg Aleksandrovich

    2012-10-01

    Full Text Available The article represents a new outlook at the boundary-value problem of natural vibrations of a homogeneous pre-stressed orthotropic plate-stripe. In the paper, the motion equation represents a new approximate hyperbolic equation (rather than a parabolic equation used in the majority of papers covering the same problem describing the vibration of a homogeneous orthotropic plate-stripe. The proposed research is based on newly derived boundary conditions describing the pin-edge, rigid, and elastic (vertical types of fixing, as well as the boundary conditions applicable to the unfixed edge of the plate. The paper contemplates the application of the Laplace transformation and a non-standard representation of a homogeneous differential equation with fixed factors. The article proposes a detailed representation of the problem of natural vibrations of a homogeneous orthotropic plate-stripe if rigidly fixed at opposite sides; besides, the article also provides frequency equations (no conclusions describing the plate characterized by the following boundary conditions: rigid fixing at one side and pin-edge fixing at the opposite side; pin-edge fixing at one side and free (unfixed other side; rigid fixing at one side and elastic fixing at the other side. The results described in the article may be helpful if applied in the construction sector whenever flat structural elements are considered. Moreover, specialists in solid mechanics and theory of elasticity may benefit from the ideas proposed in the article.

  7. Anisotropic elastic plates

    CERN Document Server

    Hwu, Chyanbin

    2010-01-01

    As structural elements, anisotropic elastic plates find wide applications in modern technology. The plates here are considered to be subjected to not only in plane load but also transverse load. In other words, both plane and plate bending problems as well as the stretching-bending coupling problems are all explained in this book. In addition to the introduction of the theory of anisotropic elasticity, several important subjects have are discussed in this book such as interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermoelastic problems and boundary element a

  8. Plating in Top Agar

    OpenAIRE

    sprotocols

    2014-01-01

    1. Warm plates to room temperature before use. Cold plates causes the top agar to solidify irregularly. DO not warm plates to 37° as the top agar will take forever to solidify. - Prepare top agar as the appropriate liquid medium with 0.7% agar. Keeping 100 mL bottles is convenient. For phages, use λ top agar, which is less rich and yields bigger plaques. - Melt top agar in the microwave completely. Allow the agar to boil after liquification; incompletely melted agar looks liquid, but is...

  9. Geometrically nonlinear behavior of piezoelectric laminated plates

    Science.gov (United States)

    Rabinovitch, Oded

    2005-08-01

    The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.

  10. Create Your Plate

    Medline Plus

    Full Text Available ... blood glucose levels and lose weight. With this method, you fill your plate with more non-starchy ... but changes the portion sizes so you are getting larger portions of non-starchy vegetables and a ...

  11. Create Your Plate

    Medline Plus

    Full Text Available ... blood glucose levels and lose weight. With this method, you fill your plate with more non-starchy ... 4/Box) Taking the guesswork out of portion control has never been easier. It can be a ...

  12. Tectonic Plate Movement.

    Science.gov (United States)

    Landalf, Helen

    1998-01-01

    Presents an activity that employs movement to enable students to understand concepts related to plate tectonics. Argues that movement brings topics to life in a concrete way and helps children retain knowledge. (DDR)

  13. MyPlate

    Science.gov (United States)

    ... our stage of life, situations, preferences, access to food, culture, traditions, and the personal decisions we make over time. All your food and beverage choices count. MyPlate offers ideas and ...

  14. Create Your Plate

    Medline Plus

    Full Text Available ... blood glucose levels and lose weight. With this method, you fill your plate with more non-starchy ... you have an easy portion control solution that works. Last Reviewed: October 8, 2015 Last Edited: September ...

  15. Designing Assemblies Of Plates

    Science.gov (United States)

    Williams, F. W.; Kennedy, D.; Butler, R.; Aston, G.; Anderson, M. S.

    1992-01-01

    VICONOPT calculates vibrations and instabilities of assemblies of prismatic plates. Designed for efficient, accurate analysis of buckling and vibration, and for optimum design of panels of composite materials. Written in FORTRAN 77.

  16. Create Your Plate

    Medline Plus

    Full Text Available ... Your Plate Gluten Free Diets Meal Planning for Vegetarian Diets Cook with Heart-Healthy Foods Holiday Meal Planning What Can I Eat? Making Healthy Food Choices Diabetes Superfoods Non-starchy Vegetables Grains and Starchy Vegetables ...

  17. Create Your Plate

    Medline Plus

    Full Text Available ... Recipes Association Cookbook Recipes Planning Meals Diabetes Meal Plans Create Your Plate Gluten Free Diets Meal Planning ... serving of dairy or both as your meal plan allows. Choose healthy fats in small amounts. For ...

  18. Create Your Plate

    Medline Plus

    Full Text Available ... 1 Diabetes Get Started Safely Get And Stay Fit Types of Activity Weight Loss Assess Your Lifestyle ... manage portion control wherever you are. Now, our best-selling, sectioned to-go plate with easy-sealing ...

  19. Create Your Plate

    Medline Plus

    Full Text Available ... Plate is a simple and effective way to manage your blood glucose levels and lose weight. With ... been easier. It can be a challenge to manage portion control wherever you are. Now, our best- ...

  20. Tectonic Plate Movement.

    Science.gov (United States)

    Landalf, Helen

    1998-01-01

    Presents an activity that employs movement to enable students to understand concepts related to plate tectonics. Argues that movement brings topics to life in a concrete way and helps children retain knowledge. (DDR)

  1. Create Your Plate

    Medline Plus

    Full Text Available ... Carbohydrates Carbohydrate Counting Make Your Carbs Count Glycemic ... to manage portion control wherever you are. Now, our best-selling, sectioned to-go plate with easy-sealing ...

  2. Origami - Folded Plate Structures

    OpenAIRE

    Buri, Hans Ulrich

    2010-01-01

    This research investigates new methods of designing folded plate structures that can be built with cross-laminated timber panels. Folded plate structures are attractive to both architects and engineers for their structural, spatial, and plastic qualities. Thin surfaces can be stiffened by a series of folds, and thus not only cover space, but also act as load bearing elements. The variation of light and shadow along the folded faces emphasizes the plas...

  3. Fractal multifiber microchannel plates

    Science.gov (United States)

    Cook, Lee M.; Feller, W. B.; Kenter, Almus T.; Chappell, Jon H.

    1992-01-01

    The construction and performance of microchannel plates (MCPs) made using fractal tiling mehtods are reviewed. MCPs with 40 mm active areas having near-perfect channel ordering were produced. These plates demonstrated electrical performance characteristics equivalent to conventionally constructed MCPs. These apparently are the first MCPs which have a sufficiently high degree of order to permit single channel addressability. Potential applications for these devices and the prospects for further development are discussed.

  4. Exact axisymmetric solution of laminated transversely isotropic piezoelectric circular plates (Ⅱ)——Exact solution for elastic circular plates and numerical results

    Institute of Scientific and Technical Information of China (English)

    丁皓江; 徐荣桥; 国凤林

    1999-01-01

    Emphasis is placed on purely elastic circular plates. Let the piezoelectric coefficients be equal to zero. Then two sets of uncoupled mechanical and electric equations are obtained and they can be solved independently. Two three-dimensional exact solutions of laminated transversely isotropic circular plate are derived under two boundary conditions, i.e. rigid slipping support and elastic simple support. For isotropic circular plates, the problem of multiple root is treated. At last, some numerical results of piezoelectric and purely elastic circular plates are presented and the applicability of classical plate theory is discussed.

  5. Integral equations

    CERN Document Server

    Tricomi, Francesco Giacomo

    1957-01-01

    This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful

  6. Free vibration and transverse stresses of viscoelastic laminated plates

    Institute of Scientific and Technical Information of China (English)

    Ming-yong HU; An-wen WANG

    2009-01-01

    Based on Reddy's layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for flee vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibra-tion, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is an-alyzed. Ratio between the transverse stress's maximum value and the in-plane stress's maximum-value is obtained. The results show that the proposed method, and the adopted equations and programs are reliable.

  7. FRACTURE CALCULATION OF BENDING PLATES BY BOUNDARY COLLOCATION METHOD

    Institute of Scientific and Technical Information of China (English)

    王元汉; 伍佑伦; 余飞

    2003-01-01

    Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it ts only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time This is an effective semi-analytical and semi-numerical method.

  8. Vibration and Buckling of Web Plate of the Plate Girder

    OpenAIRE

    高橋, 和雄; 呉, 明強; 中澤, 聡志; 筑紫, 宏之

    1998-01-01

    The vibration and buckling of the web of the plate girder are studied in this paper. The small deflection theory of the thin plate is used. The finite strip method is employed to solve vibration and buckling of the plate girder. Natural frequenies of buckling properties are shown for various plate girder bridges.

  9. Stochastic partial differential equations

    CERN Document Server

    Chow, Pao-Liu

    2014-01-01

    Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad

  10. Trapping of surface gravity waves by a vertical flexible porous plate near a wall

    Science.gov (United States)

    Kaligatla, R. B.; Koley, S.; Sahoo, T.

    2015-10-01

    The present study deals with the trapping of oblique surface gravity waves by a vertical submerged flexible porous plate located near a rigid wall in water of finite as well as infinite depths. The physical problem is based on the assumption of small amplitude water wave theory and structural response. The flexible plate is assumed to be thin and is modeled based on the Euler-Bernoulli beam equation. Using the Green's function technique to the plate equation and associated boundary conditions, an integral equation is derived which relates the normal velocity on the plate to the difference in velocity potentials across the plate involving the porous-effect parameter and structural rigidity. Further, applying Green's second identity to the free-surface Green's function and the scattered velocity potentials on the two sides of the plate, a system of three more integral equations is derived involving the velocity potentials and their normal derivatives across the plate boundary along with the velocity potential on the rigid wall. The system of integral equations is converted into a set of algebraic equations using appropriate Gauss quadrature formula which in turn solved to obtain various quantities of physical interest. Utilizing Green's identity, explicit expressions for the reflection coefficients are derived in terms of the velocity potentials and their normal derivatives across the plate. Energy balance relations are derived and used to check the accuracy of the computational results. As special cases of the submerged plate, wave trapping by the bottom-standing as well as surface-piercing plates is analyzed. Effects of various wave and structural parameters in trapping of surface waves are studied from the computational results by analyzing the reflection coefficients, wave forces exerted on the plate and the rigid wall, flow velocity, plate deflections and surface elevations. It is observed that surface-piercing plate is more effective for trapping of water waves

  11. Electrostatic and Small-Signal Analysis of CMUTs With Circular and Square Anisotropic Plates

    DEFF Research Database (Denmark)

    la Cour, Mette Funding; Christiansen, Thomas Lehrmann; Jensen, Jørgen Arendt

    2015-01-01

    Traditionally, Capacitive Micromachined Ultrasonic Transducers (CMUTs) are modeled using the isotropic plate equation and this leads to deviations between analytical calcu- lations and Finite Element Modeling (FEM). In this paper, the deflection is calculated for both circular and square plates...... using the full anisotropic plate equation. It is shown that the anisotropic calculations match perfectly with FEM while an isotropic ap- proach causes up to 10% deviations in deflection. For circular plates an exact solution can be found and for square plates using the Galerkin method and utilizing...... the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is plates is also applied to the CMUT. The deflection of a square plate was measured on fabricated CMUTs using a white light...

  12. Water wave scattering by an elastic thin vertical plate submerged in finite depth water

    Science.gov (United States)

    Chakraborty, Rumpa; Mandal, B. N.

    2013-12-01

    The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here. The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate. Using the Green's function technique, from this boundary condition, the normal velocity of the plate is expressed in terms of the difference between the velocity potentials (unknown) across the plate. The two ends of the plate are either clamped or free. The reflection and transmission coefficients are obtained in terms of the integrals' involving combinations of the unknown velocity potential on the two sides of the plate, which satisfy three simultaneous integral equations and are solved numerically. These coefficients are computed numerically for various values of different parameters and depicted graphically against the wave number in a number of figures.

  13. NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

    Institute of Scientific and Technical Information of China (English)

    DU Guo-jun; MA Jian-qing

    2006-01-01

    Based on yon Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the anslytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero,critical load is obtained.

  14. Shear flow past a flat plate in hydromagnetics

    Directory of Open Access Journals (Sweden)

    S. R. N. Sastry

    1980-01-01

    Full Text Available The problem of simple shear flow past a flat plate has been extended to the hydromagnetic case in which a viscous, electrically conducting, incompressible fluid flows past an electrically insulated flat plate with a magnetic field parallel to the plate. For simplicity all physical parameters are assumed constant. A series solution for the velocity field has been developed for small values of a magnetic parameter. The equations governing this flow field were integrated numerically It is found that the effect of the magnetic field is to diminish and increase respectively, the first and second order contributions for the skin friction.

  15. An Isoperimetric Inequality for Fundamental Tones of Free Plates

    CERN Document Server

    Chasman, L M

    2010-01-01

    We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given $\\tau>0$, the free plate eigenvalues $\\omega$ and eigenfunctions $u$ are determined by the equation $\\Delta\\Delta u-\\tau\\Delta u = \\omega u$ together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term $|D^2u|^2$. We adapt Weinberger's method from the corresponding free membrane problem, taking the fundamental modes of the unit ball as trial functions. These solutions are a linear combination of Bessel and modified Bessel functions.

  16. An isoperimetric inequality for the fundamental tone of free plates

    CERN Document Server

    Chasman, L M

    2010-01-01

    We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given $\\tau>0$, the free plate eigenvalues $\\omega$ and eigenfunctions $u$ are determined by the equation $\\Delta\\Delta u-\\tau\\Delta u = \\omega u$ together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term $|D^2u|^2$. We adapt Weinberger's method from the corresponding free membrane problem, taking the fundamental modes of the unit ball as trial functions. These solutions are a linear combination of Bessel and modified Bessel functions.

  17. Instability of modes in a partially hinged rectangular plate

    Science.gov (United States)

    Ferreira, Vanderley; Gazzola, Filippo; Moreira dos Santos, Ederson

    2016-12-01

    We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal evolution equation modeling the deformation of the plate and we prove existence, uniqueness and asymptotic behavior for the solutions for all initial data in suitable functional spaces. Then we prove results on the stability/instability of simple modes motivated by a phenomenon which is visible in actual bridges and we complement these theorems with some numerical experiments.

  18. Thermally Induced Principal Parametric Resonance in Circular Plates

    Directory of Open Access Journals (Sweden)

    Ali H. Nayfeh

    2002-01-01

    Full Text Available We consider the problem of large-amplitude vibrations of a simply supported circular flat plate subjected to harmonically varying temperature fields arising from an external heat flux (aeroheating for example. The plate is modeled using the von Karman equations. We used the method of multiple scales to determine an approximate solution for the case in which the frequency of the thermal variations is approximately twice the fundamental natural frequency of the plate; that is, the case of principal parametric resonance. The results show that such thermal loads produce large-amplitude vibrations, with associated multi-valued responses and subcritical instabilities.

  19. Dynamic Stability of Viscoelastic Plates with Finite Deformation and Shear Effects

    Institute of Scientific and Technical Information of China (English)

    李晶晶; 程昌钧; 等

    2002-01-01

    Based on Reddy's theory of plates with higher-order shear deformations and the Boltzmann superposition principles,the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects,The Galerkin method was applied to simplify the set of equations.The numerical methods in nonlinear dynamics were used to solve the simplified system.It could e seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads.The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelatic plates were investigated.

  20. Analysis and Design of Circular Plate MR Fluids Brake

    Institute of Scientific and Technical Information of China (English)

    Yang Yan; Lin Chang-Hua; Li Hui; Zhou Jing

    2004-01-01

    A magnetorheological (MR) fluids brake is a device to achieve brake by shear force of MR fluids. A MR rotary brake has the property that its braking torque changes quickly in response to an external magnetic field. In this study, the design method of the circular plate MR fluids brake is investigated theoretically. The equation of the torque transmitted by the MR fluids in the brake is derived to provide the theoretical foundation in the design of the brake. Based on this equation, after mathematically manipulated, the calculations of the volume, thickness and width of the MR fluids within the circular plate MR fluids brake are yield.

  1. Anterior cervical plating

    Directory of Open Access Journals (Sweden)

    Gonugunta V

    2005-01-01

    Full Text Available Although anterior cervical instrumentation was initially used in cervical trauma, because of obvious benefits, indications for its use have been expanded over time to degenerative cases as well as tumor and infection of the cervical spine. Along with a threefold increase in incidence of cervical fusion surgery, implant designs have evolved over the last three decades. Observation of graft subsidence and phenomenon of stress shielding led to the development of the new generation dynamic anterior cervical plating systems. Anterior cervical plating does not conclusively improve clinical outcome of the patients, but certainly enhances the efficacy of autograft and allograft fusion and lessens the rate of pseudoarthrosis and kyphosis after multilevel discectomy and fusions. A review of biomechanics, surgical technique, indications, complications and results of various anterior cervical plating systems is presented here to enable clinicians to select the appropriate construct design.

  2. Random vibrations of composite beams and plates

    Science.gov (United States)

    Abdelnaser, Ahmad Shehadeh

    In this study, a generalized modal approach is presented to solve more general vibration problems of composite beams and plates. The coupled systems of partial differential equations, representing the equations of motion, are uncoupled into modal equations by utilizing the eigenfunctions of the system and its adjoint. A method is presented to obtain these eigenfunctions for beams with arbitrary boundary conditions and for plates with Levy-type boundary conditions. The forced vibration solutions obtained by this method are then used to calculate the random response characteristics of beams and plates subjected to spatially and temporally correlated random loads. In the analysis of beams, both symmetric cross-ply and angle-ply configurations have been considered. In the symmetric cross-ply configuration with no torsional loads, of course, the warping effects are absent. The angle-ply case, however, includes torsion-warping effects and coupled bending-torsion motions. A simple displacement field is introduced to reflect warping in the third-order shear deformation theory. In the analysis of plates two configurations of the laminates have also been considered: symmetric cross-ply and antisymmetric angle-ply. At this time, these are the only two configurations which can be solved by the closed-form modal analysis approach for the Levy-type boundary conditions. In both cases of the beams and plates, the numerical results with and without shear deformations are obtained and compared. The result for no shear deformation theory are obtained with the classical lamination theory. The results have also been obtained for the first-order shear deformation theory with a somewhat simpler displacement field which has been commonly used in the past. The numerical results are obtained for the global response quantities such as frequencies, displacements, and crossing rates as well as for the local response quantities such as normal and shear stresses across a cross section. The

  3. A MEMS square Chladni plate resonator

    Science.gov (United States)

    Pala, Sedat; Azgın, Kıvanç

    2016-10-01

    This paper presents the design, fabrication and tests of a micro-fabricated MEMS ‘Chladni’ plate resonator. The proposed MEMS resonator has a square plate geometry having a side length of 1400 µm and a height of 35 µm. Its geometry and electrode layout are designed to analyze and test as many modes as possible. The MEMS plate is fabricated using a silicon-on-insulator process with a 35 µm thick silicon layer on a glass substrate. Transverse vibration of the plate is investigated to obtain closed form natural frequencies and mode shapes, which are derived using the Rayleigh-Ritz energy method, with an electrostatic softening effect included. Closed form equations for the calculation of effective stiffness’, masses and natural frequencies of the two modes (mode (1,1) and mode (2,0)-(0,2)) are presented, with and without electrostatic softening. The analytical model is verified for those modes by finite-element simulations, frequency response tests in vacuum and laser Doppler vibrometer (LDV) experiments. The derived model deviates from the finite-element analysis by 3.35% for mode (1,1) and 6.15% for mode (2,0)-(0,2). For verification, the frequency responses of the plates are measured with both electrostatic excitation-detection at around 20 mTorr vacuum ambient and LDV at around 0.364 mTorr vacuum ambient. The resonance frequency and Q-factor of mode (1,1) are measured to be 104.2 kHz and 14 300, respectively. For mode (2,0)-(0,2), the measured resonance frequency and Q-factor are 156.68 kHz and 10 700, respectively. The presented LDV results also support both natural frequencies of interest and corresponding mode shapes of the plate structure.

  4. Axisymmetric free vibrations of infinite micropolar thermoelastic plate

    Institute of Scientific and Technical Information of China (English)

    Rajneesh Kumar; Geeta Partap

    2007-01-01

    The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation.The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.

  5. License plate detection algorithm

    Science.gov (United States)

    Broitman, Michael; Klopovsky, Yuri; Silinskis, Normunds

    2013-12-01

    A novel algorithm for vehicle license plates localization is proposed. The algorithm is based on pixel intensity transition gradient analysis. Near to 2500 natural-scene gray-level vehicle images of different backgrounds and ambient illumination was tested. The best set of algorithm's parameters produces detection rate up to 0.94. Taking into account abnormal camera location during our tests and therefore geometrical distortion and troubles from trees this result could be considered as passable. Correlation between source data, such as license Plate dimensions and texture, cameras location and others, and parameters of algorithm were also defined.

  6. Casimir force between metal plate and dielectric plate

    Institute of Scientific and Technical Information of China (English)

    刘中柱; 邵成刚; 罗俊

    1999-01-01

    The Casimir effect between metal plate and dielectric plate is discussed with 1+1-dimensional potential model without using cut-off method. Calculation shows that the Casimir force between metal plate and dielectric plate is determined not only by the potential V0, the dielectric thickness and the distance α between the metal plate and dielectric plate, but also by the dimension of the vessel. When α is far less than the dimension of the vessel, the Casimir force Fc∝α(-1); conversely Fc∝α-2. This result is significant for Casimir force experiment.

  7. Capacity of the circular plate condenser: analytical solutions for large gaps between the plates

    Science.gov (United States)

    Rao, T. V.

    2005-11-01

    A solution of Love's integral equation (Love E R 1949 Q. J. Mech. Appl. Math. 2 428), which forms the basis for the analysis of the electrostatic field due to two equal circular co-axial parallel conducting plates, is considered for the case when the ratio, τ, of distance of separation to radius of the plates is greater than 2. The kernel of the integral equation is expanded into an infinite series in odd powers of 1/τ and an approximate kernel accurate to {\\cal O}(\\tau^{-(2N+1)}) is deduced therefrom by terminating the series after an arbitrary but finite number of terms, N. The approximate kernel is rearranged into a degenerate form and the integral equation with this kernel is reduced to a system of N linear equations. An explicit analytical solution is obtained for N = 4 and the resulting analytical expression for the capacity of the circular plate condenser is shown to be accurate to {\\cal O}(\\tau^{-9}) . Analytical expressions of lower orders of accuracy with respect to 1/τ are deduced from the four-term (i.e., N = 4) solution and predictions (of capacity) from the expressions of different orders of accuracy (with respect to 1/τ) are compared with very accurate numerical solutions obtained by solving the linear system for large enough N. It is shown that the {\\cal O}(\\tau^{-9}) approximation predicts the capacity extremely well for any τ >= 2 and an {\\cal O}(\\tau^{-3}) approximation gives, for all practical purposes, results of adequate accuracy for τ >= 4. It is further shown that an approximate solution, applicable for the case of large distances of separation between the plates, due to Sneddon (Sneddon I N 1966 Mixed Boundary Value Problems in Potential Theory (Amsterdam: North-Holland) pp 230-46) is accurate to {\\cal O}(\\tau^{-6}) for τ >= 2.

  8. ANALYSIS ON DYNAMIC CHARACTERISTICS FOR FERROMAGNETIC CONDUCTING PLATES IN A TRANSVERSE UNIFORM MAGNETIC FIELD

    Institute of Scientific and Technical Information of China (English)

    Zheng Xiaojing; Liu Xin'en

    2000-01-01

    In this paper, a set of basic equations for free vibration of ferromagnetic conducting plates in a transverse magnetic field are presented, in which the coupled effects of magnetization and eddy current on the mechanical behavior of the plate are included. Based on the quantitative analyses on the vibration frequency and the values of the critical magnetic field for several supporting conditions of the plate, the effects of the conductivity, the magnetic permeability, the thickness of the plate and supporting conditions on the vibration frequency of the plate and the crifcal magnetic field are discussed.

  9. Transversal vibrations of double-plate systems

    Institute of Scientific and Technical Information of China (English)

    Katica(Stevanovi(c)) Hedrih

    2006-01-01

    This paper presents an analytical and numerical analysis of free and forced transversal vibrations of an elastically connected double-plate system. Analytical solutions of a system of coupled partial differential equations, which describe corresponding dynamical free and forced processes, are obtained using Bernoulli's particular integral and Lagrange's method of variation constants. It is shown that one-mode vibrations correspond to two-frequency regime for free vibrations induced by initial conditions and to three-frequency regime for forced vibrations induced by one-frequency external excitation and corresponding initial conditions. The analytical solutions show that the elastic connection between plates leads to the appearance of twofrequency regime of time function, which corresponds to one eigenamplitude function of one mode, and also that the time functions of different vibration modes are uncoupled, for each shape of vibrations. It has been proven that for both elastically connected plates, for every pair of m and n. two possibilities for appearance of the resonance dynamical states, as well as for appearance of the dynamical absorption, are present. Using the MathCad program, the corresponding visualizations of the characteristic forms of the plate middle surfaces through time are presented.

  10. Nuclear reactor alignment plate configuration

    Energy Technology Data Exchange (ETDEWEB)

    Altman, David A; Forsyth, David R; Smith, Richard E; Singleton, Norman R

    2014-01-28

    An alignment plate that is attached to a core barrel of a pressurized water reactor and fits within slots within a top plate of a lower core shroud and upper core plate to maintain lateral alignment of the reactor internals. The alignment plate is connected to the core barrel through two vertically-spaced dowel pins that extend from the outside surface of the core barrel through a reinforcement pad and into corresponding holes in the alignment plate. Additionally, threaded fasteners are inserted around the perimeter of the reinforcement pad and into the alignment plate to further secure the alignment plate to the core barrel. A fillet weld also is deposited around the perimeter of the reinforcement pad. To accomodate thermal growth between the alignment plate and the core barrel, a gap is left above, below and at both sides of one of the dowel pins in the alignment plate holes through with the dowel pins pass.

  11. Create Your Plate

    Medline Plus

    Full Text Available ... 1 Type 2 About Us Online Community Meal Planning Sign In Search: Search More Sites Search ≡ Are ... Fitness Home Food MyFoodAdvisor Recipes Association Cookbook Recipes Planning Meals Diabetes Meal Plans Create Your Plate Gluten ...

  12. Create Your Plate

    Medline Plus

    Full Text Available ... Create Your Plate is a simple and effective way to manage your blood glucose levels and lose weight. With ... year of delicious meals to help prevent and manage diabetes. Healthy Recipes: ... to your day with this guide. Ways to Give: Wear Your Cause on Your Sleeve - ...

  13. The Plate Tectonics Project

    Science.gov (United States)

    Hein, Annamae J.

    2011-01-01

    The Plate Tectonics Project is a multiday, inquiry-based unit that facilitates students as self-motivated learners. Reliable Web sites are offered to assist with lessons, and a summative rubric is used to facilitate the holistic nature of the project. After each topic (parts of the Earth, continental drift, etc.) is covered, the students will…

  14. Create Your Plate

    Medline Plus

    Full Text Available ... tax-deductible gift today can fund critical diabetes research and support vital diabetes education services that improve the ... way to manage your blood glucose levels and lose weight. With this method, you fill your plate with more non-starchy ...

  15. Create Your Plate

    Medline Plus

    Full Text Available ... 1 Type 2 About Us Online Community Meal Planning Sign In Search: Search More Sites Search ≡ Are ... Fitness Home Food MyFoodAdvisor Recipes Association Cookbook Recipes Planning Meals Diabetes Meal Plans Create Your Plate Gluten ...

  16. Create Your Plate

    Medline Plus

    Full Text Available ... tax-deductible gift today can fund critical diabetes research and support vital diabetes education services that improve the ... way to manage your blood glucose levels and lose weight. With this method, you fill your plate with more non-starchy ...

  17. Create Your Plate

    Medline Plus

    Full Text Available ... unsweetened tea or coffee. Featured Product Precise Portions® Go Healthy Travel Pack (4/Box) Taking the guesswork ... you are. Now, our best-selling, sectioned to-go plate with easy-sealing lid is offered in ...

  18. Create Your Plate

    Medline Plus

    Full Text Available ... manage portion control wherever you are. Now, our best-selling, sectioned to-go plate with easy-sealing lid is offered in a 4-pack. Whether ... Research & Practice We Are Research Leaders We Support Your Doctor ...

  19. INL HIP Plate Fabrication

    Energy Technology Data Exchange (ETDEWEB)

    B. H. Park; C. R. Clark; J. F. Jue

    2010-02-01

    This document outlines the process used to bond monolithic fuel plates by Hot Isostatic Pressing (HIP). This method was developed at Idaho National Laboratory (INL) for the Reduced Enrichment for Research and Test Reactors (RERTR) program. These foils have been used in a number of irradiation experiments in support of the United States Global Threat Reduction Initiative (GTRI) program.

  20. The Plate Tectonics Project

    Science.gov (United States)

    Hein, Annamae J.

    2011-01-01

    The Plate Tectonics Project is a multiday, inquiry-based unit that facilitates students as self-motivated learners. Reliable Web sites are offered to assist with lessons, and a summative rubric is used to facilitate the holistic nature of the project. After each topic (parts of the Earth, continental drift, etc.) is covered, the students will…

  1. Create Your Plate

    Medline Plus

    Full Text Available ... Planning Meals > Create Your Plate Share: Print Page Text Size: A A A Listen En Español Create ... somewhere in between, you have an easy portion control solution that works. Last Reviewed: October 8, 2015 Last Edited: ... Cost of Diabetes Advocate Toolkit Call to Congress Research & ...

  2. Size-Dependent Dynamic Behavior of a Microcantilever Plate

    Directory of Open Access Journals (Sweden)

    Xiaoming Wang

    2012-01-01

    Full Text Available Material length scale considerably affects the mechanical properties of microcantilever components. Recently, cantilever-plate-like structures have been commonly used, whereas the lack of studies on their size effects constrains the design, testing, and application of these structures. We have studied the size-dependent dynamic behavior of a cantilever plate based on a modified couple stress theory and the differential quadrature method in this note. The numerical solutions of microcantilever plate equation involving the size effect have been presented. We have also analyzed the bending and vibration of the microcantilever plates considering the size effect and discussed the dependence of the size effect on their geometric dimensions. The results have shown that (1 the mechanical characteristics of the cantilever plate show obvious size effects; as a result, the bending deflection of a microcantilever plate reduces whereas the natural frequency increases effectively and (2 for the plates with the same material, the size effect becomes more obvious when the plates are thinner.

  3. Transient motion of thick anisotropic plates

    Science.gov (United States)

    Nayfeh, Adnan H.; Taylor, Timothy W.

    1991-01-01

    Analyses are developed for the response of anisotropic plate strips to a transient load. The load is taken in the form of a line load of normal stress on the surface or within the body of the strip. The characteristic free vibrational modes of the strip are derived and used to derive the secular equation for this case in closed form and to isolate the mathematical conditions for symmetric and antisymmetric wave mode propagation in completely separate terms. The applied loads are expanded in terms of these normal modes and the response of the plate is obtained by superposition of the appropriate components. Material systems of higher symmetry are contained implicitly in the analysis.

  4. A nonlinear plate control without linearization

    Directory of Open Access Journals (Sweden)

    Yildirim Kenan

    2017-03-01

    Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

  5. Induced signals in resistive plate chambers

    CERN Document Server

    Riegler, W

    2002-01-01

    We derive theorems for induced signals on electrodes embedded in a medium with a position and frequency dependent permittivity $\\vep(\\vx,s)$ and conductivity $\\sigma(\\vx,s)$ that are connected with arbitrary discrete elements. The problem is treated using the quasi-static approximation of Maxwell's equations for weakly conducting media \\cite{melcher}\\cite{quasi}. The induced signals can be derived by time dependent weighting fields and potentials and the result is the same as the one given in \\cite{gatti}. We also show how these time dependent weighting fields can be derived from electrostatic solutions. Finally we will apply the results to Resistive Plate Chambers (RPCs) where we discuss the effects of the resistive plates and thin resistive layers on the signals induced on plane electrodes and strips.

  6. New method for solving the bending problem of rectangular plates with mixed boundary conditions

    Directory of Open Access Journals (Sweden)

    Liu Xin Min

    2016-01-01

    Full Text Available A new method is used to solve the rectangular plate bending problem with mixed boundary conditions. The method overcomes the complicated derivation of the classical solution by Fourth-order differential problem into integrating question. Under uniform loading rectangular plate bending problem with one side fixed the opposite side half simply supported half fixed the other two sides free rectangular plate, one side simply supported the opposite side half simply supported half fixed the other two sides free rectangular plate is systematically solved. According to the actual boundary conditions of the rectangular plate, the corresponding characteristic equation can easily be set up. It is presented deflection curve equation and the numerical calculation. By compared the results of the equation to the finite element program, we are able to demonstrate the correctness of the method. So the method not only has certain theoretical value, but also can be directly applied to engineering practice.

  7. Linear stability analysis of fluid flow between two parallel porous stationary plates with small suction and injection

    CERN Document Server

    Hinvi, L A; Orou, J B Chabi

    2013-01-01

    In this work, the linear stability of the viscous incompressible fluid flow between two parallel horizontal porous stationary plates with the assumption that there is a small constant suction at upper plate and a small constant injection at the lower plate is studied.The Navier-Stokes and continuous equations are reduced to an equation modified by the suction Reynolds number, which we call modified Orr-Sommerfeld equation. This equation is rewritten as an eigenvalue problem and is solved numerically using Matlab (Windows Version). The effect of small suction Reynolds number on the linear stability fluid flow is discussed.

  8. Acoustic impact on the laminated plates placed between barriers

    Science.gov (United States)

    Paimushin, V. N.; Gazizullin, R. K.; Fedotenkov, G. V.

    2016-11-01

    On the basis of previously derived equations, analytical solutions are established on the forced vibrations of two-layer and three-layers rectangular plates hinged in an opening of absolutely rigid walls during the transmission of monoharmonic sound waves. It is assumed that the partition wall is situated between two absolutely rigid barriers, one of them by harmonic oscillation with a given displacements amplitude on the plate forms the incident sound wave, and the other is stationary and has a coating of deformable energy absorbing material with high damping properties. The behavior of acoustic environments in the spaces between the deformable plate and the barriers described by classical wave equation based on the ideal compressible fluid model. To describe the process of dynamic deformation of the energy absorbing coating of fixed barrier, two-dimensional equations of motion based on the use of models transversely soft layer are derived with a linear approximation of the displacement field in the thickness direction of the coating and taking into account the damping properties of the material and the hysteresis model for it. The influence of the physical and mechanical properties of the concerned mechanical system and the frequency of the incident sound wave on the parameters of its insulation properties of the plate, as well as on the parameters of the stress-strain state of the plate has been analyzed.

  9. Semi-Analytical Finite Strip Transfer Matrix Method for Buckling Analysis of Rectangular Thin Plates

    Directory of Open Access Journals (Sweden)

    Li-Ke Yao

    2015-01-01

    Full Text Available Plates and shells are main components of modern engineering structures, whose buckling analysis has been focused by researchers. In this investigation, rectangular thin plates with loaded edges simply supported can be discretized by semi-analytical finite strip technology. Then the control equations of the strip elements of the buckling plate will be rewritten as the transfer equations by transfer matrix method. A new approach, namely semi-analytical Finite Strip Transfer Matrix Method, is developed for the buckling analysis of plates. This method requires no global stiffness matrix of the system, reduces the system matrix order, and improves the computational efficiency. Comparing with some theoretical results and FEM’s results of two illustrations (the plates and the ribbed plates under six boundary conditions, the method is proved to be reliable and effective.

  10. MyPlate Food Guide

    Science.gov (United States)

    ... Choosing the Right Sport for You Shyness MyPlate Food Guide KidsHealth > For Teens > MyPlate Food Guide Print ... other sugary drinks. Avoid oversized portions. continue Five Food Groups Different food groups meet different nutrition needs. ...

  11. What Are Growth Plate Injuries?

    Science.gov (United States)

    ... plate injuries are:  Falling down  Competitive sports (like football)  Recreational activities. Other reasons for growth plate injuries are:  Child abuse  Injury from extreme cold (for ...

  12. Lectures on nonlinear evolution equations initial value problems

    CERN Document Server

    Racke, Reinhard

    2015-01-01

    This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

  13. Viscous dissipation effects on heat transfer in flow past a continuous moving plate

    Digital Repository Service at National Institute of Oceanography (India)

    Soundalgekar, V.M.; Murty, T.V.R.

    The study of thermal boundary layer on taking into account the viscous dissipative heat, on a continuously moving semi-infinite flat plate is presented here.Similarity solutions are derived and the resulting equations are integrated numerically...

  14. Heat transfer in flow past a continuously moving porous flat plate with heat flux

    Digital Repository Service at National Institute of Oceanography (India)

    Murty, T.V.R.; Sarma, Y.V.B.

    The analysis of the heat transfer in flow past a continuously moving semi-infinite plate in the presence of suction/ injection with heat flux has been presented. Similarity solutions have been derived and the resulting equations are integrated...

  15. Controlling Laminate Plate Elastic Behavior

    OpenAIRE

    Mareš, T.

    2004-01-01

    This paper aims to express the relation of a measure of laminate plate stiffness with respect to the fiber orientation of its plies. The inverse of the scalar product of the lateral displacement of the central plane and lateral loading of the plate is the measure of laminate plate stiffness. In the case of a simply supported rectangular laminate plate this measure of stiffness is maximized, and the optimum orientation of its plies is searched.

  16. Uplift Pressure of Waves on A Horizontal Plate

    Institute of Scientific and Technical Information of China (English)

    周益人; 陈国平; 黄海龙; 王登婷

    2003-01-01

    Uplift pressures of waves acting on horizontal plates are the important basis for design of maritime hollow-trussed structures. In this paper, an experimental study on the uplift pressures of waves on a horizontal plate is conducted by use of a series of model tests. Detailed analysis has been given to the formation mechanism of uplift pressures of waves. It is considered that the impact pressure intensity is mainly affected by geometrical factors (tangential angle of waves), dynamic factors (wave height, wave velocity, etc.) and air cushion. Based on the test results, an equation for calculation of the maximum uplift pressure intensity of waves on a plate is presented. A large quantity of test data shows good agreement of the present equation with the test results.

  17. Laminar film boiling on inclined isothermal flat plates.

    Science.gov (United States)

    Nagendra, H. R.

    1973-01-01

    Laminar film boiling from an inclined flat plate has been investigated analytically. Using the singular perturbation scheme, the complete set of Navier-Stokes equations is solved. The zeroth-order perturbation coinciding with the boundary-layer equations for vertical flat plates governs the problem. The higher-order perturbations become important near the leading edge and for large values of the inclination angle from the vertical. The assumption of zero interfacial velocity shows that, except for fluids having large (rho x mu) ratios, the results can be predicted using the vertical flat plate results by defining a modified Grashof parameter containing a cos phi term. When the interfacial shear is considered, the solutions indicate that for fluids having large (rho x mu) ratios, the heat transfer rates will be larger (approximately 15% maximum) than those predicted by the simplified model using zero interfacial velocity. In general, the inclination decreases the rate of heat transfer as well as the rate of evaporation.

  18. An elastic plate on a thin viscous film

    CERN Document Server

    Trinh, Philippe H; Stone, Howard A

    2014-01-01

    We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity, viscosity, surface tension, and pressure forces is derived, and consists of a third-order Landau-Levich equation for the thin film, and a fifth-order beam equation for the plate. A numerical and asymptotic analysis is presented in the relevant limits of the elasticity and Capillary numbers. We demonstrate the emergence of boundary-layer effects near the ends of the plate, which are likely to be a generic phenomenon for singularly perturbed elastocapillary problems.

  19. Investigation of the nonlinear dynamics of a partially cracked plate

    Energy Technology Data Exchange (ETDEWEB)

    Israr, A [School of Engineering and Physical Sciences, Heriot Watt University - Dubai Campus, Block 2, Dubai International Academic City, P O Box 294345, Dubai (United Arab Emirates); Atepor, L, E-mail: a.israr@hw.ac.u, E-mail: katepor@yahoo.co [Department of Mechanical Engineering, James Watt South Building, University of Glasgow, Glasgow, G12 8QQ Scotland (United Kingdom)

    2009-08-01

    In this paper the nonlinear vibration of an aircraft panel structure modelled as an isotropic cracked plate and subjected to transverse harmonic excitation is considered for studying the dynamic response, both analytically and experimentally. A crack is arbitrarily located at the centre of the plate, consisting of a continuous line. This mathematical model is in the form of Duffing equation with a cubic nonlinear term. The perturbation method of multiple scales is used to solve the algebraic equation, and then investigated with the results of the direct integration within Mathematica{sup TM} and finite element analysis in ABAQUS for the first mode only. In addition, experimental measurements are also carried out to verify the dependence of the cracked plate's fundamental mode shape and resonance frequency on the vibration displacement amplitude. An extermely close agreement between these results is observed.

  20. FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.

  1. Microchannel plate streak camera

    Science.gov (United States)

    Wang, Ching L.

    1989-01-01

    An improved streak camera in which a microchannel plate electron multiplier is used in place of or in combination with the photocathode used in prior streak cameras. The improved streak camera is far more sensitive to photons (UV to gamma-rays) than the conventional x-ray streak camera which uses a photocathode. The improved streak camera offers gamma-ray detection with high temporal resolution. It also offers low-energy x-ray detection without attenuation inside the cathode. Using the microchannel plate in the improved camera has resulted in a time resolution of about 150 ps, and has provided a sensitivity sufficient for 1000 KeV x-rays.

  2. Characteristic curve method for analyzing movement of flyer plate based on universal equation of state of explosive%基于通用炸药状态方程分析飞板运动规律的特征线法

    Institute of Scientific and Technical Information of China (English)

    李晓杰; 赵春风

    2012-01-01

    From the physical definition of perturbation propagation (Mach waves), the characteristic equations of a two-dimensional supersonic flow were deduced into the forms which were uncorrelated with the formula of EOS.Meanwhile, a new Prantl-Meyer function was expressed into a simple variable function of fluid density also.Based on characteristic difference, a solution method of the two-dimensional supersonic flow was built up.Therefore, as an application example of the solution method, the movement of the flyer plate driven by glancing detonation was analyzed.For comparison, Detonation drives of the TNT and emulsion explosives were calculated with JWL and polytropic EOSs.The numerical results show that characteristic difference solutions completely agree with the expanding works of explosive EOSs.%从小扰动波(马赫波)的物理概念出发,导出了不依赖流体状态方程表达形式的平面二维超声速定常流的特征线方程;重新定义了以流体密度为单自变量的Prantl-Meyer函数,形成了求解平面二维超声速定常流的封闭方程组.还利用这种通用物态方程的特征线差分解法,针对滑移爆轰驱动飞板运动问题构建了爆轰产物流场内部和飞板边界特征线差分法格式.对TNT炸药和乳化炸药采用JWL状态方程和多方方程进行了对比计算.结果表明,炸药爆轰对飞板的驱动能力与状态方程表示的炸药的做功能力是一致的.

  3. The Effect of the Configuration of the Absorber on the Performance of Flat Plate Thermal Collector

    OpenAIRE

    Yan, Moyu; Qu, Ming; Peng, Steve

    2016-01-01

    In this study, a numerical thermal analysis for a new designed flat plate thermal collector was conducted through modeling. The new flat plate thermal collector has ellipse shaped tubes inside a wavy shaped absorber, which is made of stainless steel. For the comparison, the conventional flat plate thermal collector with circular copper tubes served as a base case was also modeled. Hottel-Whillier equations were utilized to formulate thermal networks for both models developed in Engineering Eq...

  4. Elastic plate spallation

    Science.gov (United States)

    Oline, L.; Medaglia, J.

    1972-01-01

    The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.

  5. Plate Tearing by a Cone

    DEFF Research Database (Denmark)

    Simonsen, Bo Cerup

    1997-01-01

    The present paper is concerned with steady-state plate tearing by a cone. This is a scenario where a cone is forced through a ductile metal plate with a constant lateral tip penetration in a motion in the plane of the plate. The considered process could be an idealisaton of the damage, which...

  6. Plate Tearing by a Cone

    DEFF Research Database (Denmark)

    Simonsen, Bo Cerup

    1998-01-01

    The present paper is concerned with steady-state plate tearing by a cone. This is a scenario where a cone is forced through a ductile metal plate with a constant lateral tip penetration in a motion in the plane of the plate. The considered process could be an idealisation of the damage, which...

  7. On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

    NARCIS (Netherlands)

    Zarubinskaya, M.A.; Van Horssen, W.T.

    2003-01-01

    In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is a

  8. A global attractor for a fluid--plate interaction model accounting only for longitudinal deformations of the plate

    CERN Document Server

    Chueshov, Igor

    2010-01-01

    We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and the classical (nonlinear) elastic plate equation for in-plane motions on a flexible flat part of the boundary. The main peculiarity of the model is the assumption that the transversal displacements of the plate are negligible relative to in-plane displacements. This kind of models arises in the study of blood flows in large arteries. Our main result states the existence of a compact global attractor of finite dimension. We also show that the corresponding linearized system generates exponentially stable $C_0$-semigroup. We do not assume any kind of mechanical damping in the plate component. Thus our results means that dissipation of the energy in the fluid due to viscosity is sufficient to stabilize the system.

  9. SOLUTION TO THE THERMOELASTIC PLATE VIBRATION PROBLEM IF THE THREE PLATE EDGES ARE SIMPLY SUPPORTED AND THE FOURTH ONE IS RIGIDLY FIXED

    Directory of Open Access Journals (Sweden)

    Egorychev Oleg Aleksandrovich

    2012-10-01

    Full Text Available Operating conditions of uneven heating can cause changes in the physical and mechanical properties of materials. Awareness of the values and nature of thermal stresses are required for a comprehensive structural strength analysis. The authors propose their solution to the problem of identification of natural frequencies of vibrations of rectangular plates using a thermal factor. The introductory part of the paper covers the derivation of equations of (a the thermoelastic vibration of a plate, (b initial and boundary conditions. In the next part of the paper, the authors describe a method of frequency equation derivation for plates exposed to special boundary conditions, if the two opposite edges of the plate are simply supported, the temperature of the plate surface is equal to zero degrees Celsius, while the two other edges have an arbitrary type of fixation and an arbitrary thermal mode. The authors have derived a general solution for the above boundary conditions, and by altering the method of fixation of the two edges of a plate, the authors obtain transcendental trigonometric equations reducible to algebraic frequency equations by using expanding in series. Thus, derivation of frequency equations different from the general solution is feasible for various types of boundary conditions. The final part of the paper contains a derivation of the solution to the selected problem using the proposed method. The results demonstrate that the thermoelastic plate has four natural frequencies, two of them being equal to the frequencies of a plate free from the temperature influence, while the other two are close to the frequency of free vibrations of a plate.

  10. Initial stage of flat plate impact onto liquid free surface

    Science.gov (United States)

    Iafrati, Alessandro; Korobkin, Alexander A.

    2004-07-01

    The liquid flow and the free surface shape during the initial stage of flat plate impact onto liquid half-space are investigated. Method of matched asymptotic expansions is used to derive equations of motion and boundary conditions in the main flow region and in small vicinities of the plate edges. Asymptotic analysis is performed within the ideal and incompressible liquid model. The liquid flow is assumed potential and two dimensional. The ratio of the plate displacement to the plate width plays the role of a small parameter. In the main region the flow is given in the leading order by the pressure-impulse theory. This theory provides the flow field around the plate after a short acoustic stage and predicts unbounded velocity of the liquid at the plate edges. In order to resolve the singular flow caused by the normal impact of a flat plate, the fine pattern of the flow in small vicinities of the plate edges is studied. It is shown that the initial flow close to the plate edges is self-similar in the leading order and is governed by nonlinear boundary-value problem with unknown shape of the free surface. The Kutta conditions are imposed at the plate edges, in order to obtain a nonsingular inner solution. This boundary-value problem is solved numerically by iterations. At each step of iterations the "inner" velocity potential is calculated by the boundary-element method. The asymptotics of the inner solution in both the far field and the jet region are obtained to make the numerical algorithm more efficient. The numerical procedure is carefully verified. Agreement of the computed free surface shape with available experimental data is fairly good. Stability of the numerical solution and its convergence are discussed.

  11. Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

    Energy Technology Data Exchange (ETDEWEB)

    Anjomshoa, Amin; Tahani, Masoud [Ferdowsi University, Mashhad (Iran, Islamic Republic of)

    2016-06-15

    In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded ortho tropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.

  12. Plate tectonics conserves angular momentum

    Directory of Open Access Journals (Sweden)

    C. Bowin

    2009-03-01

    Full Text Available A new combined understanding of plate tectonics, Earth internal structure, and the role of impulse in deformation of the Earth's crust is presented. Plate accelerations and decelerations have been revealed by iterative filtering of the quaternion history for the Euler poles that define absolute plate motion history for the past 68 million years, and provide an unprecedented precision for plate angular rotation variations with time at 2-million year intervals. Stage poles represent the angular rotation of a plate's motion between adjacent Euler poles, and from which the maximum velocity vector for a plate can be determined. The consistent maximum velocity variations, in turn, yield consistent estimates of plate accelerations and decelerations. The fact that the Pacific plate was shown to accelerate and decelerate, implied that conservation of plate tectonic angular momentum must be globally conserved, and that is confirmed by the results shown here (total angular momentum ~1.4 E+27 kgm2s−1. Accordingly, if a plate decelerates, other plates must increase their angular momentums to compensate. In addition, the azimuth of the maximum velocity vectors yields clues as to why the "bend" in the Emperor-Hawaiian seamount trend occurred near 46 Myr. This report summarizes processing results for 12 of the 14 major tectonic plates of the Earth (except for the Juan de Fuca and Philippine plates. Plate accelerations support the contention that plate tectonics is a product of torques that most likely are sustained by the sinking of positive density anomalies due to phase changes in subducted gabbroic lithosphere at depth in the upper lower mantle (above 1200 km depth. The tectonic plates are pulled along by the sinking of these positive mass anomalies, rather than moving at near constant velocity on the crests of convection cells driven by rising heat. These results imply that spreading centers are primarily passive reactive

  13. Vehicle License Plate Recognition Syst

    Directory of Open Access Journals (Sweden)

    Meenakshi,R. B. Dubey

    2012-12-01

    Full Text Available The vehicle license plate recognition system has greater efficiency for vehicle monitoring in automatic zone access control. This Plate recognition system will avoid special tags, since all vehicles possess a unique registration number plate. A number of techniques have been used for car plate characters recognition. This system uses neural network character recognition and pattern matching of characters as two character recognition techniques. In this approach multilayer feed-forward back-propagation algorithm is used. The performance of the proposed algorithm has been tested on several car plates and provides very satisfactory results.

  14. Using plate mapping to examine portion size and plate composition for large and small divided plates.

    Science.gov (United States)

    Sharp, David E; Sobal, Jeffery; Wansink, Brian

    2014-12-01

    Does the size of a plate influence the serving of all items equally, or does it influence the serving of some foods - such as meat versus vegetables - differently? To examine this question, we used the new method of plate mapping, where people drew a meal on a paper plate to examine sensitivity to small versus large three-compartment divided plates in portion size and meal composition in a sample of 109 university students. The total drawn meal area was 37% bigger on large plates than small plates, which showed that the portion of plate coverage did not differ by plate size. Men and women drew bigger vegetable portions and men drew bigger meat portions on large plates when compared to small plates. These results suggest that men and women are differentially sensitive to plate size for overall meal size and for meal composition. Implications for decreasing portion size and improving meal balance are that plate size may influence portion size and change the proportions of foods served.

  15. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  16. Dynamics of Shells and Fluid-Loaded Plates.

    Science.gov (United States)

    Wang, Zhang

    This thesis is composed of two parts. The first part is concerned with wave propagation on elastic structures in vacuum. An asymptotic approximation is obtained for the dispersion relation of flexural waves propagating in an infinite, flat plate, with material and/or geometric properties periodic in one direction. A matrix approach is proposed to investigate waves in circular cylindrical thin shells joined with circular plates. Both the general propagator matrix and S-matrix formalisms are presented, with emphasis on the latter. The second part is devoted to structures with ambient fluid loading. The Green's function for a fluid-loaded plate under line loading is expressed as a sum of five fluid-loaded plate waves and an acoustic wave with magnitude given by an infinite integral, similar to a branch cut integral. A scattering matrix approach is presented to solve wave propagation problems on fluid-loaded plates with attached ribs. The low frequency asymptotic dispersion relation for a fluid-loaded plate with infinite number of equally spaced identical ribs is derived, from which an equation of motion for the plate is inferred which is valid also at low frequencies.

  17. Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thicknessn

    Institute of Scientific and Technical Information of China (English)

    ZHOU Yinfeng; WANG Zhongmin

    2009-01-01

    Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.

  18. APPROXIMATE SOLUTIONS FOR TRANSIENT RESPONSE OF CONSTRAINED DAMPING LAMINATED CANTILEVER PLATE

    Institute of Scientific and Technical Information of China (English)

    Liuwei Mao; Anwen Wang; Mingyong Hu

    2010-01-01

    The series composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates,and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work.By solving Lagrange's equation,the frequencies and model loss factors of free vibration of the plate are obtained,then the transient response of constrained damping of laminated cantilever plate is obtained,when the concentrated force is withdrawn suddenly.The theoretical calculations are compared with the experimental data,the results show:both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results.Also,the response time of steel cantilever plate,unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison,which shows that the constrained damping structure can effectively suppress the vibration.

  19. Real Plates and Dubious Microplates

    Science.gov (United States)

    Kogan, M. G.; Steblov, G. M.

    2008-12-01

    From the onset of plate tectonics, the existence of most of the plates was never put in doubt, although the boundaries of some plates, like Africa, were later revised. There are however, two microplates in northeast Asia, the Amurian and Okhotsk, whose existence and the sense of rotation was revised several times. The rms value of plate-residual GPS velocities is 0.5-0.9 mm/a for sets of stations representing the motion of the following plates: Antarctic, Australian, Eurasian, North American, Nubian, Pacific, and South American. This value can be regarded as an upper bound on deviation of real plates from infinite stiffness. The rms value of plate-residual GPS velocities is 1.2-1.8 mm/a for the Indian, Nazca, and Somalian plates. Higher rms values for India and Nazca are attributed to the noisier data. The higher rms value for Somalia appears to arise from the distributed deformation to the east of the East African Rift; whether this statement is true can only be decided from observations of denser network in the future. From the analysis of plate-residual GPS velocities, the Canadian Arctic and northeastern Siberia belong to the North American plate. The detailed GPS survey on Sakhalin Island shows that the Sea of Okhotsk region also belongs to the North American plate while the region to the west of it belongs to the Eurasian plate. These results provide a constraint on the geometry of the North American plate and put in doubt the existence of smaller plates in northeast Asia.

  20. Electrostatic and Small-Signal Analysis of CMUTs With Circular and Square Anisotropic Plates.

    Science.gov (United States)

    Funding la Cour, Mette; Christiansen, Thomas Lehrmann; Jensen, Jørgen Arendt; Thomsen, Erik Vilain

    2015-08-01

    Traditionally, capacitive micromachined ultrasonic transducers (CMUTs) are modeled using the isotropic plate equation, and this leads to deviations between analytical calculations and finite element modeling (FEM). In this paper, the deflection is calculated for both circular and square plates using the full anisotropic plate equation. It is shown that the anisotropic calculations match excellently with FEM, whereas an isotropic approach causes up to 10% deviations in deflection. For circular plates, an exact solution can be found. For square plates using the Galerkin method, and utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is white light interferometer. Fitting the plate parameter for the anisotropic calculated deflection to the measurement, a deviation of 0.07% is seen. Electrostatic and small-signal dynamic analysis are performed using energy considerations including anisotropy. The stable position, effective spring constant, pullin distance, and pull-in voltage are found for both circular and square anisotropic plates, and the pressure dependence is included by comparison with the corresponding analysis for a parallel plate. Measurements on fabricated devices with both circular and square plates subjected to increasing bias voltage are performed, and it is observed that the models including anisotropic effects are within the uncertainty interval of the measurements. Finally, a lumped element small-signal model for both circular and square anisotropic plates is derived to describe the dynamics of the CMUT.

  1. Plate Full of Color

    Centers for Disease Control (CDC) Podcasts

    2008-08-04

    The Eagle Books are a series of four books that are brought to life by wise animal characters - Mr. Eagle, Miss Rabbit, and Coyote - who engage Rain That Dances and his young friends in the joy of physical activity, eating healthy foods, and learning from their elders about health and diabetes prevention. Plate Full of Color teaches the value of eating a variety of colorful and healthy foods.  Created: 8/4/2008 by National Center for Chronic Disease Prevention and Health Promotion (NCCDPHP).   Date Released: 8/5/2008.

  2. Multipactor saturation in parallel-plate waveguides

    Energy Technology Data Exchange (ETDEWEB)

    Sorolla, E.; Mattes, M. [Ecole Polytechnique Federale de Lausanne, Laboratoire d' Electromagnetisme et d' Acoustique (LEMA), Station 11, CH-1015 Lausanne (Switzerland)

    2012-07-15

    The saturation stage of a multipactor discharge is considered of interest, since it can guide towards a criterion to assess the multipactor onset. The electron cloud under multipactor regime within a parallel-plate waveguide is modeled by a thin continuous distribution of charge and the equations of motion are calculated taking into account the space charge effects. The saturation is identified by the interaction of the electron cloud with its image charge. The stability of the electron population growth is analyzed and two mechanisms of saturation to explain the steady-state multipactor for voltages near above the threshold onset are identified. The impact energy in the collision against the metal plates decreases during the electron population growth due to the attraction of the electron sheet on the image through the initial plate. When this growth remains stable till the impact energy reaches the first cross-over point, the electron surface density tends to a constant value. When the stability is broken before reaching the first cross-over point the surface charge density oscillates chaotically bounded within a certain range. In this case, an expression to calculate the maximum electron surface charge density is found whose predictions agree with the simulations when the voltage is not too high.

  3. SYMPLECTIC SOLUTION SYSTEM FOR REISSNER PLATE BENDING

    Institute of Scientific and Technical Information of China (English)

    姚伟岸; 隋永枫

    2004-01-01

    Based on the Hellinger-Reissner variatonal principle for Reissner plate bending and introducing dual variables, Hamiltonian dual equations for Reissner plate bending were presented. Therefore Hamiltonian solution system can also be applied to Reissner plate bending problem, and the transformation from Euclidian space to symplectic space and from Lagrangian system to Hamiltonian system was realized. So in the symplectic space which consists of the original variables and their dual variables, the problem can be solved via effective mathematical physics methods such as the method of separation of variables and eigenfunction-vector expansion. All the eigensolutions and Jordan canonical form eigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail,and their physical meanings are showed clearly. The adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are formed. It is showed that the all eigensolutions for zero eigenvalue are basic solutions of the Saint-Venant problem and they form a perfect symplectic subspace for zero eigenvalue. And the eigensolutions for nonzero eigenvalue are covered by the Saint-Venant theorem. The symplectic solution method is not the same as the classical semi- inverse method and breaks through the limit of the traditional semi-inverse solution. The symplectic solution method will have vast application.

  4. Viscous Boussinesq equations for internal waves

    Science.gov (United States)

    Liu, Chi-Min

    2016-04-01

    In this poster, Boussinesq wave equations for internal wave propagation in a two-fluid system bounded by two impermeable plates are derived and analyzed. Using the perturbation method as well as the Padé approximation, a set of three equations accurate up to the fourth order are derived and displayed by three unknowns: the interfacial elevation, upper and lower velocity potentials at arbitrary vertical positions. No limitation on nonlinearity is made while weakly dispersive effects are originally considered in the derivation. The derived equations are examined by comparing its dispersion relation with those of existing models to verify the accuracy. The results show that present model equations provide an excellent base for simulating internal waves not only in shallower configuration but also medium configuration.

  5. UNSYMMETRICAL NONLINEAR BENDING PROBLEM OF CIRCULAR THIN PLATE WITH VARIABLE THICKNESS

    Institute of Scientific and Technical Information of China (English)

    WANG Xin-zhi; ZHAO Yong-gang; JU Xu; ZHAO Yan-ying; YEH Kai-yuan

    2005-01-01

    Firstly, the cross large deflection equation of circular thin plate with variable thickness in rectangular coordinates system was transformed into unsymmetrical large deflection equation of circular thin plate with variable thickness in polar coordinates system.This cross equation in polar coordinates system is united with radical and tangential equations in polar coordinates system, and then three equilibrium equations were obtained. Physical equations and nonlinear deformation equations of strain at central plane are substituted into superior three equilibrium equations, and then three unsymmetrical nonlinear equations with three deformation displacements were obtained. Solution with expression of Fourier series is substituted into fundamental equations; correspondingly fundamental equations with expression of Fourier series were obtained. The problem was solved by modified iteration method under the boundary conditions of clamped edges. As an example, the problem of circular thin plate with variable thickness subjected to loads with cosin form was studied.Characteristic curves of the load varying with the deflection were plotted. The curves vary with the variation of the parameter of variable thickness. Its solution is accordant with physical conception.

  6. MAGNETIC-ELASTIC BUCKLING OF A THIN CURRENT CARRYING PLATE SIMPLY SUPPORTED AT THREE EDGES

    Institute of Scientific and Technical Information of China (English)

    WANG Zhiren; WANG Ping; BAI Xiangzhong

    2008-01-01

    The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic equation, physical equations, geometric equations, the expression for Lorenz force and the electrical dynamic equation, the magnetic-elasticity dynamic buckling equation is derived. The equation is changed into a standard form of the Mathieu equation using Galerkin's method. Thus, the buckling problem can be solved with a Mathieu equation. The criterion equation of the buckling problem also has been obtained by discussing the eigenvalue relation of the coefficients λ and η in the Mathieu equation. As an example, a thin plate simply supported at three edges is solved here. Its magnetic-elasticity dynamic buckling equation and the relation curves of the instability state with variations in some parameters are also shown in this paper. The conclusions show that the electrical magnetic forces may be controlled by changing the parameters of the current or the magnetic field so that the aim of controlling the deformation, stress, strain and stability of the current carrying plate is achieved.

  7. Research on relationships between Lamb wave velocity and static stress in metal plate

    Institute of Scientific and Technical Information of China (English)

    WANG Jun; WANG Yinguan

    2006-01-01

    On the fact that an isotropic metal solid produces anisotropic property in the state of static stress, based on the theory of the nonlinear acoustoelasticity, the equivalent secondorder elastic constants are calculated for metal plate with static stress. For the case of thin metal plate with stress, the two kinds of dispersion equation for Lamb waves propagating parallel and vertical to the direction of static stress are derived. Using the equations, the relationships between Lamb wave velocity and static stress in a metal plate are discussed.

  8. CMS Resistive plate Champers

    CERN Document Server

    Zainab, Karam

    2013-01-01

    There are many types of gas detectors which are used in CERN in LHC project, There is a main parts for the gas detectors which must be in all gas detectors types like Multiwire proportional chambers, such as the micromesh gaseous structure chamber (the MicroMegas), Gas-electron multiplier (GEM) detector, Resistive Plate Champers... Compact Muon Solenoid (CMS) experiment detecting muons which are powerful tool for recognizing signatures of interesting physics processes. The CMS detector uses: drift tube (DT), cathode strip chamber (CSC) and resistive plate chamber (RPC). Building RPC’s was my project in summer student program (hardware). RPC’s have advantages which are triggering detector and Excellent time resolution which reinforce the measurement of the correct beam crossing time. RPC’s Organized in stations :  RPC barrel (RB) there are 4 stations, namely RB1, RB2, RB3, and RB4  While in the RPC endcap (RE) the 3 stations are RE1, RE2, and RE3. In the endcaps a new starion will be added and this...

  9. Localised Plate Motion on Venus

    Science.gov (United States)

    Ghail, R. C.

    1996-03-01

    The volcanic and tectonic features observed in Dali Vinculum, Parga Vinculum and Imdr Regio are concentrated at long, narrow, curvilinear zones, with relatively minor volcanism and tectonism between these zones. These zones, whilst more diffuse than terrestrial plate boundaries, nevertheless define the margins of tectonic plates. In contrast to Earth, however, it appears that venusian plates are neither created nor destroyed by lateral motion. Rather, plates are thinned and intruded at vincula plate boundaries, vertically accreted by small-scale intra-plate (planitia) volcanism and perhaps destroyed by delamination of thickened crust in tesserae and montane regions such as Thetis Regio and Ishtar Terra. The diversity in age both between and within these three areas together with the evidence for infrequent, small scale resurfacing in the planitiae are difficult to reconcile with a non-uniformitarian geological process.

  10. Tectonics of the Easter plate

    Science.gov (United States)

    Engeln, J. F.; Stein, S.

    1984-01-01

    A new model for the Easter plate is presented in which rift propagation has resulted in the formation of a rigid plate between the propagating and dying ridges. The distribution of earthquakes, eleven new focal mechanisms, and existing bathymetric and magnetic data are used to describe the tectonics of this area. Both the Easter-Nazca and Easter-Pacific Euler poles are sufficiently close to the Easter plate to cause rapid changes in rates and directions of motion along the boundaries. The east and west boundaries are propagating and dying ridges; the southwest boundary is a slow-spreading ridge and the northern boundary is a complex zone of convergent and transform motion. The Easter plate may reflect the tectonics of rift propagation on a large scale, where rigid plate tectonics requires boundary reorientation. Simple schematic models to illustrate the general features and processes which occur at plates resulting from large-scale rift propagation are used.

  11. Tectonics of the Easter plate

    Science.gov (United States)

    Engeln, J. F.; Stein, S.

    1984-01-01

    A new model for the Easter plate is presented in which rift propagation has resulted in the formation of a rigid plate between the propagating and dying ridges. The distribution of earthquakes, eleven new focal mechanisms, and existing bathymetric and magnetic data are used to describe the tectonics of this area. Both the Easter-Nazca and Easter-Pacific Euler poles are sufficiently close to the Easter plate to cause rapid changes in rates and directions of motion along the boundaries. The east and west boundaries are propagating and dying ridges; the southwest boundary is a slow-spreading ridge and the northern boundary is a complex zone of convergent and transform motion. The Easter plate may reflect the tectonics of rift propagation on a large scale, where rigid plate tectonics requires boundary reorientation. Simple schematic models to illustrate the general features and processes which occur at plates resulting from large-scale rift propagation are used.

  12. LOW VELOCITY RESPONSE CHARACTERISTICS OF COMPOSITE PLATE WITH EMBEDDED SHAPE MEMORY ALLOY

    Institute of Scientific and Technical Information of China (English)

    WuYongdong; ZhongWeifang; LiangYide

    2004-01-01

    This paper analyzes the characteristics of utilizing shape memory effect (SME) of shape memory alloy (SMA) in improving the low velocity impact resistance performance of composite plate by using finite element method. The constitutive relation for SMA hybrid composite plates is presented. The analytic model of finite element for SMA composite plate subjected to low velocity impact is established. The modified Hertz's contact law is used to determine the impact contact force. The computing procedures for solving the finite element equation using Newmark direct integration method are given. The numerical modelling results show that the SMA can effectively improve the low velocity impact resistance performance of composite plate.

  13. Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

    Science.gov (United States)

    Zhu, F. H.; Fu, Y. M.

    2008-12-01

    By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.

  14. Studies on the Dynamic Buckling of Circular Plate Irradiated by Laser Beam

    Institute of Scientific and Technical Information of China (English)

    黄晨光; 段祝平

    2002-01-01

    The dynamic buckling of thin copper plate induced by laser beam, was analyzed with the numerical integration and disturbance methods of controlling equation. The buckling and post-buckling of thin plate were shown, with the consideration of the temperature distribution, inertia effect and initial deflection. At last, the buckling criterion about the circular plate was obtained and used to investigate the relation between the critical laser intensity and the ratio of thickness and diameter of the plate. The results fit the experimental observation and the FEM simulation very well, and benefit to the understanding of failure phenomenon of structures irradiated by laser beam.

  15. A dynamic performance simulation model of flat-plate solar collectors for a heat pump system

    Energy Technology Data Exchange (ETDEWEB)

    Arinze, E.A.; Schoenau, G.J.; Sokhansanj, S. (Saskatchewan Univ., Saskatoon, SK (Canada). College of Engineering); Adefila, S.S.; Mumah, S.M. (Ahmadu Bello Univ., Zaria (Nigeria). Dept. of Chemical Engineering)

    1993-01-01

    Flat-plate collectors are inherently exposed to time-varying meteorological and system parameters. Thus, dynamic modeling, rather than the commonly used steady-state models, is a more accurate approach for the design and performance evaluation of flat-plate solar collectors. The dynamic model presented in this study describes the fluid, plate and cover temperatures of the collector by three different differential equations. Taylor series expansion and the Runge-Kutta method are used in the solution of the differential equations. The accuracy of the dynamic model was tested by comparing the results predicted by the model with experimental performance data obtained for a liquid-cooled flat-plate solar collector with a corrugated transparent fiberglass cover. The predicted results by the dynamic model agreed favorably with the measured experimental data for the flat-plate solar collector. Experimentally determined collector temperatures varied by a maximum of [+-]3[sup o]C from values predicted by the model. (Author)

  16. NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION

    Institute of Scientific and Technical Information of China (English)

    XIAO Yong-gang; FU Yi-ming; ZHA Xu-dong

    2005-01-01

    Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.

  17. Aluminum Manganese Molten Salt Plating

    Science.gov (United States)

    2006-06-01

    Dry fixture thoroughly with the air gun. Be especially careful to dry water out of crevices. Note: water is a contaminant to the plating process...easily destroyed if blown with the air. Be especially careful to dry water out of crevices. Note: water is a contaminant to the plating process and...especially careful to dry water out of crevices. 13. Carefully remove part from fixture. If residual plating solution is present at attachments points

  18. Buckling of laminated composite plates subjected to mechanical and thermal loads using meshless collocations

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Sandeep; Shukla, K. K. [Motilal Nehru National Institute of Technology, Allahabad (India); Shingh, Jeeoot [Department of Mechanical Engineering, Birla Institute of Technology Mesra, Ranchi (India)

    2013-02-15

    Meshless collocations utilizing Gaussian and Multi quadric radial basis functions for the stability analysis of orthotropic and cross ply laminated composite plates subjected to thermal and mechanical loading are presented. The governing differential equations of plate are based on higher order shear deformation theory considering two different transverse shear stress functions. The plate governing differential equations are discretized using radial basis functions to cast a set of simultaneous equations. The convergence of both radial basis functions is studied for different values of shape parameters. Several numerical examples are undertaken to demonstrate the accuracy of present method and the effects of orthotropy ratio of the material, span to thickness ratio of the plate, and fiber orientation on critical load/temperature are also presented.

  19. EFFECT OF DAMAGE ON NONLINEAR DYNAMIC PROPERTIES OF VISCOELASTIC RECTANGULAR PLATES

    Institute of Scientific and Technical Information of China (English)

    ZHENG Yu-fang; FU Yi-ming

    2005-01-01

    The nonlinear dynamic behaviors of viscoelastic rectangular plates including the damage effects under the action of a transverse periodic load were studied. Using the von Karman equations, Boltzmann superposition principle and continuum damage mechanics, the nonlinear dynamic equations in terms of the mid-plane displacements for the viscoelastic thin plates with damage effect were derived. By adopting the finite difference method and Newmark method, these equations were solved. The results were compared with the available data. In the numerical calculations, the effects of the external loading parameters and geometric dimensions of the plate on the nonlinear dynamic responses of the plate were discussed. Research results show that the nonlinear dynamic response of the structure will change remarkably when the damage effect is considered.

  20. Dynamic stress concentrations in thick plates with two holes based on refined theory

    Institute of Scientific and Technical Information of China (English)

    周伟平; 胡超; 刘殿魁

    2014-01-01

    Based on complex variables and conformal mapping, the elastic wave scat-tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonal function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen-tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

  1. Modal radiation patterns of baffled circular plates and membranes

    DEFF Research Database (Denmark)

    Christiansen, Thomas Lehrmann; Hansen, Ole; Thomsen, Erik Vilain

    2014-01-01

    The far field velocity potential and radiation pattern of baffled circular plates and membranes are found analytically using the full set of modal velocity profiles derived from the corresponding equation of motion. The derivation is valid for a plate or membrane subjected to an external excitation...... that of a monopole, while the non-axisymmetric modes exhibit multipole behavior. Numerical results are also given, demonstrating the implications of having non-axisymmetric excitation using both a point excitation with varying eccentricity and a homogeneous excitation acting on half of the circular radiator....

  2. On the breakup of tectonic plates by polar wandering

    Science.gov (United States)

    Liu, H.-S.

    1974-01-01

    The equations for the stresses in a homogeneous shell of uniform thickness caused by a shift of the axis of rotation are derived. The magnitude of these stresses reaches a maximum value of the order of 10 to the 9th power dyn/sq cm, which is sufficient for explaining a tectonic breakup. In order to deduce the fracture pattern according to which the breakup of tectonic plates can be expected the theory of plastic deformation of shells is applied. The analysis of this pattern gives an explanation of the existing boundary systems of the major tectonic plates as described by Morgan (1968), LePichon (1968) and Isacks et al. (1968).

  3. Non-stationary oscillations of sandwich plates under local dynamic loading

    NARCIS (Netherlands)

    Skvortsov, Vitaly; Krakhmalev, Sergey; Koysin, V.; Shipsha, Andrey

    2003-01-01

    The paper addresses the elastic response of composite sandwich panels to local dynamic loading. The plane and axisymmetric formulations are considered; no overall bending is assumed. The governing equations are derived using the static Lamé equations for the core and the plate Kirchoff-Love dynamic

  4. Glass-bead peen plating

    Science.gov (United States)

    Graves, J. R.

    1974-01-01

    Peen plating of aluminum, copper, and nickel powders was investigated. Only aluminum was plated successfully within the range of peen plating conditions studied. Optimum plating conditions for aluminum were found to be: (1) bead/powder mixture containing 25 to 35% powder by weight, (2) peening intensity of 0.007A as measured by Almen strip, and (3) glass impact bead diameter of at least 297 microns (0.0117 inches) for depositing-100 mesh aluminum powder. No extensive cleaning or substrate preparation is required beyond removing loose dirt or heavy oil.

  5. Intermittent plate tectonics?

    Science.gov (United States)

    Silver, Paul G; Behn, Mark D

    2008-01-04

    Although it is commonly assumed that subduction has operated continuously on Earth without interruption, subduction zones are routinely terminated by ocean closure and supercontinent assembly. Under certain circumstances, this could lead to a dramatic loss of subduction, globally. Closure of a Pacific-type basin, for example, would eliminate most subduction, unless this loss were compensated for by comparable subduction initiation elsewhere. Given the evidence for Pacific-type closure in Earth's past, the absence of a direct mechanism for termination/initiation compensation, and recent data supporting a minimum in subduction flux in the Mesoproterozoic, we hypothesize that dramatic reductions or temporary cessations of subduction have occurred in Earth's history. Such deviations in the continuity of plate tectonics have important consequences for Earth's thermal and continental evolution.

  6. VISAS AND GREEN PLATES

    CERN Multimedia

    2000-01-01

    From 3 April 2000, all questions relating to visa requests for Switzerland, France, or Russia for a member of the personnel must be addressed to Ms. Agnita Querrou (telephone 72838, office 5-2-019, e-mail Agnita.Querrou@cern.ch).The Users' Office continues to deal with requests for letters of invitation and questions concerning visas for users in EP Division.Questions relating to removals, requests for green plates, to privileges of members of the personnel and to the importation of vehicles are still dealt with by Ms Zuzana Miller (telephone 79257, office 33-1-017, e-mail Zuzana.Muller@cern.ch) and Ms Joëlle Belleman (telephone 73962, office 33-1-019, e-mail Joelle.Belleman@cern.ch).

  7. Plate osteosynthesis of simple forearm fractures : LCP versus DC plates

    NARCIS (Netherlands)

    Stevens, Charles Tjerk; Ten Duis, Henk Jan

    2008-01-01

    The aim of this study was to compare the time to radiological bony union of simple A-type fractures of the forearm, treated with either a locking compression plate (LCP) or a dynamic compression plate (DCP). For each fracture, the relation between the use of compression and radiological healing time

  8. Plate osteosynthesis of simple forearm fractures : LCP versus DC plates

    NARCIS (Netherlands)

    Stevens, Charles Tjerk; Ten Duis, Henk Jan

    The aim of this study was to compare the time to radiological bony union of simple A-type fractures of the forearm, treated with either a locking compression plate (LCP) or a dynamic compression plate (DCP). For each fracture, the relation between the use of compression and radiological healing time

  9. The vibroacoustic response and sound absorption performance of multilayer, microperforated rib-stiffened plates

    Science.gov (United States)

    Zhou, Haian; Wang, Xiaoming; Wu, Huayong; Meng, Jianbing

    2017-04-01

    The vibroacoustic response and sound absorption performance of a structure composed of multilayer plates and one rigid back wall are theoretically analyzed. In this structure, all plates are two-dimensional, microperforated, and periodically rib-stiffened. To investigate such a structural system, semianalytical models of one-layer and multilayer plate structures considering the vibration effects are first developed. Then approaches of the space harmonic method and Fourier transforms are applied to a one-layer plate, and finally the cascade connection method is utilized for a multilayer plate structure. Based on fundamental acoustic formulas, the vibroacoustic responses of microperforated stiffened plates are expressed as functions of a series of harmonic amplitudes of plate displacement, which are then solved by employing the numerical truncation method. Applying the inverse Fourier transform, wave propagation, and linear addition properties, the equations of the sound pressures and absorption coefficients for the one-layer and multilayer stiffened plates in physical space are finally derived. Using numerical examples, the effects of the most important physical parameters—for example, the perforation ratio of the plate, sound incident angles, and periodical rib spacing—on sound absorption performance are examined. Numerical results indicate that the sound absorption performance of the studied structure is effectively enhanced by the flexural vibration of the plate in water. Finally, the proposed approaches are validated by comparing the results of stiffened plates of the present work with solutions from previous studies.

  10. Measurement of Equation of State of Silicone Elastomer

    Science.gov (United States)

    Winter, R. E.; Whiteman, G.; Haining, G. S.; Salisbury, D. A.; Tsembelis, K.

    2004-07-01

    Silicone Elastomer, ("Sylgard 184 ®"), samples were mounted between copper plates. Manganin stress gauges were placed within the front copper plate, halfway through the Sylgard and at the interface between the Sylgard and the rear copper plate. A series of experiments was performed in which the front plate was impacted by copper plates projected at a range of velocities. It was assumed that a Grüneisen Gamma form with a constant Γ could fit the Equation of State of the sample. A trial set of EoS parameters, including Gamma, was entered into a spreadsheet, then the state variables for the different stress jumps were calculated with the aid of a "Goalseek" function. This enabled the stresses and times for each jump to be calculated. Comparing these predictions with the experimentally determined parameters enabled optimum values of the EoS parameters to be identified.

  11. Thermal buckling analysis of truss-core sandwich plates

    Institute of Scientific and Technical Information of China (English)

    陈继伟; 刘咏泉; 刘伟; 苏先樾

    2013-01-01

    Truss-core sandwich plates have received much attention in virtue of the high values of strength-to-weight and stiffness-to-weight as well as the great ability of impulse-resistance recently. It is necessary to study the stability of sandwich panels under the influence of the thermal load. However, the sandwich plates are such complex three-dimensional (3D) systems that direct analytical solutions do not exist, and the finite element method (FEM) cannot represent the relationship between structural parameters and mechanical properties well. In this paper, an equivalent homogeneous continuous plate is idealized by obtaining the effective bending and transverse shear stiffness based on the characteristics of periodically distributed unit cells. The first order shear deformation theory for plates is used to derive the stability equation. The buckling temperature of a simply supported sandwich plate is given and verified by the FEM. The effect of related parameters on mechanical properties is investigated. The geometric parameters of the unit cell are optimized to attain the maximum buckling temperature. It is shown that the optimized sandwich plate can improve the resistance to thermal buckling significantly.

  12. Dynamic stiffness matrix of a rectangular plate for the general case

    Science.gov (United States)

    Banerjee, J. R.; Papkov, S. O.; Liu, X.; Kennedy, D.

    2015-04-01

    The dynamic stiffness matrix of a rectangular plate for the most general case is developed by solving the bi-harmonic equation and finally casting the solution in terms of the force-displacement relationship of the freely vibrating plate. Essentially the frequency dependent dynamic stiffness matrix of the plate when all its sides are free is derived, making it possible to achieve exact solution for free vibration of plates or plate assemblies with any boundary conditions. Previous research on the dynamic stiffness formulation of a plate was restricted to the special case when the two opposite sides of the plate are simply supported. This restriction is quite severe and made the general purpose application of the dynamic stiffness method impossible. The theory developed in this paper overcomes this long-lasting restriction. The research carried out here is basically fundamental in that the bi-harmonic equation which governs the free vibratory motion of a plate in harmonic oscillation is solved in an exact sense, leading to the development of the dynamic stiffness method. It is significant that the ingeniously sought solution presented in this paper is completely general, covering all possible cases of elastic deformations of the plate. The Wittrick-Williams algorithm is applied to the ensuing dynamic stiffness matrix to provide solutions for some representative problems. A carefully selected sample of mode shapes is also presented.

  13. Application of Normal Mode Expansion to AE Waves in Finite Plates

    Science.gov (United States)

    Gorman, M. R.; Prosser, W. H.

    1997-01-01

    Breckenridge et al. (1975), Hsu (1985) and Pao (1978) adapted approaches from seismology to calculate the response at the surface of an infinite half-space and an infinite plate. These approaches have found use in calibrating acoustic emission (AE) transducers. However, it is difficult to extend this theoretical approach to AE testing of practical structures. Weaver and Pao (1982) considered a normal mode solution to the Lamb equations. Hutchinson (1983) pointed out the potential relevance of Mindlin's plate theory (1951) to AE. Pao (1982) reviewed Medick s (1961) classical plate theory for a point source, but rejected it as useful for AE and no one seems to have investigated its relevance to AE any further. Herein, a normal mode solution to the classical plate bending equation was investigated for its applicability to AE. The same source-time function chosen by Weaver and Pao is considered. However, arbitrary source and receiver positions are chosen relative to the boundaries of the plate. This is another advantage of the plate theory treatment in addition to its simplicity. The source does not have to be at the center of the plate as in the axisymmetric treatment. The plate is allowed to remain finite and reflections are predicted. The importance of this theory to AE is that it can handle finite plates, realistic boundary conditions, and can be extended to composite materials.

  14. Kinetic energy equations for the average-passage equation system

    Science.gov (United States)

    Johnson, Richard W.; Adamczyk, John J.

    1989-01-01

    Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

  15. Kinetic energy equations for the average-passage equation system

    Science.gov (United States)

    Johnson, Richard W.; Adamczyk, John J.

    1989-01-01

    Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

  16. Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdi Rashidi

    2008-01-01

    Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

  17. Plate tectonics, damage and inheritance.

    Science.gov (United States)

    Bercovici, David; Ricard, Yanick

    2014-04-24

    The initiation of plate tectonics on Earth is a critical event in our planet's history. The time lag between the first proto-subduction (about 4 billion years ago) and global tectonics (approximately 3 billion years ago) suggests that plates and plate boundaries became widespread over a period of 1 billion years. The reason for this time lag is unknown but fundamental to understanding the origin of plate tectonics. Here we suggest that when sufficient lithospheric damage (which promotes shear localization and long-lived weak zones) combines with transient mantle flow and migrating proto-subduction, it leads to the accumulation of weak plate boundaries and eventually to fully formed tectonic plates driven by subduction alone. We simulate this process using a grain evolution and damage mechanism with a composite rheology (which is compatible with field and laboratory observations of polycrystalline rocks), coupled to an idealized model of pressure-driven lithospheric flow in which a low-pressure zone is equivalent to the suction of convective downwellings. In the simplest case, for Earth-like conditions, a few successive rotations of the driving pressure field yield relic damaged weak zones that are inherited by the lithospheric flow to form a nearly perfect plate, with passive spreading and strike-slip margins that persist and localize further, even though flow is driven only by subduction. But for hotter surface conditions, such as those on Venus, accumulation and inheritance of damage is negligible; hence only subduction zones survive and plate tectonics does not spread, which corresponds to observations. After plates have developed, continued changes in driving forces, combined with inherited damage and weak zones, promote increased tectonic complexity, such as oblique subduction, strike-slip boundaries that are subparallel to plate motion, and spalling of minor plates.

  18. Magnetic fluid based squeeze film between porous annular curved plates with the effect of rotational inertia

    Indian Academy of Sciences (India)

    Rajesh C Shah; S R Tripathi; M V Bhat

    2002-03-01

    The squeeze film behaviour between rotating annular plates was analysed theoretically when the curved upper plate with a uniform porous facing approached the impermeable and flat lower plate, considering a magnetic fluid lubricant in the presence of an external magnetic field oblique to the plates. Expressions were obtained for pressure and load capacity; and response time is given by a differential equation. The increases in pressure and load capacity depended only on the magnetization. However, the increase in response time depended on magnetization, fluid inertia and speed of rotation of the plates.

  19. Calculation of similarity solutions of partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1980-08-01

    When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/.

  20. Theoretical analysis based on fundamental functions of thin plate and experimental measurement for vibration characteristics of a plate coupled with liquid

    Science.gov (United States)

    Liao, Chan-Yi; Wu, Yi-Chuang; Chang, Ching-Yuan; Ma, Chien-Ching

    2017-04-01

    This study combined theoretical, experimental, and numerical analysis to investigate the vibration characteristics of a thin rectangular plate positioned horizontally at the bottom of a rectangular container filled with liquid. Flow field pressure was derived using an equation governing the behavior of incompressible fluids. Analytic solutions to vibrations in a thin plate in air served as the fundamental function of the thin plate coupled with liquid. We then used liquid pressure, and the out-of-plane deflection of the thin plate for the construction of frequency response functions for the analysis of vibration characteristics in the liquid-plate coupling system. Two experimental methods were employed to measure the vibration characteristics of the thin plate immersed in water. The first involved using sensors of polyvinylidene difluoride (PVDF) to measure transient signals of fluid-plate system subjected an impact at the thin plate. These were then converted to the frequency domain in order to obtain the resonant frequencies of the fluid-plate coupling system. The second method was amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), which was used to measure the dynamic characteristics of the thin plate in the flow field. This method was paired with the image processing techniques, temporal speckle pattern interferometry (TSPI) and temporal standard deviation (TSTD), to obtain clear mode shapes of the thin plate and resonant frequencies. Comparison of the results from theoretical analysis, finite element method, and experimental measurements confirmed the accuracy of our theoretical analysis, which was superior to the conventional approach based on beam mode shape functions. The experimental methods proposed in this study can be used to measure the resonant frequencies of underwater thin plates, and clear mode shapes can be obtained using AF-ESPI. Our results indicate that the resonant frequencies of thin plates underwater are lower than

  1. Solving Nonlinear Wave Equations by Elliptic Equation

    Institute of Scientific and Technical Information of China (English)

    FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo

    2003-01-01

    The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.

  2. Casimir Effect for Dielectric Plates

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    We generalize Kupisewska method to the three-dimensional system and another derivation of the Casimir effect between two dielectric plates is presented based on the explicit quantization of the electromagnetic field in the presence of dielectrics, where the physical meaning of "evanescent mode" is discussed. The Lifshitz's formula is rederived perfect metallic plates will the evanescent modes become unimportant.

  3. Micro-channel plate detector

    Science.gov (United States)

    Elam, Jeffrey W.; Lee, Seon W.; Wang, Hsien -Hau; Pellin, Michael J.; Byrum, Karen; Frisch, Henry J.

    2015-09-22

    A method and system for providing a micro-channel plate detector. An anodized aluminum oxide membrane is provided and includes a plurality of nanopores which have an Al coating and a thin layer of an emissive oxide material responsive to incident radiation, thereby providing a plurality of radiation sensitive channels for the micro-channel plate detector.

  4. Gold plating on spectacle frames.

    Science.gov (United States)

    Kenny, I; Mitchell, J W; Walsh, G

    1997-05-01

    An investigation was carried out into the thickness and standard of application of the plating and lacquer coatings applied to three metal spectacle frames. All conform to BS 6625 (1991) for plating thickness, but there was considerable variation in regularity and porosity.

  5. Discrete Simulation of Flexible Plate Structure Using State-Space Formulation

    Institute of Scientific and Technical Information of China (English)

    S. Md. Salleh; M. O. Tokhi

    2008-01-01

    This paper presents the development of dynamic simulation of a flexible plate structure with various boundary conditions. A flexible square plate is considered. A finite-difference method is used to discretise the governing partial differential equation formulation describing its dynamic behaviour. The model thus developed has been validated against characteristic parameters of the plate. The model thus developed is further formulated using discrete state-space representation, to allow easy and fast implementation for simulating the dynamic behaviour of the plate with various boundary conditions. The simulation algorithm thus developed is validated, and accurate results with representation of the first five modes of vibration of the plate have been achieved. The algorithm thus developed is used in subsequent research work as a platform for development and verification of suitable control strategies for vibration suppression of flexible plate structures.

  6. Flexural-torsional buckling analysis of angle-bar stiffened plates

    Energy Technology Data Exchange (ETDEWEB)

    Ahmad, Rahbar Ranji [Amirkabir University of Technology, Tehran (Iran, Islamic Republic of)

    2015-09-15

    The interaction of flexural-torsional buckling modes is critical for stiffened plates with asymmetric stiffeners. However, this interaction is ignored in all design rules because it is complex to characterize. In the literature, the presence of an attached plate is ignored, and stiffened plate is treated as an ordinary asymmetric beam. In the flexural buckling mode, stiffener and the attached plate buckle together; in the torsional buckling mode, the attached plate cannot freely rotate with stiffener. Basic equations of the flexural-torsional buckling modes are deduced based on hybrid beam concept and a new strain distribution assumption for sideway bending of stiffeners. Elastic buckling stresses of different angle-bar stiffened plates are calculated and compared with those generated by the Finite element method (FEM) and those available in the literature. The present method has better agreements with FEM.

  7. EXACT SOLUTION FOR TEMPERATURE-DEPENDENT BUCKLING ANALYSIS OF FG-CNT-REINFORCED MINDLIN PLATES

    Directory of Open Access Journals (Sweden)

    Seyed Mohammad Mousavi

    2016-03-01

    Full Text Available This research deals with the buckling analysis of nanocomposite polymeric temperature-dependent plates reinforced by single-walled carbon nanotubes (SWCNTs. For the carbon-nanotube reinforced composite (CNTRC plate, uniform distribution (UD and three types of functionally graded (FG distribution patterns of SWCNT reinforcements are assumed. The material properties of FG-CNTRC plate are graded in the thickness direction and estimated based on the rule of mixture. The CNTRC is located in a elastic medium which is simulated with temperature-dependent Pasternak medium. Based on orthotropic Mindlin plate theory, the governing equations are derived using Hamilton’s principle and solved by Navier method. The influences of the volume fractions of carbon nanotubes, elastic medium, temperature and distribution type of CNTs are considered on the buckling of the plate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the stiffness of plates.

  8. Vibrations of Poroelastic Plates: Mixed Displacement-Pressure Modelisation and Experiments

    OpenAIRE

    2009-01-01

    International audience; This paper presents the equations of motion of air saturated rectangular poroelastic plates. The model is based on a mixed displacement-pressure formulation of Biot's theory. Two equations of motion are obtained and solved with the Galerkin method for any boundary conditions. These equations take into account the solid-fluid coupling effects. Simulations of the bending vibrations of a rectangular water saturated sandstone and air saturated acoustic foam are performed f...

  9. Plate shell structures of glass

    DEFF Research Database (Denmark)

    Bagger, Anne

    . This modelling technique is used to model a plate shell structure with a span of 11.5 meters in the FE software \\textsc{Abaqus}. The structure is analyzed with six different connection details with varying stiffness characteristics, to investigate the influence of these characteristics on the structural effects...... University, a script has been developed for an automated generation of a given plate shell geometry and a corresponding finite element (FE) model. A suitable FE modelling technique is proposed, suggesting a relatively simple method of modelling the connection detail's stiffness characteristics....... Based on these investigations, and FE analysis of other plate shell models, the structural behaviour is described. Possible methods of estimating the stresses in a given plate shell structure are proposed. The non-linear behaviour of a plate shell structure is investigated for varying parameters...

  10. The moving plate capacitor paradox

    Science.gov (United States)

    Davis, B. R.; Abbott, D.; Parrondo, J. M. R.

    2000-03-01

    For the first time we describe an apparent paradox concerning a moving plate capacitor driven by thermal noise from a resistor. A demon restores the plates of the capacitor to their original position, only when the voltage across the capacitor is small—hence only small forces are present for the demon to work against. The demon has to work harder than this to avoid the situation of perpetual motion, but the question is how? We explore the concept of a moving plate capacitor, driven by noise, a step further by examining the case where the restoring force on the capacitor plates is provided by a simple spring, rather than some unknown demon. We display simulation results with interesting behavior, particularly where the capacitor plates collide with each other.

  11. SAMI Automated Plug Plate Configuration

    CERN Document Server

    Lorente, Nuria P F; Goodwin, Michael

    2012-01-01

    The Sydney-AAO Multi-object Integral field spectrograph (SAMI) is a prototype wide-field system at the Anglo-Australian Telescope (AAT) which uses a plug-plate to mount its 13 x 61-core imaging fibre bundles (hexabundles) in the optical path at the telescope's prime focus. In this paper we describe the process of determining the positions of the plug-plate holes, where plates contain three or more stacked observation configurations. The process, which up until now has involved several separate processes and has required significant manual configuration and checking, is now being automated to increase efficiency and reduce error. This is carried out by means of a thin Java controller layer which drives the configuration cycle. This layer controls the user interface and the C++ algorithm layer where the plate configuration and optimisation is carried out. Additionally, through the Aladin display package, it provides visualisation and facilitates user verification of the resulting plates.

  12. Thin plate neotectonic models of the Australian plate

    Science.gov (United States)

    Burbidge, D. R.

    2004-10-01

    Thin plate finite element models of the neotectonic deformation of the Australian plate have been calculated in order to estimate the stress and strain rate within the plate, specifically concentrating on the Australian continent. The model includes plate-bounding faults, an anelastic brittle-ductile layered rheology and the option of laterally varying elevation and heat flow. The results of the models are compared to (1) the velocity of geodetic benchmarks on the Australian plate, (2) the spreading rate of the mid-oceanic ridges along the Australian plate's margins, (3) the direction of the maximum horizontal principal stress, (4) the stress regime within the plate, and (5) the crustal thickness estimated from the depth to the base of Mohorovicic discontinuity's transition zone. A variety of models are tested with a wide range of input parameters. The model with the smallest misfit with observations predicts that the strain rate for most of the Australian continent is approximately 10-17 s-1. This model has a slightly lower strain rate in the central Australia and is higher off the northern coast of Australia than for the rest of the continent. Strain rates of this magnitude would be difficult to observe from geodetic or geologic data for most parts of Australia but would be enough to generate much of the seismicity that has been observed over the last century.

  13. Underwater electrical discharge in plate to plate configuration

    Science.gov (United States)

    Stelmashuk, Vitaliy

    2016-09-01

    Two main configurations of high voltage electrodes submersed in water have been used for an electrical discharge generation: pin to pin and pin to plate. An electrical breakdown between plate electrodes is generally difficult to reproduce, because there is a uniform and weak electric field. One major advantage of using plate electrodes is their greater ``wear hardness'' to high-energy discharges. The plate electrodes can withstand extremely high energy deposition at which the pin electrode is quickly destroyed. The electrical discharge between plate electrodes can be initiated by creating an inhomogeneity in the electrical field. Two methods of discharge initiation between plate electrodes are proposed for this aim: 1) focusing of a shock wave in the interelectrode region; 2) a bubble injection into the electrode gap. The shock wave creates favourable conditions for the electrical breakdown between the two plate electrodes: it causes that numerous microbubbles of dissolved air start to grow and serve as locations for streamer initiation. In the second method the gas bubble is injected from the one of the electrodes, which has a gas inlet hole on the lateral face for this purpose. A ``volcano'' like morphology of positive streamers are observed in the experiments with weak electric field. The authors are grateful to MEYS grant INGO LG 15013.

  14. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  15. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    EvangelosChaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.

  16. A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

    Directory of Open Access Journals (Sweden)

    Shi-Chao Yi

    2017-01-01

    Full Text Available Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs. Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

  17. ACOUSTIC REFLECTION FROM A PERIODIC ELASTIC/PIEZOELECTRIC PLATE

    Institute of Scientific and Technical Information of China (English)

    ZhaoHanzhong

    2003-01-01

    The acoustic reflected pressure from a periodic elastic/piezoelectric laminated plate is studied for the purpose of acoustic reflection control. A finite difference/boundary integral procedure to determine the reflected pressure from the fluid-loaded plate is described. In the numerical model, a Green's function in the form of infinite sum is employed and a boundary integral is performed to replace the fluid pressure at fluid/solid interface by a continuum of point sources weighted by the normal acceleration of the elastic plate. The equation system is then solved only in the solid domain. It is demonstrated that an appropriate applied voltage potential across the piezoelectric layer has the effect of cancelling the fundamental propagating mode, and there is no reflection for frequencies up to the cut-off frequency of the next propagating mode if the fundamental mode has been eliminated.

  18. ELASTIC DYNAMIC ANALYSIS OF MODERATELY THICK PLATE USING MESHLESS LRPIM

    Institute of Scientific and Technical Information of China (English)

    Ping Xia; Shuyao Long; Hongxue Cui

    2009-01-01

    A meshless local radial point interpolation method (LRPIM) for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function (RBF) coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function, and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.

  19. A Review on Heat Transfer Improvent of Plate Heat Exchanger

    Directory of Open Access Journals (Sweden)

    Abhishek Nandan

    2015-03-01

    Full Text Available Plate heat exchanger has found a wide range of application in various industries like food industries, chemical industries, power plants etc. It reduces the wastage of energy and improves the overall efficiency of the system. Hence, it must be designed to obtain the maximum heat transfer possible. This paper is presented in order to study the various theories and results given over the improvement of heat transfer performance in a plate heat exchanger. However, there is still a lack in data and generalized equations for the calculation of different parameters in the heat exchanger. It requires more attention to find out various possible correlations and generalized solutions for the performance improvement of plate heat exchanger.

  20. Novel boundary element method for resolving plate bending problems

    Institute of Scientific and Technical Information of China (English)

    陈颂英; 王乐勤; 焦磊

    2003-01-01

    This paper discusses the application of the boundary contour method for resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirchhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points, even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corner point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.

  1. Propagation of elastic waves in a plate with rough surfaces

    Institute of Scientific and Technical Information of China (English)

    DAI Shuwu; ZHANG Hailan

    2003-01-01

    The characteristics of Lamb wave propagating in a solid plate with rough surfacesare studied on the basis of small perturbation approximation. The Rayleigh-Lamb frequencyequation expressed with SA matrix is presented. The Rayleigh-Lamb frequency equation fora rough surface plate is different from that for a smooth surface plate, resulting in a smallperturbation Ak on Lamb wave vector k. The imaginary part of Ak gives the attenuationcaused by wave scattering. An experiment is designed to test our theoretical predications.By using wedge-shape pipes, different Lamb wave modes are excited. The signals at differentpositions are received and analyzed to get the dispersion curves and attenuations of differentmodes. The experimental results are compared with the theoretical predications.

  2. Higher-order hybrid stress triangular Mindlin plate element

    Science.gov (United States)

    Li, Tan; Ma, Xu; Xili, Jing; Chen, Wanji

    2016-12-01

    A 6-node triangular hybrid stress element is presented for Mindlin plate in this paper. The proposed element, denoted by TH6-27β, can pass both the zero shear stress patch test and the non-zero constant shear stress enhanced patch test and, it can be employed to analyze very thin plate. To accomplish this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is used successfully to derive the displacement interpolation along each side of the element. According to the equilibrium equations, an appropriate stress approximation is rationally obtained. The assumed stress field is modified by using 27β instead of 15β to improve the accuracy. Numerical results show that the element is free of shear locking, and reliable for thick and thin plates. Moreover, it has no spurious zero energy modes and with geometric invariance (coordinate invariance, node sequencing independence).

  3. A judging principle of crucial vibrational transmission paths in plates

    Science.gov (United States)

    Wang, Bin; Li, Dong-Xu; Jiang, Jian-Ping; Liao, Yi-Huan

    2016-10-01

    This paper developed a judging principle of crucial vibrational transmission path (VTP) in plates. Novel generalized definitions of VTPs are given referred to the meaning of streamlines. And by comparing governing equations, the similarity between energy flow and fluid motion is firstly found so that an analytic method of VTPs in plates is proposed by analogy with fluid motion. Hereafter, the crucial VTP is defined for energy flows at objective points and relative judging criteria is given. Finally, based on two numerical experiments of passive control, the judging principle is indirectly verified by comparing the reduction effects of energy flows at focused points and relative judgment results of crucial VTPs. This paper is meaningful for analyzing and applying the VTPs in plates to guide the control design in future.

  4. Dynamics of multilayered orthotropic viscoelastic plates of Maxwell solids

    Directory of Open Access Journals (Sweden)

    P. Pal Roy

    1988-01-01

    Full Text Available This paper is concerned with a simplified dynamical analysis of orthotropic viscoelastic plates that are made up of an arbitrary number of layers each of which is a Maxwell type solid. This study includes the case where some or all the layers are themselves constituted by thinly laminated materials with couple stresses. The recurrence equations for the shear stresses are obtained for an arbitrary number of layers and then applied to plates with two or three layers. The viscoelastic damping effect is determined by the process of linearization and then illustrated by a plate composed of one, two or three layers. It is found that the damping increases with anisotropy and wave number. These results are shown by graphical representations.

  5. PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

    Institute of Scientific and Technical Information of China (English)

    ZhouYouhe; GaoYuanwen; ZhengXiaojing

    2004-01-01

    The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic field. After the distribution of magnetic fields related to the deflected configuration of plate is imaginably divided into two parts, i.e.,one is related to the flat plate and the other dependent on the perturbation of magnetic fields for which the plate configuration changes from the flat into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic fields in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic field, which leads to some analytical formulae/solutions for the magnetic fields and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic field is discussed, and the critical magnetic field is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic field. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an amplification function, is obtained by solving the dynamic equation of deflection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic field is sensitive to the plastic characteristic, e.g., hardening coefficient, and the instability mode and deflection of the plate are dependent on the geometrical imperfection as well.

  6. Highly curved microchannel plates

    Science.gov (United States)

    Siegmund, O. H. W.; Cully, S.; Warren, J.; Gaines, G. A.; Priedhorsky, W.; Bloch, J.

    1990-01-01

    Several spherically curved microchannel plate (MCP) stack configurations were studied as part of an ongoing astrophysical detector development program, and as part of the development of the ALEXIS satellite payload. MCP pairs with surface radii of curvature as small as 7 cm, and diameters up to 46 mm have been evaluated. The experiments show that the gain (greater than 1.5 x 10 exp 7) and background characteristics (about 0.5 events/sq cm per sec) of highly curved MCP stacks are in general equivalent to the performance achieved with flat MCP stacks of similar configuration. However, gain variations across the curved MCP's due to variations in the channel length to diameter ratio are observed. The overall pulse height distribution of a highly curved surface MCP stack (greater than 50 percent FWHM) is thus broader than its flat counterpart (less than 30 percent). Preconditioning of curved MCP stacks gives comparable results to flat MCP stacks, but it also decreases the overall gain variations. Flat fields of curved MCP stacks have the same general characteristics as flat MCP stacks.

  7. Static and Monoharmonic Acoustic Impact on a Laminated Plate

    Science.gov (United States)

    Paimushin, V. N.; Gazizullin, R. K.

    2017-07-01

    A discrete layered damping model of a multilayer plate at small displacements and deformations, with account of the internal damping of layers according to the Thompson-Kelvin-Voight model, is presented. Based on the equations derived, an analytical solution to the static deformation problem for single-layer rectangular plate hinge-supported along its contour and subjected of a uniformly distributed pressure applied to one of its boundary planes is obtained. Its convergence to the three-dimensional solution is analyzed in relation to the dimension of mesh in the thickness direction of the plate. It is found that, for thin plates, the dimension of the problem formulated can be reduced on the basis of simplified hypotheses applied to each layer. An analytical solutions is also constructed for the forced vibrations of two- and three-layer rectangular plates hinged in the opening of an absolutely stiff dividing wall upon transmission of a monoharmonic sound wave through them. It was assumed that the dividing wall is situated between two absolutely stiff barriers; one of them, owing to the harmonic vibration with a given displacement amplitude of the plate, forms an incident sound wave, and the other is stationary and is coated by a energy-absorbing material with high damping properties. Behavior of the acoustic media in spaces between the deformable plate and the barriers is described by the classical wave equations based on the model of an ideal compressible fluid. To describe the process of dynamic deformation of the energy-absorbing coating of the fixed barrier, two-dimensional equations of motion are derived based on the model of a transversely soft layer, a linear approximation of displacement fields in the thickness direction of the coating, and the account of damping properties of its material by using the hysteresis model. The effect of physical and mechanical parameters of the mechanical system considered and of frequency of the incident sound wave on the

  8. Indonesian Landforms and Plate Tectonics

    Directory of Open Access Journals (Sweden)

    Herman Th. Verstappen

    2014-06-01

    Full Text Available DOI: 10.17014/ijog.v5i3.103The horizontal configuration and vertical dimension of the landforms occurring in the tectonically unstable parts of Indonesia were resulted in the first place from plate tectonics. Most of them date from the Quaternary and endogenous forces are ongoing. Three major plates – the northward moving Indo-Australian Plate, the south-eastward moving SE-Asian Plate and the westward moving Pacific Plate - meet at a plate triple-junction situated in the south of New Guinea’s Bird’s Head. The narrow North-Moluccan plate is interposed between the Asia and Pacific. It tapers out northward in the Philippine Mobile Belt and is gradually disappearing. The greatest relief amplitudes occur near the plate boundaries: deep ocean trenches are associated with subduction zones and mountain ranges with collision belts. The landforms of the more stable areas of the plates date back to a more remote past and, where emerged, have a more subdued relief that is in the first place related to the resistance of the rocks to humid tropical weathering Rising mountain ranges and emerging island arcs are subjected to rapid humid-tropical river erosions and mass movements. The erosion products accumulate in adjacent sedimentary basins where their increasing weight causes subsidence by gravity and isostatic compensations. Living and raised coral reefs, volcanoes, and fault scarps are important geomorphic indicators of active plate tectonics. Compartmental faults may strongly affect island arcs stretching perpendicular to the plate movement. This is the case on Java. Transcurrent faults and related pull-apart basins are a leading factor where plates meet at an angle, such as on Sumatra. The most complicated situation exists near the triple-junction and in the Moluccas. Modern research methods, such as GPS measurements of plate movements and absolute dating of volcanic outbursts and raised coral reefs are important tools. The mega-landforms resulting

  9. Indonesian Landforms and Plate Tectonics

    Directory of Open Access Journals (Sweden)

    Herman Th. Verstappen

    2014-06-01

    Full Text Available DOI: 10.17014/ijog.v5i3.103The horizontal configuration and vertical dimension of the landforms occurring in the tectonically unstable parts of Indonesia were resulted in the first place from plate tectonics. Most of them date from the Quaternary and endogenous forces are ongoing. Three major plates – the northward moving Indo-Australian Plate, the south-eastward moving SE-Asian Plate and the westward moving Pacific Plate - meet at a plate triple-junction situated in the south of New Guinea’s Bird’s Head. The narrow North-Moluccan plate is interposed between the Asia and Pacific. It tapers out northward in the Philippine Mobile Belt and is gradually disappearing. The greatest relief amplitudes occur near the plate boundaries: deep ocean trenches are associated with subduction zones and mountain ranges with collision belts. The landforms of the more stable areas of the plates date back to a more remote past and, where emerged, have a more subdued relief that is in the first place related to the resistance of the rocks to humid tropical weathering Rising mountain ranges and emerging island arcs are subjected to rapid humid-tropical river erosions and mass movements. The erosion products accumulate in adjacent sedimentary basins where their increasing weight causes subsidence by gravity and isostatic compensations. Living and raised coral reefs, volcanoes, and fault scarps are important geomorphic indicators of active plate tectonics. Compartmental faults may strongly affect island arcs stretching perpendicular to the plate movement. This is the case on Java. Transcurrent faults and related pull-apart basins are a leading factor where plates meet at an angle, such as on Sumatra. The most complicated situation exists near the triple-junction and in the Moluccas. Modern research methods, such as GPS measurements of plate movements and absolute dating of volcanic outbursts and raised coral reefs are important tools. The mega-landforms resulting

  10. Numerical simulation of droplet evaporation between two circular plates

    Energy Technology Data Exchange (ETDEWEB)

    Bam, Hang Jin; Son, Gi Hun [Sogang University, Seoul (Korea, Republic of)

    2015-06-15

    Numerical simulation is performed for droplet evaporation between two circular plates. The flow and thermal characteristics of the droplet evaporation are numerically investigated by solving the conservation equations of mass, momentum, energy and mass fraction in the liquid and gas phases. The liquid-gas interface is tracked by a sharp-interface level-set method which is modified to include the effects of evaporation at the liquid-gas interface and contact angle hysteresis at the liquid-gas-solid contact line. An analytical model to predict the droplet evaporation is also developed by simplifying the mass and vapor fraction equations in the gas phase. The numerical results demonstrate that the 1-D analytical prediction is not applicable to the high rate evaporation process. The effects of plate gap and receding contact angle on the droplet evaporation are also quantified.

  11. Vibration and Buckling Analysis of Moderately Thick Plates using Natural Element Method

    Directory of Open Access Journals (Sweden)

    Mohammad Etemadi

    2015-07-01

    Full Text Available Using natural element method (NEM, the buckling and the free vibration behaviors of moderate thick plates is studied here. The basis of NEM is natural neighbors and Voronoi cells concepts. The shape functions of nodes located in the domain is equal to the proportion of common natural neighbors area divided by area that related by each Voronoi cells. First step in analyzing the moderate thick plates is identification boundaries. This is done by nodes scattering on problem domain. Mindlin/Reissner theory is used to express the equations of moderate thick plate. First and second order shape functions obtained from natural element method are used to discretize differential equations. Using numerical integration on whole discrete equations of domain, stiffness, geometry and mass matrices of plate are obtained. Buckling loads and vibration modes are expressed by substituting these matrices in plate equations of motions. Arbitrary shapes of plate are selected for solution. Comparing the results of the current approach with those obtained by other numerical analytical methods, it is shown that natural element method can solve problems with complex areas accurately.

  12. Nonlinear Resonance of the Rotating Circular Plate under Static Loads in Magnetic Field

    Institute of Scientific and Technical Information of China (English)

    HU Yuda; WANG Tong

    2015-01-01

    The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.

  13. Heat transfer in flow past a continuously moving semi-infinite flat plate in transverse magnetic field with heat flux

    Digital Repository Service at National Institute of Oceanography (India)

    Murty, T.V.R.

    Thermal boundary layer on a continuously moving semi-infinite flat plate in the presence of transverse magnetic field with heat flux has been examined. Similarity solutions have been derived and the resulting equations are integrated numerically...

  14. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    George F R Ellis

    2007-07-01

    The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.

  15. The concept of locking plates.

    Science.gov (United States)

    Cronier, P; Pietu, G; Dujardin, C; Bigorre, N; Ducellier, F; Gerard, R

    2010-05-01

    After a short historical review of locking bone plates since their inception more than a century ago to the success of the concept less than 15 years ago with today's plates, the authors present the main locking mechanisms in use. In the two broad categories - plates with fixed angulation and those with variable angulation - the screw head is locked in the plate with a locknut by screwing in a threaded chamber on the plate or by screwing through an adapted ring. The authors then provide a concrete explanation, based on simple mechanical models, of the fundamental differences between conventional bone plates and locking plates and why a locking screw system presents greater resistance at disassembly, detailing the role played by the position and number of screws. The advantages of epiphyseal fixation are then discussed, including in cases of mediocre-quality bone. For teaching purposes, the authors also present assembly with an apple fixed with five locking screws withstanding a 47-kg axial load with no resulting disassembly. The principles of plate placement are detailed for both the epiphysis and diaphysis, including the number and position of screws and respect of the soft tissues, with the greatest success assured by the minimally invasive and even percutaneous techniques. The authors then present the advantages of locking plates in fixation of periprosthetic fractures where conventional osteosynthesis often encounters limited success. Based on simplified theoretical cases, the economic impact in France of this type of implant is discussed, showing that on average it accounts for less than 10% of the overall cost of this pathology to society. Finally, the possible problems of material ablation are discussed as well as the means to remediate these problems.

  16. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  17. Renormalizing Partial Differential Equations

    OpenAIRE

    Bricmont, J.; Kupiainen, A.

    1994-01-01

    In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.

  18. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  19. Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy’s third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton’s principle.Then,the Galerkin procedure is applied to the partial differential governing equation to obtain a two-degrees-of-freedom nonlinear system including the quadratic and cubic nonlinear terms.Such equations are utilized to deal with the resonant case of 1:1 internal resonance and primary parametric resonance-1/2 subharmonic resonance.Furthermore,the stability analysis is given for the steady-state solutions of the averaged equation.Based on the averaged equation obtained by the asymptotic perturbation method,the phase portrait and power spectrum are used to analyze the multi-pulse chaotic motions of the angle-ply composite laminated rectangular thin plate.Under certain conditions the various chaotic motions of the angle-ply composite laminated rectangular thin plate are found.

  20. Non-linear resonances in the forced responses of plates. I - Symmetric responses of circular plates

    Science.gov (United States)

    Sridhar, S.; Mook, D. T.; Nayfeh, A. H.

    1975-01-01

    The dynamic analogue of the von Karman equations is used to study the symmetric response of a circular plate to a harmonic excitation when the frequency of the excitation is near one of the natural frequencies. It is shown that, in general, when there is no internal resonance (i.e., the natural frequencies are not commensurable), only the mode having a frequency near that of the excitation is strongly excited (i.e., is needed to represent the response in the first approximation). A clamped, circular plate is used as a numerical example to show that, when there is an internal resonance, more than one of the modes involved in this resonance can be strongly excited; moreover, when more than one mode is strongly excited, the lower modes can dominate the response, even when the frequency of the excitation is near that of the highest mode. This possibility was not revealed by any of the earlier studies which were based on the same governing equations.

  1. Optical Near-Field Plates

    Science.gov (United States)

    2015-04-08

    color filtering and spectral imaging ,” Nat. Comm. 1, 59 (2010). 3. H.-F. Shi and L. J. Guo, “Design of Plasmonic Near Field Plate at Opitical...AFRL-OSR-VA-TR-2015-0085 OPTICAL NEAR-FILED PLATES Roberto Merlin UNIVERSITY OF MICHIGAN Final Report 04/08/2015 DISTRIBUTION A: Distribution...03-2015 Final 09/01/2009-12/31/2014 Optical Near-Field Plates FA9550-09-1-0636 erlin, Roberto, D. The University of Michigan Ann Arbor, MI 48109

  2. Plate shell structures of glass

    DEFF Research Database (Denmark)

    Bagger, Anne

    to their curved shape. A plate shell structure maintains a high stiffness-to-weight ratio, while facilitating the use of plane structural elements. The study focuses on using laminated glass panes for the load bearing facets. Various methods of generating a plate shell geometry are suggested. Together with Ghent......, such as facet size, imperfections, and connection characteristics. The critical load is compared to that of a similar, but smoothly curved, shell structure. Based on the investigations throughout the study, a set of guidelines for the structural design of plate shells of glass is proposed....

  3. Application of Homotopy Analysis Method to the Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdi Rashidi

    2010-01-01

    Full Text Available We investigated an axisymmetric unsteady two-dimensional flow of nonconducting, incompressible second grade fluid between two circular plates. The similarity transformation is applied to reduce governing partial differential equation (PDE to a nonlinear ordinary differential equation (ODE in dimensionless form. The resulting nonlinear boundary value problem is solved using homotopy analysis method and numerical method. The effects of appropriate dimensionless parameters on the velocity profiles are studied. The total resistance to the upper plate has been calculated.

  4. Hierarchical self-organization of tectonic plates

    OpenAIRE

    2010-01-01

    The Earth's surface is subdivided into eight large tectonic plates and many smaller ones. We reconstruct the plate tessellation history and demonstrate that both large and small plates display two distinct hierarchical patterns, described by different power-law size-relationships. While small plates display little organisational change through time, the structure of the large plates oscillate between minimum and maximum hierarchical tessellations. The organization of large plates rapidly chan...

  5. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    Evangelos Chaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.

  6. Singular stochastic differential equations

    CERN Document Server

    Cherny, Alexander S

    2005-01-01

    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  7. Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Jianping Zhao

    2012-01-01

    Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.

  8. Stress measurement in thick plates using nonlinear ultrasonics

    Energy Technology Data Exchange (ETDEWEB)

    Abbasi, Zeynab, E-mail: zabbas5@uic.edu, E-mail: dozevin@uic.edu; Ozevin, Didem, E-mail: zabbas5@uic.edu, E-mail: dozevin@uic.edu [University of Illinois at Chicago, Civil and Materials Engineering, 842 W Taylor Street ERF 2095, Chicago, IL 60607 (United States)

    2015-03-31

    In this paper the interaction between nonlinear ultrasonic characteristics and stress state of complex loaded thick steel plates using fundamental theory of nonlinear ultrasonics is investigated in order to measure the stress state at a given cross section. The measurement concept is based on phased array placement of ultrasonic transmitter-receiver to scan three angles of a given cross section using Rayleigh waves. The change in the ultrasonic data in thick steel plates is influenced by normal and shear stresses; therefore, three measurements are needed to solve the equations simultaneously. Different thickness plates are studied in order to understand the interaction of Rayleigh wave penetration depth and shear stress. The purpose is that as the thickness becomes smaller, the shear stress becomes negligible at the angled measurement. For thicker cross section, shear stress becomes influential if the depth of penetration of Rayleigh wave is greater than the half of the thickness. The influences of plate thickness and ultrasonic frequency on the identification of stress tensor are numerically studied in 3D structural geometry and Murnaghan material model. The experimental component of this study includes uniaxial loading of the plate while measuring ultrasonic wave at three directions (perpendicular, parallel and angled to the loading direction). Instead of rotating transmitter-receiver pair for each test, a device capable of measuring the three angles is designed.

  9. Stress measurement in thick plates using nonlinear ultrasonics

    Science.gov (United States)

    Abbasi, Zeynab; Ozevin, Didem

    2015-03-01

    In this paper the interaction between nonlinear ultrasonic characteristics and stress state of complex loaded thick steel plates using fundamental theory of nonlinear ultrasonics is investigated in order to measure the stress state at a given cross section. The measurement concept is based on phased array placement of ultrasonic transmitter-receiver to scan three angles of a given cross section using Rayleigh waves. The change in the ultrasonic data in thick steel plates is influenced by normal and shear stresses; therefore, three measurements are needed to solve the equations simultaneously. Different thickness plates are studied in order to understand the interaction of Rayleigh wave penetration depth and shear stress. The purpose is that as the thickness becomes smaller, the shear stress becomes negligible at the angled measurement. For thicker cross section, shear stress becomes influential if the depth of penetration of Rayleigh wave is greater than the half of the thickness. The influences of plate thickness and ultrasonic frequency on the identification of stress tensor are numerically studied in 3D structural geometry and Murnaghan material model. The experimental component of this study includes uniaxial loading of the plate while measuring ultrasonic wave at three directions (perpendicular, parallel and angled to the loading direction). Instead of rotating transmitter-receiver pair for each test, a device capable of measuring the three angles is designed.

  10. Wave Propagation In Plates Studied By Pulsed Hologram Interferometry

    Science.gov (United States)

    Wahlin, Anders; Fallstrom, Karl-Evert; Gustavsson, H.; Molin, Nils-Erik

    1989-07-01

    Isotropic and non-isotropic plates are impacted by a ballistic pendulum. The bending waves that are generated are studied with holographic interferometry using a double pulsed ruby laser as light source. The pulse shape changes with time because of the dispersivity of the waves. Initially the fringe pattern in the isotropic case is cylindrically symmetric and determined from an initial value problem. Later, when the waves have reached the plate rim, in-and outgoing waves gradually develop fringe patterns which in the end will be a combination of eigenmodes of the plate. A solution to the corresponding Kirchhoff plate equation is presented, which in the special case when the impact is modelled as a Dirac-pulse in space and time, is shown to depend only of the distance to the impact point divided by the square root of the time after impact and a parameter containing plate parameters. From the slope of the central deflection material parameters can be determined. Another solution, assuming a finite inpact time, is shown to agree better with experiments. Results from investigations of non-isotropic materials are also presented.

  11. Chaos control for the plates subjected to subsonic flow

    Science.gov (United States)

    Norouzi, Hamed; Younesian, Davood

    2016-07-01

    The suppression of chaotic motion in viscoelastic plates driven by external subsonic air flow is studied. Nonlinear oscillation of the plate is modeled by the von-Kármán plate theory. The fluid-solid interaction is taken into account. Galerkin's approach is employed to transform the partial differential equations of the system into the time domain. The corresponding homoclinic orbits of the unperturbed Hamiltonian system are obtained. In order to study the chaotic behavior of the plate, Melnikov's integral is analytically applied and the threshold of the excitation amplitude and frequency for the occurrence of chaos is presented. It is found that adding a parametric perturbation to the system in terms of an excitation with the same frequency of the external force can lead to eliminate chaos. Variations of the Lyapunov exponent and bifurcation diagrams are provided to analyze the chaotic and periodic responses. Two perturbation-based control strategies are proposed. In the first scenario, the amplitude of control forces reads a constant value that should be precisely determined. In the second strategy, this amplitude can be proportional to the deflection of the plate. The performance of each controller is investigated and it is found that the second scenario would be more efficient.

  12. The multigap resistive plate chamber

    Energy Technology Data Exchange (ETDEWEB)

    Zeballos, E. Cerron [European Organization for Nuclear Research (CERN), Geneva (Switzerland); World Lab., Lausanne (Switzerland); Crotty, I. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Hatzifotiadou, D. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); World Lab., Lausanne (Switzerland); Valverde, J. Lamas [European Organization for Nuclear Research (CERN), Geneva (Switzerland); World Lab., Lausanne (Switzerland); Univ. Louis Pasteur, Strasbourg (France); Neupane, S. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); World Lab., Lausanne (Switzerland); Williams, M. C. S. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Zichichi, A. [Univ. of Bologna, Bologna (Italy)

    2015-02-03

    The paper describes the multigap resistive plate chamber (RPC). This is a variant of the wide gap RPC. However it has much improved time resolution, while keeping all the other advantages of the wide gap RPC design.

  13. An efficient rectangular plate element

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    A new 12-parameter rectangular plate element is presented by useof the double set parameter method. The error in the energy norm is of order O(h2), one order higher than the commonly used Adini nonconforming element.

  14. Tectonics: Changing of the plates

    Science.gov (United States)

    Brandon, Alan

    2016-10-01

    The composition of Earth's crust depends on the style of plate tectonics and of the melting regimes in the mantle. Analyses of the oldest identified rocks suggest that these styles and the resulting crust have changed over Earth's history.

  15. Rhodium platings – experimental study

    Directory of Open Access Journals (Sweden)

    R. Rudolf

    2013-07-01

    Full Text Available Modern rhodium plating solutions are based on either sulphate or phosphate. Although in theory there are four possible combinations, in practice only three different rhodium electrolytes are used. These are based on dilutions of rhodium sulphate or phosphate concentrates with added sulphuric or phosphoric acid. These processes are be discussed in this paper with a demonstration of Rh platings in the Slovenian firm Zlatarna Celje d.d.

  16. Horizontal versus vertical plate motions

    Directory of Open Access Journals (Sweden)

    M. Cuffaro

    2006-07-01

    Full Text Available We review both present and past motions at major plate boundaries, which have the horizontal component in average 10 to 100 times faster (10–100 mm/yr than the vertical component (0.01–1 mm/yr in all geodynamic settings. The steady faster horizontal velocity of the lithosphere with respect to the upward or downward velocities at plate boundaries supports dominating tangential forces acting on plates. This suggests a passive role of plate boundaries with respect to far field forces determining the velocity of plates. The forces acting on the lithosphere can be subdivided in coupled and uncoupled, as a function of the shear at the lithosphere base. Higher the asthenosphere viscosity, more significant should be the coupled forces, i.e., the mantle drag and the trench suction. Lower the asthenosphere viscosity, more the effects of uncoupled forces might result determinant, i.e., the ridge push, the slab pull and the tidal drag. Although a combination of all forces acting on the lithosphere is likely, the decoupling between lithosphere and mantle suggests that a torque acts on the lithosphere independently of the mantle drag. Slab pull and ridge push are candidates for generating this torque, but, unlike these boundary forces, the advantage of the tidal drag is to be a volume force, acting simultaneously on the whole plates, and being the decoupling at the lithosphere base controlled by lateral variations in viscosity of the low-velocity layer.

  17. Horizontally oriented plates in clouds

    CERN Document Server

    Bréon, François-Marie

    2011-01-01

    Horizontally oriented plates in clouds generate a sharp specular reflectance signal in the glint direction, often referred to as "subsun". This signal (amplitude and width) may be used to analyze the relative area fraction of oriented plates in the cloud top layer and their characteristic tilt angle to the horizontal. We make use of spaceborne measurements from the POLDER instrument to provide a statistical analysis of these parameters. More than half of the clouds show a detectable maximum reflectance in the glint direction, although this maximum may be rather faint. The typical effective fraction (area weighted) of oriented plates in clouds lies between 10-3 and 10-2. For those oriented plates, the characteristic tilt angle is less than 1 degree in most cases. These low fractions imply that the impact of oriented plates on the cloud albedo is insignificant. The largest proportion of clouds with horizontally oriented plates is found in the range 500-700 hPa, in agreement with typical in situ observation of p...

  18. Nonlinear vibration and buckling of circular sandwich plate under complex load

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condition were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

  19. Control of Rayleigh-like waves in thick plate Willis metamaterials

    CERN Document Server

    Diatta, Andre; Brûlé, Stéphane; Enoch, Stefan; Guenneau, Sébastien

    2016-01-01

    Recent advances in control of anthropic seismic sources in structured soil led us to explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are $40$ m in depth and the plate is $100$ m in thickness, so that typical frequencies under study are in the frequency range 4 to 8 Hz, which is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks' configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. These designs are inspired by some ideal cloaks' parameters deduced from a geometric transform in the Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis' equations as corroborated by numerical simulations. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite...

  20. Free Vibration of Embedded Porous Plate Using Third-Order Shear Deformation and Poroelasticity Theories

    Directory of Open Access Journals (Sweden)

    Ali Ghorbanpour Arani

    2017-01-01

    Full Text Available This research aims at studying free vibration of rectangular plate made of porous materials in which Y-foam, G-foam, and Coustone are used and compared with each other. To obtain the Biot formulation of the constitutive equations for a porous material, linear poroelasticity theory is used. Young modulus and density of porous plate are different in transverse direction versus porosity. In order to increase the accuracy of results in comparison with classical plate and first-order shear deformation theories, Reddy’s theory was utilized in this research. Besides, five coupled equations of motion have been studied using Hamilton’s principle and are solved by differential quadrature method (DQM. Detailed results of this study show the significant effect of aspect ratio, thickness ratio, boundary conditions, and porosity on dimensionless frequency and deflection of porous plate. Results of this study can contribute to the design of pneumatic conveying, handling, and control systems.

  1. Simplified Procedure For The Free Vibration Analysis Of Rectangular Plate Structures With Holes And Stiffeners

    Directory of Open Access Journals (Sweden)

    Cho Dae Seung

    2015-04-01

    Full Text Available Thin and thick plates, plates with holes, stiffened panels and stiffened panels with holes are primary structural members in almost all fields of engineering: civil, mechanical, aerospace, naval, ocean etc. In this paper, a simple and efficient procedure for the free vibration analysis of such elements is presented. It is based on the assumed mode method and can handle different plate thickness, various shapes and sizes of holes, different framing sizes and types as well as different combinations of boundary conditions. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equations. Mindlin theory is applied for a plate and Timoshenko beam theory for stiffeners. The applicability of the method in the design procedure is illustrated with several numerical examples obtained by the in-house developed code VAPS. Very good agreement with standard commercial finite element software is achieved.

  2. Two-dimensional simulations of steady perforated-plate stabilized premixed flames

    KAUST Repository

    Altay, H. Murat

    2010-03-17

    The objective of this work is to examine the impact of the operating conditions and the perforated-plate design on the steady, lean premixed flame characteristics. We perform two-dimensional simulations of laminar flames using a reduced chemical kinetics mechanism for methane-air combustion, consisting of 20 species and 79 reactions. We solve the heat conduction problem within the plate, allowing heat exchange between the gas mixture and the solid plate. The physical model is based on a zero-Mach-number formulation of the axisymmetric compressible conservation equations. The results suggest that the flame consumption speed, the flame structure, and the flame surface area depend significantly on the equivalence ratio, mean inlet velocity, the distance between the perforated-plate holes and the plate thermal conductivity. In the case of an adiabatic plate, a conical flame is formed, anchored near the corner of the hole. When the heat exchange between themixture and the plate is finite, the flame acquires a Gaussian shape stabilizing at a stand-off distance, that grows with the plate conductivity. The flame tip is negatively curved; i.e. concave with respect to the reactants. Downstream of the plate, the flame base is positively curved; i.e. convex with respect to the reactants, stabilizing above a stagnation region established between neighboring holes. As the plate\\'s thermal conductivity increases, the heat flux to the plate decreases, lowering its top surface temperature. As the equivalence ratio increases, the flame moves closer to the plate, raising its temperature, and lowering the flame stand-off distance. As the mean inlet velocity increases, the flame stabilizes further downstream, the flame tip becomes sharper, hence raising the burning rate at that location. The curvature of the flame base depends on the distance between the neighboring holes; and the flame there is characterized by high concentration of intermediates, like carbon monoxide. © 2010 Taylor

  3. How mantle slabs drive plate tectonics.

    Science.gov (United States)

    Conrad, Clinton P; Lithgow-Bertelloni, Carolina

    2002-10-04

    The gravitational pull of subducted slabs is thought to drive the motions of Earth's tectonic plates, but the coupling between slabs and plates is not well established. If a slab is mechanically attached to a subducting plate, it can exert a direct pull on the plate. Alternatively, a detached slab may drive a plate by exciting flow in the mantle that exerts a shear traction on the base of the plate. From the geologic history of subduction, we estimated the relative importance of "pull" versus "suction" for the present-day plates. Observed plate motions are best predicted if slabs in the upper mantle are attached to plates and generate slab pull forces that account for about half of the total driving force on plates. Slabs in the lower mantle are supported by viscous mantle forces and drive plates through slab suction.

  4. On the capillary interaction between solid plates forming menisci on the surface of a liquid

    Science.gov (United States)

    Saif, Taher A.

    2002-12-01

    A hydrophilic or a hydrophobic long rigid solid plate of finite width, forming a meniscus with a liquid in a uniform gravitational field is considered. The one-dimensional meniscus with prescribed heights of the triple point from the far-field liquid surface is investigated analytically using the Young Laplace equation. It is found that for a hydrophilic plate, the vertical force necessary to break the meniscus during removal of the plate from the liquid is larger than the force necessary to break the meniscus during submersion of the plate into the liquid. Furthermore, the capillary force on the plate reaches a maximum before the meniscus collapses during removal, but no maximum exists before collapse during submersion. The reverse is true when the plate is hydrophobic. The study is then extended to investigate the interaction force between two plates, each forming a meniscus with the liquid. The elevations of the plates from the far-field liquid surface are prescribed, in contrast to earlier studies where interaction between long cylinders floating under self weight was considered. Here, the menisci are determined exactly using the Young Laplace equation. It is shown that for prescribed plate elevations, there can be at most two possible pairs of menisci between them. Each pair bifurcates from a meniscus that is determined by the elevations of the plates and the gap between them. Furthermore, as known for solids floating under self-weight, the horizontal component of the interaction force is attractive for similar menisci (e.g. when the two plates are equally displaced in or out of the liquid), and repulsive when they form opposite menisci. It is shown that if the two menisci are of the same type, but not similar (e.g. one plate is pushed more into the liquid than the other), then the force is attractive at long distances, and may be repulsive at shorter distances with a stable equilibrium at a finite distance between the plates, depending on the elevations of

  5. Geometry of the Cocos Plate Under North American Plate

    Science.gov (United States)

    Perez-Campos, X.

    2015-12-01

    The Cocos plate subducts under the North American plate with a complex geometry, and previous seismicity studies revealed some of this complexity. However, details of the geometry and the depth that the plate penetrates werelargely unknown. Since 2004, temporary experiments and the expansion of the permanent network of the Servicio Sismológico Nacional (SSN, Mexican National Seismological Service) have improved resolution of the plate geometry and have helped to map its descent into the upper mantle. Going from northwest to southeast, the Cocos plate appears to be fragmenting into north and south segments. The north segment subducts with an angle of ~30º and the south with an angle of ~10-15º. The transition is smooth near the trench and progresses to a tear at depth; this coincides with the projection of the Orozco Fracture Zone to depth. Also, this transition marks the limit of the presence to the south of an ultra slow velocity layer (USL) on top of the slab.South of this transition, the Cocos plate subducts horizontally , underplating the North American plate for a distance of ~140 to ~300 km from the trench. Along this horizontal region, silent slow events (SSE) and tectonic tremor (TT) have been observed. At a distance of 300 km from the trench (beneath central Mexico), the plate dives into the mantle with an angle of 76º to a depth of 500 km. This geometry changes abruptly to the south, marking the eastern limit of the USL. This change seems to be also characterized by a tear on the slab. Finally to the south, the Cocos plate subducts with a constant angle of 26º. This presentation summarizes the work of many contributors including A. Arciniega-Ceballos, M. Brudzinski, E. Cabral-Cano, T. Chen, R. Clayton,F. Cordoba-Montiel,P. Davis,S. Dougherty,F. Green, M. Gurnis, D. V. Helmberger, A. Husker,A. Iglesias, Y. Kim, V. Manea, D. Melgar, M. Rodríguez-Domínguez,S. K. Singh, T.-R. A. Song, C. M. Valdés-González, D. Valencia-Cabrera

  6. MHD Stagnation Flow of a Newtonian Fluid towards a Uniformly Heated and Moving Vertical Plate

    Directory of Open Access Journals (Sweden)

    Mehmet Şirin Demir

    2016-01-01

    Full Text Available Stagnation flow of an electrically conducting incompressible viscous fluid towards a moving vertical plate in the presence of a constant magnetic field is investigated. By using the appropriate transformations for the velocity components and temperature, the partial differential equations governing flow and heat transfer are reduced to a set of nonlinear ordinary differential equations. These equations are solved approximately using a numerical technique for the following two problems: (i two-dimensional stagnation-point flow on a moving vertical plate, (ii axisymmetric stagnation-point flow on a moving vertical plate. The effects of non-dimensional parameters on the velocity components, wall shear stresses, temperature and heat transfer are examined carefully.

  7. EFFECTS OF THERMAL CONDUCTIVITY ON UNSTEADY MHD FREE CONVECTIVE FLOW OVER A SEMI INFINITE VERTICAL PLATE

    Directory of Open Access Journals (Sweden)

    P. LOGANATHAN,

    2010-11-01

    Full Text Available The numerical study of effects of thermal conductivity on unsteady MHD free convective flow over an isothermal semi infinite vertical plate is presented. It is assumed that the thermal conductivity of the fluid as a linear function of temperature. A magnetic field is applied transversely to the direction of the flow. The boundary layer equations of continuity, momentum and energy equations are transformed into non-linear coupled equations and then solved using implicit finite-difference method of Crank-Nicholson type. A parametric study is performed to illustrate the influence of thermal conductivity, magnetic parameter and Prandtl number on the velocity and temperature profiles. In addition, the local and average skin friction, Nusselt number at the plate are shown graphically for both air and water. An analysis of the results obtained shows that the flowfield is influenced appreciably by the strength of magnetic field, thermal conductivity at the wall of the plate.

  8. Nonlinear Forced Vibration Analysis for Thin Rectangular Plate on Nonlinear Elastic Foundation

    Directory of Open Access Journals (Sweden)

    Zhong Zhengqiang

    2013-02-01

    Full Text Available Nonlinear forced vibration is analyzed for thin rectangular plate with four free edges on nonlinear elastic foundation. Based on Hamilton variation principle, equations of nonlinear vibration motion for thin rectangular plate under harmonic loads on nonlinear elastic foundation are established. In the case of four free edges, viable expressions of trial functions for this specification are proposed, satisfying all boundary conditions. Then, equations are transformed to a system of nonlinear algebraic equations by using Galerkin method and are solved by using harmonic balance method. In the analysis of numerical computations, the effect on the amplitude-frequency characteristic curve due to change of the structural parameters of plate, parameters of foundation and parameters of excitation force are discussed.

  9. The numerical solution of the vorticity transport equation

    CERN Document Server

    Dennis, S C R

    1973-01-01

    A method of approximating the two-dimensional vorticity transport equation in which the matrix associated with the difference equations is diagonally dominant and the truncation error is the same as that of the fully central-difference approximation, is discussed. An example from boundary layer theory is given by calculating the viscous stagnation point flow at the nose of a cylinder. Some new solutions of the Navier-Stokes equations are obtained for symmetrical flow past a flat plate of finite length. (16 refs).

  10. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  11. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  12. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  13. Fractional Chemotaxis Diffusion Equations

    CERN Document Server

    Langlands, T A M

    2010-01-01

    We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.

  14. Symplectic system based analytical solution for bending of rectangular orthotropic plates on Winkler elastic foundation

    Institute of Scientific and Technical Information of China (English)

    Wei-An Yao; Xiao-Fei Hu; Feng Xiao

    2011-01-01

    This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.

  15. Solitary and cnoidal wave scattering by a submerged horizontal plate in shallow water

    Science.gov (United States)

    Hayatdavoodi, Masoud; Ertekin, R. Cengiz; Valentine, Benjamin D.

    2017-06-01

    Solitary and cnoidal wave transformation over a submerged, fixed, horizontal rigid plate is studied by use of the nonlinear, shallow-water Level I Green-Naghdi (GN) equations. Reflection and transmission coefficients are defined for cnoidal and solitary waves to quantify the nonlinear wave scattering. Results of the GN equations are compared with the laboratory experiments and other theoretical solutions for linear and nonlinear waves in intermediate and deep waters. The GN equations are then used to study the nonlinear wave scattering by a plate in shallow water. It is shown that in deep and intermediate depths, the wave-scattering varies nonlinearly by both the wavelength over the plate length ratio, and the submergence depth. In shallow water, however, and for long-waves, only the submergence depth appear to play a significant role on wave scattering. It is possible to define the plate submergence depth and length such that certain wave conditions are optimized above, below, or downwave of the plate for different applications. A submerged plate in shallow water can be used as a means to attenuate energy, such as in wave breakers, or used for energy focusing, and in wave energy devices.

  16. Plate tectonics of the Mediterranean region.

    Science.gov (United States)

    McKenzie, D P

    1970-04-18

    The seismicity and fault plane solutions in the Mediterranean area show that two small rapidly moving plates exist in the Eastern Mediterranean, and such plates may be a common feature of contracting ocean basins. The results show that the concepts of plate tectonics apply to instantaneous motions across continental plate boundaries.

  17. 30 CFR 18.13 - Certification plate.

    Science.gov (United States)

    2010-07-01

    ... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Certification plate. 18.13 Section 18.13... Certification plate. Each certified component shall be identified by a certification plate attached to the... characteristics of the component. The plate shall be of serviceable material, acceptable, to MSHA, and shall...

  18. 21 CFR 872.4760 - Bone plate.

    Science.gov (United States)

    2010-04-01

    ... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Bone plate. 872.4760 Section 872.4760 Food and... DENTAL DEVICES Surgical Devices § 872.4760 Bone plate. (a) Identification. A bone plate is a metal device... plate with screws to prevent movement of the segments. (b) Classification. Class II. ...

  19. 30 CFR 18.11 - Approval plate.

    Science.gov (United States)

    2010-07-01

    ... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Approval plate. 18.11 Section 18.11 Mineral... plate. (a)(1) The notice of approval will be accompanied by a photograph of an approval plate, bearing... number shall be added to the original approval number on the approval plate. (Example: Original approval...

  20. Drift-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    K. Banoo

    1998-01-01

    equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

  1. Developmental Partial Differential Equations

    OpenAIRE

    Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto

    2015-01-01

    In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...

  2. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  3. Stability mechanisms for plate-like nanoparticles immersed in a macroion dispersion

    Energy Technology Data Exchange (ETDEWEB)

    Jimenez-Angeles, Felipe; Odriozola, Gerardo; Lozada-Cassou, Marcelo [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, DF (Mexico)

    2009-10-21

    An integral equation theory and Monte Carlo simulations are applied to study a model macroion solution confined between two parallel plates immersed in a 1:1 electrolyte and the macroions' counterions. We analyze the cases in which plates are: (a) uncharged; (b) when they are like-charged to the macroions; (c) when they are oppositely charged to the macroions. For all cases a long range oscillatory behavior of the induced charge density between the plates is found (implying an overcompensation/undercompensation of the plates' charge density) and a correlation between the confined and outside fluids. The behavior of the force is discussed in terms of the macroion and ion structure inside and outside the plates. A good agreement is found between theoretical and simulation results.

  4. Buckling analysis of thick isotropic plates by using exponential shear deformation theory

    Directory of Open Access Journals (Sweden)

    Sayyad A. S.

    2012-12-01

    Full Text Available In this paper, an exponential shear deformation theory is presented for the buckling analysis of thick isotropic plates subjected to uniaxial and biaxial in-plane forces. The theory accounts for a parabolic distribution of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations and associated boundary conditions of the theory are obtained using the principle of virtual work. The simply supported thick isotropic square plates are considered for the detailed numerical studies. A closed form solutions for buckling analysis of square plates are obtained. Comparison studies are performed to verify the validity of the present results. The effects of aspect ratio on the critical buckling load of isotropic plates is investigated and discussed.

  5. Low-velocity impact response of a pre-stressed isotropic Uflyand-Mindlin plate

    Directory of Open Access Journals (Sweden)

    Rossikhin Yury

    2017-01-01

    Full Text Available The low-velocity impact response of a precompressed circular isotropic elastic plate is investigated in the case when the dynamic behavior of the plate is described by equations taking the rotary inertia and transverse shear deformations into account. Contact interaction between the rigid impactor and the target is modeled by a generalized Hertz contact force, since it is assumed that the viscoelastic features of the plate represent themselves only in the place of contact and are governed by the standard linear solid model with fractional derivatives due to the fact that during the impact process decrosslinking occurs within the domain of the contact of the plate with the sphere, resulting in more free displacements of molecules with respect to each other, and finally in the decrease of the plate material viscosity in the contact zone.

  6. Modeling and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate

    Directory of Open Access Journals (Sweden)

    Minghui Yao

    2014-01-01

    Full Text Available This paper investigates the multipulse heteroclinic bifurcations and chaotic dynamics of a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. According to the von Karman type equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. The method of multiple scales and Galerkin’s approach are applied to the partial differential governing equation. Then, the four-dimensional averaged equation is obtained for the case of 1 : 3 internal resonance and primary parametric resonance. The extended Melnikov method is used to study the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multipulse chaotic dynamics are analytically obtained. From the investigation, the geometric structure of the multipulse orbits is described in the four-dimensional phase space. Numerical simulations show that the Shilnikov type multipulse chaotic motions can occur. To sum up, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists for the laminated composite piezoelectric rectangular plate.

  7. Porosity-dependent nonlinear forced vibration analysis of functionally graded piezoelectric smart material plates

    Science.gov (United States)

    Qing Wang, Yan; Zu, Jean W.

    2017-10-01

    This work investigates the porosity-dependent nonlinear forced vibrations of functionally graded piezoelectric material (FGPM) plates by using both analytical and numerical methods. The FGPM plates contain porosities owing to the technical issues during the preparation of FGPMs. Two types of porosity distribution, namely, even and uneven distribution, are considered. A modified power law model is adopted to describe the material properties of the porous FGPM plates. Using D’Alembert’s principle, the out-of-plane equation of motion is derived by taking into account the Kármán nonlinear geometrical relations. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by employing the harmonic balance method. The approximate analytical results are verified by using the adaptive step-size fourth-order Runge–Kutta method. By means of the perturbation technique, the stability of approximate analytical solutions is examined. An interesting nonlinear broadband vibration phenomenon is detected in the FGPM plates with porosities. Nonlinear frequency-response characteristics of the present smart structures are investigated for various system parameters including the porosity type, the porosity volume fraction, the electric potential, the external excitation, the damping and the constituent volume fraction. It is found that these parameters have significant effects on the nonlinear vibration characteristics of porous FGPM plates.

  8. Ordinary differential equations

    CERN Document Server

    Pontryagin, Lev Semenovich

    1962-01-01

    Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

  9. 3D analysis of functionally graded material plates with complex shapes and various holes

    Institute of Scientific and Technical Information of China (English)

    Zhi-yuan CAO; Shou-gao TANG; Guo-hua CHENG

    2009-01-01

    In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.

  10. A Transverse Dynamic Deflection Model for Thin Plate Made of Saturated Porous Materials

    Science.gov (United States)

    Feng-xi, Zhou; Xiao-lin, Cao

    2016-10-01

    In this article, a transverse dynamic deflection model is established for thin plate made of saturated porous materials. Based on the Biot's model for fluid-saturated porous media, using the Love-Kirchhoff hypothesis, the governing equations of transverse vibrations of fluid-saturated poroelastic plates are derived in detail, which take the inertial, fluid viscous, mechanical couplings, compressibility of solid, and fluid into account. The free vibration and forced vibration response of a simply supported poroelastic rectangular plate is obtained by Fourier series expansion method. Through numerical examples, the effect of porosity and permeability on the dynamic response, including the natural frequency, amplitude response, and the resonance areas is assessed.

  11. DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT

    Institute of Scientific and Technical Information of China (English)

    GAO Suo-wen; WANG Yue-sheng; ZHANG Zi-mao; MA Xing-rui

    2005-01-01

    The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given.The results obtained demonstrate good agreement with other reported results and show high accuracy.

  12. A simplified four-unknown shear and normal deformations theory for bidirectional laminated plates

    Indian Academy of Sciences (India)

    A M Zenkour

    2015-02-01

    This paper presents a simplified 4-unknown shear and normal deformations theory for the bending analysis of cross-ply laminated plates. The present theory accounts for an adequate distribution of transverse shear strains through the plate thickness and tangential stress-free on the plate surfaces. The effect of normal strain is also included. The governing, equilibrium equations and boundary conditions are derived by employing the virtual work principle. Numerical results for stresses and displacements are compared well with those obtained using 3-D elasticity solution.

  13. Three-dimensional Analysis of Functionally Graded Piezoelectric Plate with Arbitrarily Distributed Material Properties

    Institute of Scientific and Technical Information of China (English)

    LIU Wuxiang; MA Shaokun; WU Hao

    2014-01-01

    An orthotropic functionally graded piezoelectric rectangular plate with arbitrarily distributed material properties was studied, which is simply supported and grounded (electrically) on its four lateral edges. The state equations of the functionally graded piezoelectric material were obtained using the state-space approach, and a Peano-Baker series solution was obtained for the coupled electroelastic fields of the functionally graded piezoelectric plate subjected to mechanical and electric loading on its upper and lower surfaces. The influence of different distributions of material properties on the structural response of the plate was studied using the obtained solutions.

  14. Stress and Strain Analysis of Functionally Graded Rectangular Plate with Exponentially Varying Properties

    Directory of Open Access Journals (Sweden)

    Amin Hadi

    2013-01-01

    Full Text Available The bending of rectangular plate made of functionally graded material (FGM is investigated by using three-dimensional elasticity theory. The governing equations obtained here are solved with static analysis considering the types of plates, which properties varying exponentially along direction. The value of Poisson’s ratio has been taken as a constant. The influence of different functionally graded variation on the stress and displacement fields was studied through a numerical example. The exact solution shows that the graded material properties have significant effects on the mechanical behavior of the plate.

  15. Variational principle and vibration properties of functionally graded circular plate with temperature changes

    Science.gov (United States)

    Fan, Tao; Zou, Guangping

    2012-04-01

    In this paper, the variational principle of functionally graded circular plate is presented by the variational integral method taking temperature change into account. The vibration governing equation is illustrated, which will be benefit for the numerical simulation with finite element method in further investigations. The numerical results show that the natural frequency increases as the graded coefficient increases in the chosen domain. It can be observed that the vibration characteristics are influenced by the temperature changes obviously. Moreover, the natural frequency is larger for thicker FGM circular plates, while it is lower for thinner ones. Furthermore, the first four vibration mode shapes with different thickness of FGM circular plate are illustrated.

  16. Asymptotic Behavior of a Structure Made by a Plate and a Straight Rod

    Institute of Scientific and Technical Information of China (English)

    Dominique BLANCHARD; Georges GRISO

    2013-01-01

    This paper is devoted to describing the asymptotic behavior of a structure made by a thin plate and a thin perpendicular rod in the framework of nonlinear elasticity.The authors scale the applied forces in such a way that the level of the total elastic energy leads to the Von-Kármán's equations (or the linear model for smaller forces) in the plate and to a one-dimensional rod-model at the limit.The junction conditions include in particular the continuity of the bending in the plate and the stretching in the rod at the junction.

  17. Stress State Of Plate With Incisions Under The Action Of Oscillating Concentrated Forces

    Directory of Open Access Journals (Sweden)

    Shvabyuk Vasyl’

    2015-09-01

    Full Text Available This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of oscillating forces. Calculation of dynamic stresses at the incisions of plates is held using the boundary-integral equation method and the theory of complex variable functions. The numerical implementation of the developed algorithmis based on the method of mechanical quadratures and collocation technique. The algorithm is effective in the analysis of the stress state caused by steady-state vibrations of plates.

  18. Beyond plate tectonics - Looking at plate deformation with space geodesy

    Science.gov (United States)

    Jordan, Thomas H.; Minster, J. Bernard

    1988-01-01

    The requirements that must be met by space-geodetic systems in order to constrain the horizontal secular motions associated with the geological deformation of the earth's surface are explored. It is suggested that in order to improve existing plate-motion models, the tangential components of relative velocities on interplate baselines must be resolved to an accuracy of less than 3 mm/yr. Results indicate that measuring the velocities between crustal blocks to + or - 5 mm/yr on 100-km to 1000-km scales can produce geologically significant constraints on the integrated deformation rates across continental plate-boundary zones such as the western United States.

  19. Plating on some difficult-to-plate metals and alloys

    Energy Technology Data Exchange (ETDEWEB)

    Dini, J.W.; Johnson, H.R.

    1980-02-01

    Electrodeposition of coatings on metals such as beryllium, beryllium-copper, Kovar, lead, magnesium, thorium, titanium, tungsten, uranium, zirconium, and their alloys can be problematic. This is due in most cases to a natural oxide surface film that readily reforms after being removed. The procedures we recommend for plating on these metals rely on replacing the oxide film with a displacement coating, or etching to allow mechanical keying between the substrate and plated deposit. The effectiveness of the procedures is demonstrated by interface bond strengths found in ring-shear and conical-head tensile tests.

  20. Beyond plate tectonics - Looking at plate deformation with space geodesy

    Science.gov (United States)

    Jordan, Thomas H.; Minster, J. Bernard

    1988-01-01

    The requirements that must be met by space-geodetic systems in order to constrain the horizontal secular motions associated with the geological deformation of the earth's surface are explored. It is suggested that in order to improve existing plate-motion models, the tangential components of relative velocities on interplate baselines must be resolved to an accuracy of less than 3 mm/yr. Results indicate that measuring the velocities between crustal blocks to + or - 5 mm/yr on 100-km to 1000-km scales can produce geologically significant constraints on the integrated deformation rates across continental plate-boundary zones such as the western United States.

  1. Chladni's law for vibrating plates

    Science.gov (United States)

    Rossing, Thomas D.

    1982-03-01

    The normal vibrational modes of free circular plates can be classified according to the number of nodal diameters m and the number of nodal circles n. Chladni observed that the addition of one nodal circle raised the frequency f about the same amount as adding two nodal diameters, and Rayleigh pointed out that f is proportional to (m+2n)2 for large f. Waller, however, concluded that the number of nodal diameters necessary to raise the frequency as much as a nodal circle varies from two to five. We have examined data on the vibrations of flat and non-flat circular plates and fitted their vibration frequencies to the relationship f = c(m+bn)k. By proper choice of c it is possible to satisfy Chladni's law (b = 2, k = 2) over quite a wide range of frequency in flat plates. Non-flat plates such as cymbals and bells, require different choices of b and k. A brief history of Chladni patterns, and suggestions for observing and demonstrating the vibrational modes of plates are included (AIP).

  2. Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

    Science.gov (United States)

    Xu, T. F.; Xing, Y. F.

    2016-12-01

    This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/ b on frequencies.

  3. Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

    Science.gov (United States)

    Xu, T. F.; Xing, Y. F.

    2016-09-01

    This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.

  4. FREE VIBRATION OF FUNCTIONALLY GRADED,MAGNETO-ELECTRO-ELASTIC, AND MULTILAYERED PLATES

    Institute of Scientific and Technical Information of China (English)

    Chen Jiangyi; Chen Hualing; Pan Ernian

    2006-01-01

    The state-space method is employed to evaluate the modal parameters of functionally graded, magneto-electro-elastic, and multilayered plates. Based on the assumption that the properties of the functionally graded material are exponential, the state equation of structural vibration which takes the displacement and stress of the structure as state variables is derived. The natural frequencies and modal shapes are calculated based on the general solutions of the state equation and boundary conditions given in this paper. The influence of the functionally graded exponential factor on the elastic displacement, electric, and magnetic fields of the structure are discussed by assuming a sandwich plate model with different stacking sequences.

  5. ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

    Institute of Scientific and Technical Information of China (English)

    李显方; 范天佑

    2002-01-01

    Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four cases of combined mechanical-electrical Ioads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations . Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate are obtained. The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recoveredfrom the present results only if the thickness of the plate h → ∞.

  6. Complex dynamics of functionally graded plates with thermal load in 1:2 internal resonance

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Complex dynamics of the simply-supported functionally graded(FG)rectangular plates with thermal load is investigated.Based on Reddy’s third-order shear deformation theory and the von Karman nonlinear strain-displacement relations,ordinary differential equations(ODEs)of the plate’s transversal oscillation are derived by using Hamilton’s principle and Galerkin’s approach.Solutions’classification of the equations in 1:2 internal resonance is analyzed.Particular results of a simplysupported aluminum-alumina rectangular FG plate are given.Effects of temperature and volume fraction on the responses’ stabilities are discussed.

  7. Numerical solution of the problem on the constant current flow around a dielectric plate

    Energy Technology Data Exchange (ETDEWEB)

    Stadnik, I.P.

    1977-01-01

    The problem of a harmonic field circumvention of a plate of arbitrary form is reduced to a second species integral equation for the density of a binary layer. A feature of this integral equation is that the integration is performed along the entire plate except the circle contained in the center of the observation point. The method's agreement with sequential approximations is proven. An examination is made of the plane-parallel case and an example illustrating good agreement in results for the plane-parallel case which were obtained by the proposed method and method of conformal depictions. 2 references, 4 figures.

  8. ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

    Institute of Scientific and Technical Information of China (English)

    FuYiming; LiPing'en; ZhengYufang

    2004-01-01

    Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional fibre reinforced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are established. By applying the finite difference method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial differential governing equations are solved. Some examples are given and the results are compared with available data.

  9. Multiregional evaluation of the SimPlate heterotrophic plate count method compared to the standard plate count agar pour plate method in water.

    Science.gov (United States)

    Jackson, R W; Osborne, K; Barnes, G; Jolliff, C; Zamani, D; Roll, B; Stillings, A; Herzog, D; Cannon, S; Loveland, S

    2000-01-01

    A new SimPlate heterotrophic plate count (HPC) method (IDEXX Laboratories, Westbrook, Maine) was compared with the pour plate method at 35 degrees C for 48 h. Six laboratories tested a total of 632 water samples. The SimPlate HPC method was found to be equivalent to the pour plate method by regression analysis (r = 0. 95; y = 0.99X + 0.06).

  10. Multiregional Evaluation of the SimPlate Heterotrophic Plate Count Method Compared to the Standard Plate Count Agar Pour Plate Method in Water

    OpenAIRE

    Jackson, R. Wayne; Osborne, Karen; Barnes, Gary; Jolliff, Carol; Zamani, Dianna; Roll, Bruce; Stillings, Amy; Herzog, David; Cannon, Shelly; Loveland, Scott

    2000-01-01

    A new SimPlate heterotrophic plate count (HPC) method (IDEXX Laboratories, Westbrook, Maine) was compared with the pour plate method at 35°C for 48 h. Six laboratories tested a total of 632 water samples. The SimPlate HPC method was found to be equivalent to the pour plate method by regression analysis (r = 0.95; y = 0.99X + 0.06).

  11. Multiple-Dynode-Layer Microchannel Plate

    Science.gov (United States)

    Woodgate, Bruce E.

    1990-01-01

    Improved microchannel-plate electron image amplifier made of stack of discrete microchannel-plate layers. New plates easier to manufacture because no need to etch long, narrow holes, to draw and bundle thin glass tubes, or to shear plates to give microchannels curvatures necessary for reduction of undesired emission of ions. Discrete dynode layers stacked with slight offset from layer to layer to form microchannel plate with curved channels. Provides for relatively fast recharging of microchannel dynodes, with consequent enhancement of performance.

  12. Thermal stability analysis of eccentrically stiffened Sigmoid-FGM plate with metal–ceramic–metal layers based on FSDT

    Directory of Open Access Journals (Sweden)

    Pham Hong Cong

    2016-12-01

    Full Text Available This paper researches the thermal stability of eccentrically stiffened plates made of functionally graded materials (FGM with metal–ceramic–metal layers subjected to thermal load. The equilibrium and compatibility equations for the plates are derived by using the first-order shear deformation theory of plates, taking into account both the geometrical nonlinearity in the von Karman sense and initial geometrical imperfections with Pasternak type elastic foundations. By applying Galerkin method and using stress function, effects of material and geometrical properties, elastic foundations, temperature-dependent material properties, and stiffeners on the thermal stability of the eccentrically stiffened S-FGM plates in thermal environment are analyzed and discussed.

  13. NON-LINEAR DYNAMIC BEHAVIOR OF THERMOELASTIC CIRCULAR PLATE WITH VARYING THICKNESS SUBJECTED TO NON- CONSERVATIVE LOADING

    Institute of Scientific and Technical Information of China (English)

    WANG Zhongmin; GAO Jingbo; LI Huixia; LIU Hongzhao

    2008-01-01

    The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.

  14. A NUMERICAL SOLUTION OF A SYSTEM OF LINEAR INTEGRO-PARTIAL DIFFERENTIAL EQUATIONS,

    Science.gov (United States)

    The numerical solution to a system of linear integro- partial differential equations is treated. A numerical solution to the system was obtained by...using difference approximations to the partial differential equations . To assure convergence, a stability condition derived from the related plate

  15. Ultimately Thin Metasurface Wave Plates

    CERN Document Server

    Keene, David; Durach, Maxim

    2015-01-01

    Optical properties of a metasurface which can be considered a monolayer of two classical uniaxial metamaterials, parallel-plate and nanorod arrays, are investigated. It is shown that such metasurface acts as an ultimately thin sub-50 nm wave plate. This is achieved via an interplay of epsilon-near-zero and epsilon-near-pole behavior along different axes in the plane of the metasurface allowing for extremely rapid phase difference accumulation in very thin metasurface layers. These effects are shown to not be disrupted by non-locality and can be applied to the design of ultrathin wave plates, Pancharatnam-Berry phase optical elements and plasmon-carrying optical torque wrench devices.

  16. Reinforcement of a plate weakened by multiple holes with several patches for different types of plate-patch attachment

    KAUST Repository

    Zemlyanova, A.

    2014-01-24

    The most general situation of the reinforcement of a plate with multiple holes by several patches is considered. There is no restriction on the number and the location of the patches. Two types of patch attachment are considered: only along the boundary of the patch or both along the boundary of the patch and the boundaries of the holes which this patch covers. The unattached boundaries of the holes may be loaded with given in-plane stresses. The mechanical problem is reduced to a system of singular integral equations which can be further reduced to a system of Fredholm equations. A new numerical procedure for the solution of the system of singular integral equations is proposed in this paper. It is demonstrated on numerical examples that this procedure has advantages in the case of multiple patches and holes and allows achievement of better numerical convergence with less computational effort.

  17. A true polar wander model for Neoproterozoic plate motions

    Energy Technology Data Exchange (ETDEWEB)

    Ripperdan, R.L. (Weizmann Inst. of Science, Rehovot (Israel))

    1992-01-01

    Recent paleogeographic reconstructions for the interval 750--500 Ma (Neoproterozoic to Late Cambrian) require rapid rates of plate motion and/or rotation around an equatorial Euler pole to accommodate reconstructions for the Early Paleozoic. Motions of this magnitude appear to be very uncommon during the Phanerozoic. A model for plate motions based on the hypothesis that discrete intervals of rapid true polar wander (RTPW) occurred during the Neoproterozoic can account for the paleogeographic changes with minimum amounts of plate motion. The model uses the paleogeographic reconstructions of Hoffman (1991). The following constraints were applied during derivation of the model: (1) relative motions between major continental units were restricted to be combinations of great circle or small circle translations with Euler poles of rotation = spin axis; (2) maximum rates of relative translational plate motion were 0.2 m/yr. Based on these constraints, two separate sets of synthetic plate motion trajectories were determined. The sequence of events in both can be summarized as: (1) A rapid true polar wander event of ca 90[degree] rafting a supercontinent to the spin axis; (2) breakup of the polar supercontinent into two fragments, one with the Congo, West Africa, Amazonia, and Baltica cratons, the other with the Laurentia, East Gondwana, and Kalahari cratons; (3) great circle motion of the blocks towards the equator; (4) small circle motion leading to amalgamation of Gondwana and separation of Laurentia and Baltica. In alternative 1, rifting initiates between East Antarctica and Laurentia and one episode of RTPW is required. Alternative 2 requires two episodes of RTPW; and that rifting occurred first along the eastern margin and later along the western margin of Laurentia. Synthetic plate motion trajectories are compared to existing paleomagnetic and geological data, and implications of the model for paleoclimatic changes during the Neoproterozoic are discussed.

  18. Large Amplitude Flexural Vibration of the Orthotropic Composite Plate Embedded with Shape Memory Alloy Fibers

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The free and forced vibration of large deformation composite plate embedded with shape memory alloy (SMA) fibers is investigated. A thermo-mechanical constitutive equation of SMA proposed by Brinson et al. is employed and the constitutive equations for evaluation of the properties of a hybrid SMA composite laminate are obtained. Based on the nonlinear theory of symmetrically laminated anisotropic plates, the governing equations of flexural vibration in terms of displacement and stress functions are derived. The Galerkin method has been used to convert the original partial differential equation into a nonlinear ordinary differential equation, which is then solved with harmonic balance method. The numerical results show that the relationship between nonlinear natural frequency ratio and temperature for the nonlinear plate has similar characteristics compared with that of the linear one, and the effects of temperature on forced response behavior during phase transformation from Martensite to Austenite are significant. The effects of the volume fraction of the SMA fiber, aspect ratio and free vibration amplitude on the dynamical behavior of the plate are also discussed.

  19. A new dual-plate slipometer for measuring slip between molten polymers and extrusion die materials.

    Science.gov (United States)

    Schmalzer, A M; Giacomin, A J

    2014-04-01

    In this work, we study the slip behaviors common to plastics die extrusion metals or platings using a new instrument called a dual-plate slipometer. By dual-plate, we mean that whereas the stationary plate incorporates a local shear stress transducer, the moving plate does not. The stationary plate and transducer are made of one stainless steel, but the moving plate is made from, or plated with, different extrusion die materials under study. This new instrument allows slip velocity to be measured without having to build a new shear stress transducer from each extrusion metal or plating under study. We explore the effect of extrusion die composition and die metal surface morphology on the slip properties of polyolefins using a sliding plate rheometer. In this work, we studied the slip behaviors of polyolefins on four common plastics die extrusion metals or platings, without having to build a new shear stress transducer from each. Specifically, our new method replaces the moving plate; with each of the four die metals or platings under study without changing the stainless steel material of the shear stress transducer and its stationary plate. Our experiments include high-density polyethylene, low-density polyethylene, and polypropylene (PP) on four different die metals or platings. We use steady simple shear to obtain shear stress versus nominal shear rate for different gaps, from which we can then deduce the slip velocity using the Mooney analysis. We then fit four slip models to our experimental measurements, and we find the Hatzikiriakos hyperbolic sine model to be accurate, even for the measured inflections in the slip velocity as a function of shear stress curves. Our analysis includes detailed characterization of the die metal plating surfaces, including measurements of the composition of the sliding plates by energy dispersive spectroscopy, surface energy by contact angle goniometry, and surface roughness by both white light interference and stylus

  20. The Wouthuysen equation

    NARCIS (Netherlands)

    Hazewinkel, M.

    1995-01-01

    Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-

  1. Functional Cantor equation

    Science.gov (United States)

    Shabat, A. B.

    2016-12-01

    We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.

  2. Dissipative Boussinesq equations

    CERN Document Server

    Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys

    2007-01-01

    The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.

  3. Navier-Stokes equation

    Directory of Open Access Journals (Sweden)

    Hannelore Breckner

    2000-01-01

    Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.

  4. Differential Equation of Equilibrium

    African Journals Online (AJOL)

    user

    than the classical method in the solution of the aforementioned differential equation. Keywords: ... present a successful approximation of shell ... displacement function. .... only applicable to cylindrical shell subject to ..... (cos. 4. 4. 4. 3 β. + β. + β. -. = β. - β x x e ex. AL. xA w. Substituting equations (29); (30) and (31) into.

  5. Plate-like osteoma cutis.

    Science.gov (United States)

    Orme, Charisse M; Hale, Christopher S; Meehan, Shane A; Long, Wendy

    2014-12-16

    Osteoma cutis is the aberrant development of bone within the skin. The bone formation may be de novo (primary) or result from an injury to the skin (secondary). Here we present a healthy 53-year-old man with no known abnormalities in calcium or phosphate metabolism with plate-like osteoma cutis of the scalp. Plate- or plaque-like osteoma cutis was initially described as a congenital condition but has now been reported several times in the literature as an idiopathic process that occurs in adults. Treatment options are limited and are only required if the lesion is bothersome to the patient.

  6. Hydroelasticity of a Floating Plate

    DEFF Research Database (Denmark)

    Chen, X.; Jensen, Jørgen Juncher; Cui, W.

    2003-01-01

    The membrane forces are included in the hydroelastic analysis of a floating plate undergoing large vertical deflections in regular monochromatic multidirectional waves. The first-order vertical displacements induced by the linear wave exciting forces are calculated by the mode expansion method...... in the frequency domain. The second-order vertical displacements induced by the membrane forces are calculated by the von Karman plate theory. The results show that the membrane contribution both in terms of the axial stresses and the effect on the bending stresses can be important...

  7. Orifice plates and venturi tubes

    CERN Document Server

    Reader-Harris, Michael

    2015-01-01

    This book gives the background to differential-pressure flow measurement and goes through the requirements explaining the reason for them. For those who want to use an orifice plate or a Venturi tube the standard ISO 5167 and its associated Technical Reports give the instructions required.  However, they rarely tell the users why they should follow certain instructions.  This book helps users of the ISO standards for orifice plates and Venturi tubes to understand the reasons why the standards are as they are, to apply them effectively, and to understand the consequences of deviations from the standards.

  8. Outer rise seismicity of the subducting Nazca Plate: Plate stress distribution, fault orientation and plate hydration

    Science.gov (United States)

    Barama, Louisa

    Subduction of the Nazca plate beneath the South American plate drives frequent and sometimes large magnitude earthquakes. During the past 40 years, significant numbers of outer rise earthquakes have occurred in the offshore regions of Colombia and Chile. In this study, we investigate the distribution of stress due to lithospheric bending and the extent of faults within the subducting plate. To calculate more accurate epicenters and to constrain which earthquakes occurred within the outer rise, we use hypocentroidal decomposition to relocate earthquakes with Global Centroid Moment Tensor (GCMT) solutions occurring after 1976 offshore Colombia and Chile. We determine centroid depths of outer rise earthquakes by inverting teleseismic P-, SH-, and SV- waveforms for earthquakes occurring from 1993 to 2014 with Mw ≥ 5.5. In order to further constrain the results of the waveform inversion, we estimate depths by comparing earthquake duration, amplitude, and arrival times for select stations with waveforms with good signal to noise ratios. Our results indicate that tensional earthquakes occur at depths down to 13 km and 24 km depth beneath the surface in the Colombia and Chile regions, respectively. Since faulting within the outer rise can make the plate susceptible to hydration and mantle serpentinization, we therefore infer the extent of possible hydration of the Nazca plate to extend no deeper than the extent of tensional outer rise earthquakes.

  9. Electromagnetic Confinement and Shaping for Plate-Form Part

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The relationship between melt shape, electromagnetic pressure and magnetic field is studied for electromagnetic confinement and shaping of plate-form part. The results of experimental observation and theoretical inference can be summarized as follows. As the melt thickness a is large enough, causing the ratio of plate thickness to current theoretic skin depth a/δ larger ???B2than 2.2, the electromagnetic pressure acting on melt can be simply expressed as Pn =2μ-, andthe melt shape would be known only by measuring the distribution of magnetic flux density. As a is small and makes the ratio a/δ less than 2.2, the melt shape and electromagnetic pressure for confining and shaping are determined not only by magnetic flux density B but also by melt thickness a, electromagnetic parameterμγ and current frequency f. In this paper, an equation used to calculate electromagnetic pressure acting on “thin plate-form melt” is brought forward.The equation gives a precise relationship between electromagnetic pressure factor p and melt thickness a, electromagnetic parameterμγ and current frequency f.

  10. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  11. Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets

    CERN Document Server

    Beuthe, Mikael

    2007-01-01

    Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this article we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associ...

  12. Numerical evaluation of plate heat exchanger performance in geothermal district heating systems

    Energy Technology Data Exchange (ETDEWEB)

    Karlsson, T. [Iceland Univ., Reykjavik (Iceland)

    1996-12-31

    This paper describes the performance of plate heat exchangers in residential water radiator heating systems receiving their heat from geothermal resources. Radiator theory is reviewed and determination of annual hot water requirements for space heating is discussed. Performance evaluation is made of plate heat exchangers and results obtained by means of two equations commonly used for this purpose, the Sieder-Tate and the Dittus-Boelter equations, compared to results obtained with a simplified equation where heat transfer in the heat exchanger is assumed to depend only on the fluid mass flow on both sides. It is found that for prevailing temperature ranges in Icelandic geothermal systems the mass pow approximation gives results very close to those determined by the more complicated conventional equations. (UK)

  13. Dimensional analysis of detrimental ozone generation by positive wire-to-plate corona discharge in air

    Science.gov (United States)

    Bo, Z.; Chen, J. H.

    2010-02-01

    The dimensional analysis technique is used to formulate a correlation between ozone generation rate and various parameters that are important in the design and operation of positive wire-to-plate corona discharges in indoor air. The dimensionless relation is determined by linear regression analysis based on the results from 36 laboratory-scale experiments. The derived equation is validated by experimental data and a numerical model published in the literature. Applications of such derived equation are illustrated through an example selection of the appropriate set of operating conditions in the design/operation of a photocopier to follow the federal regulations of ozone emission. Finally, a new current-voltage characteristic equation is proposed for positive wire-to-plate corona discharges based on the derived dimensionless equation.

  14. Inverse problem of pulsed eddy current field of ferromagnetic plates

    Science.gov (United States)

    Chen, Xing-Le; Lei, Yin-Zhao

    2015-03-01

    To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters, it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate. Project supported by the National Defense Basic Technology Research Program of China (Grant No. Z132013T001).

  15. Light splitting with imperfect wave plates.

    Science.gov (United States)

    Jackson, Jarom S; Archibald, James L; Durfee, Dallin S

    2017-02-01

    We discuss the use of wave plates with arbitrary retardances, in conjunction with a linear polarizer, to split linearly polarized light into two linearly polarized beams with an arbitrary splitting fraction. We show that for non-ideal wave plates, a much broader range of splitting ratios is typically possible when a pair of wave plates, rather than a single wave plate, is used. We discuss the maximum range of splitting fractions possible with one or two wave plates as a function of the wave plate retardances, and how to align the wave plates to achieve the maximum splitting range possible when simply rotating one of the wave plates while keeping the other one fixed. We also briefly discuss an alignment-free polarization rotator constructed from a pair of half-wave plates.

  16. Effects of a sliding plate on morphology of the epiphyseal plate in goat distal femur.

    Science.gov (United States)

    Lin, Da-sheng; Lian, Ke-jian; Hong, Jia-yuan; Ding, Zhen-qi; Zhai, Wen-liang

    2012-01-01

    The aim of this study was to observe the effects of a sliding plate on the morphology of the epiphyseal plate in goat distal femur. Eighteen premature female goats were divided randomly into sliding plate, regular plate and control groups. Radiographic analysis and histological staining were performed to evaluate the development of epiphyseal plate at 4 and 8 weeks after surgery. In the sliding plate group, the plate extended accordingly as the epiphyseal plate grows, and the epiphyseal morphology was kept essential normal. However, the phenomenon of the epiphyseal growth retardation and premature closure were very common in the regular plate group. In addition, the sliding plate group exhibited more normal histologic features and Safranin O staining compared to the regular plate group. Our results suggest that the sliding plate can provide reliable internal fixation of epiphyseal fracture without inhibiting epiphyseal growth.

  17. Effects of a Sliding Plate on Morphology of the Epiphyseal Plate in Goat Distal Femur

    Directory of Open Access Journals (Sweden)

    Da-sheng LIN, Ke-jian LIAN, Jia-yuan HONG, Zhen-qi DING, Wen-liang ZHAI

    2012-01-01

    Full Text Available The aim of this study was to observe the effects of a sliding plate on the morphology of the epiphyseal plate in goat distal femur. Eighteen premature female goats were divided randomly into sliding plate, regular plate and control groups. Radiographic analysis and histological staining were performed to evaluate the development of epiphyseal plate at 4 and 8 weeks after surgery. In the sliding plate group, the plate extended accordingly as the epiphyseal plate grows, and the epiphyseal morphology was kept essential normal. However, the phenomenon of the epiphyseal growth retardation and premature closure were very common in the regular plate group. In addition, the sliding plate group exhibited more normal histologic features and Safranin O staining compared to the regular plate group. Our results suggest that the sliding plate can provide reliable internal fixation of epiphyseal fracture without inhibiting epiphyseal growth.

  18. Comment on "Intermittent plate tectonics?".

    Science.gov (United States)

    Korenaga, Jun

    2008-06-06

    Silver and Behn (Reports, 4 January 2008, p. 85) proposed that intermittent plate tectonics may resolve a long-standing paradox in Earth's thermal evolution. However, their analysis misses one important term, which subsequently brings their main conclusion into question. In addition, the Phanerozoic eustasy record indicates that the claimed effect of intermittency is probably weak.

  19. License plate recognition using DTCNNs

    NARCIS (Netherlands)

    ter Brugge, M.H; Stevens, J.H; Nijhuis, J.A G; Spaanenburg, L; Tavsanonoglu, V

    1998-01-01

    Automatic license plate recognition requires a series of complex image processing steps. For practical use, the amount of data to he processed must be minimized early on. This paper shows that the computationally most intensive steps can be realized by DTCNNs. Moreover; high-level operations like fi

  20. Corrosion resistant metallic bipolar plate

    Science.gov (United States)

    Brady, Michael P.; Schneibel, Joachim H.; Pint, Bruce A.; Maziasz, Philip J.

    2007-05-01

    A corrosion resistant, electrically conductive component such as a bipolar plate for a PEM fuel cell includes 20 55% Cr, balance base metal such as Ni, Fe, or Co, the component having thereon a substantially external, continuous layer of chromium nitride.

  1. The seismotectonics of plate boundaries

    Science.gov (United States)

    Berger, J.; Brune, J. N.; Goodkind, J.; Wyatt, F.; Agnew, D. C.; Beaumont, C.

    1981-01-01

    Research on the seismotectonics of plate boundaries is summarized. Instrumental development and an observational program designed to study various aspects of the seismotectonics of southern California and the northern Gulf of California are described. A unique superconducting gravimeter was further developed and supported under this program for deployment and operation at several sites. Work on Earth tides is also discussed.

  2. MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

    Institute of Scientific and Technical Information of China (English)

    丁方允; 丁睿; 李炳杰

    2003-01-01

    The boundary value problem of plate bending problem on two-parameter foundation was discussed. Using two series of the high-order fundamental solution sequences, namely, the fundamental solution sequences for the multi-harmonic operator and Laplace operator, applying the multiple reciprocity method (MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high-order fundamental solution sequences.

  3. Forced convection on a heated horizontal flat plate with finite thermal conductivity in a non-Darcian porous medium

    Energy Technology Data Exchange (ETDEWEB)

    Luna, N. [Direccion de Operacion Petrolera, Direccion General de Exploracion y Explotacion de Hidrocarburos, Secretaria de Energia, 03100 Mexico DF (Mexico); Mendez, F. [Facultad de Ingenieria, UNAM, 04510 Mexico DF (Mexico)

    2005-07-01

    The steady-state analysis of conjugated heat transfer process for the hydrodynamically developed forced convection flow on a heated flat plate embedded in a porous medium is studied. The governing equations for the fluid-saturated porous medium are solved analytically using the integral boundary layer approximation. This integral solution is coupled to the energy equation for the flat plate, where the longitudinal heat conduction effects are taken into account. The resulting equations are then reduced to an integro-differential equation which is solved by regular perturbation techniques and numerical methods. The analytical and numerical predictions for the temperature profile of the plate and appropriate local and average Nusselt numbers are plotted for finite values of the conduction parameter, {alpha}, which represents the presence of the longitudinal heat conduction effects. (authors)

  4. The Effective Equation Method

    Science.gov (United States)

    Kuksin, Sergei; Maiocchi, Alberto

    In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.

  5. Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates

    Energy Technology Data Exchange (ETDEWEB)

    Siddiqui, A.M. [Pennsylvania State University, York Campus, York, PA 17403 (United States); Zeb, A. [COMSATS Institute of Information Technology, 30 H-8/1, Islamabad (Pakistan)], E-mail: amtaz56@yahoo.co.uk; Ghori, Q.K. [COMSATS Institute of Information Technology, 30 H-8/1, Islamabad (Pakistan); Benharbit, A.M. [Pennsylvania State University, York Campus, York, PA 17403 (United States)

    2008-04-15

    The present paper studies the heat transfer flow of a third grade fluid between two heated parallel plates for the constant viscosity model. Three flow problems, namely plane Couette flow, plane Poiseuille flow and plane Couette-Poiseuille flow have been considered. In each case the non-linear momentum equation and the energy equation have been solved using the homotopy perturbation method. Explicit analytical expressions for the velocity field and the temperature distribution have been derived.

  6. Natural convection of nanofluids over a convectively heated vertical plate embedded in a porous medium

    OpenAIRE

    M. Ghalambaz; Noghrehabadi,A.; Ghanbarzadeh, A.

    2014-01-01

    In this paper, the natural convective flow of nanofluids over a convectively heated vertical plate in a saturated Darcy porous medium is studied numerically. The governing equations are transformed into a set of ordinary differential equations by using appropriate similarity variables, and they are numerically solved using the fourth-order Runge-Kutta method associated with the Gauss-Newton method. The effects of parametric variation of the Brownian motion parameter (Nb), thermophoresis param...

  7. Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates

    Directory of Open Access Journals (Sweden)

    Woo-Young Jung

    2014-01-01

    Full Text Available The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT. The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. On the basis of those numerical results, the relations between nonlocal and local theory are investigated and discussed, as are the nonlocal parameter, aspect ratio, side-to-thickness ratio, nano-scale plate size, and time step effects on the dynamic response. In order to validate the present solutions, the reference solutions are employed and examined. The results of nano-scale plates using the nonlocal theory can be used as a benchmark test for the transient analysis.

  8. Parametric study on nonlinear vibration of composite truss core sandwich plate with internal resonance

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Jia Nen; Liu, Jun [Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechatronical System, Tianjin University of Technology, Tianjin (China); Zhang, Wei; Yao, Ming Hui [College of Mechanical Engineering, Beijing University of Technology, Beijing (China); Sun, Min [School of Science, Tianjin Chengjian University, Tianjin (China)

    2016-09-15

    Nonlinear vibrations of carbon fiber reinforced composite sandwich plate with pyramidal truss core are investigated. The governing equation of motion for the sandwich plate is derived by using a Zig-Zag theory under consideration of geometrically nonlinear. The natural frequencies of sandwich plates with different dimensions are calculated and compared with those obtained from the classic laminated plate theory and Reddy's third-order shear deformation plate theory. The frequency responses and waveforms of the sandwich plate when 1:3 internal resonance occurs are obtained, and the characteristics of the internal resonance are discussed. The influences of layer number of face sheet, strut radius, core height and inclination angle on the nonlinear responses of the sandwich plate are analyzed. The results demonstrate that the strut radius and inclination angle mainly affect the resonance frequency band of the sandwich plate, and the layer number and core height not only influence the resonance frequency band but also significantly affect the response amplitude.

  9. A Comparative Study of Solutions Concerning Thick Elastic Plates on Bi-modulus Foundation

    Directory of Open Access Journals (Sweden)

    Ioana Vlad

    2004-01-01

    Full Text Available The classical bending theory of elastic plates is based upon the assumption that the internal moments are proportional to the curvatures of the median deformed surface. This theory does not include the effects of shear and normal pressure in the plate. The model of a bi-modulus foundation is a realistic generalization of the Winkler’s classical one and is widely used to represent the subgrade of railroad systems, airport lanes [1], [2]. The derived equation of elastic thick plates on bi-modulus foundation considers shear and normal stress as linear variable across the plate thickness. This paper presents numerical solutions for thick plate resting on bi-modulus subgrade. These solutions take into account the shear distortion, and they are compared to the solution obtained by Finite Element Analysis and with the Winkler’s model. Particular solutions for the rectangular plate of clamped boundary, for the hinged rectangular plate and for a semi-elliptical plate, are discussed. The numerical solutions consist of double power series and they were obtained based on the minimum of the total strain energy [1]. Parametric studies have been performed in order to emphasize the effects of the chosen foundation and that of the geometry.

  10. Effect of Fluid Viscoelasticity on Turbulence and Large-Scale Vortices behind Wall-Mounted Plates

    Directory of Open Access Journals (Sweden)

    Takahiro Tsukahara

    2014-03-01

    Full Text Available Direct numerical simulations of turbulent viscoelastic fluid flows in a channel with wall-mounted plates were performed to investigate the influence of viscoelasticity on turbulent structures and the mean flow around the plate. The constitutive equation follows the Giesekus model, valid for polymer or surfactant solutions, which are generally capable of reducing the turbulent frictional drag in a smooth channel. We found that turbulent eddies just behind the plates in viscoelastic fluid decreased in number and in magnitude, but their size increased. Three pairs of organized longitudinal vortices were observed downstream of the plates in both Newtonian and viscoelastic fluids: two vortex pairs were behind the plates and the other one with the longest length was in a plate-free area. In the viscoelastic fluid, the latter vortex pair in the plate-free area was maintained and reached the downstream rib, but its swirling strength was weakened and the local skin-friction drag near the vortex was much weaker than those in the Newtonian flow. The mean flow and small spanwise eddies were influenced by the additional fluid force due to the viscoelasticity and, moreover, the spanwise component of the fluid elastic force may also play a role in the suppression of fluid vortical motions behind the plates.

  11. Equation of state measurements in liquid deuterium to 100 GPa

    CERN Document Server

    Knudson, M D; Bailey, J E; Lemke, R W; Hall, C A; Deeney, C; Asay, J R

    2003-01-01

    Using intense magnetic pressure, a method was developed to launch flyer plates to velocities in excess of 20 km s sup - sup 1. This technique was used to perform plate-impact, shock wave experiments on cryogenic liquid deuterium (LD sub 2) to examine its high-pressure equation of state (EOS). Using an impedance matching method, Hugoniot measurements were obtained in the pressure range of 22-100 GPa. The results of these experiments disagree with the previously reported Hugoniot measurements of LD sub 2 in the pressure range above approx 40 GPa, but are in good agreement with first principles, ab initio models for hydrogen and its isotopes.

  12. Structural Analysis of Plate Based Tensegrity Structures

    DEFF Research Database (Denmark)

    Hald, Frederik; Kirkegaard, Poul Henning; Damkilde, Lars

    2013-01-01

    Plate tensegrity structures combine tension cables with a cross laminated timber plate and can then form e.g. a roof structure. The topology of plate tensegrity structures is investigated through a parametric investigation. Plate tensegrity structures are investigated, and a method...... for determination of the structures pre-stresses is used. A parametric investigation is performed to determine a more optimized form of the plate based tensegrity structure. Conclusions of the use of plate based tensegrity in civil engineering and further research areas are discussed....

  13. Structural Analysis of Plate Based Tensegrity Structures

    DEFF Research Database (Denmark)

    Hald, Frederik; Kirkegaard, Poul Henning; Damkilde, Lars

    2013-01-01

    Plate tensegrity structures combine tension cables with a cross laminated timber plate and can then form e.g. a roof structure. The topology of plate tensegrity structures is investigated through a parametric investigation. Plate tensegrity structures are investigated, and a method...... for determination of the structures pre-stresses is used. A parametric investigation is performed to determine a more optimized form of the plate based tensegrity structure. Conclusions of the use of plate based tensegrity in civil engineering and further research areas are discussed....

  14. Avionics Box Cold Plate Damage Prevention

    Science.gov (United States)

    Stambolian, Damon B.; Larchar, Steven W.; Henderson, Gena; Tran, Donald; Barth, Tim

    2012-01-01

    Problem Introduction: 1. Prevent Cold Plate Damage in Space Shuttle. 1a. The number of cold plate problems had increased from an average of 16.5 per/year between 1990 through 2000, to an average of 39.6 per year between 2001through 2005. 1b. Each complete set of 80 cold plates cost approximately $29 million, an average of $362,500 per cold plate. 1c It takes four months to produce a single cold plate. 2. Prevent Cold Plate Damage in Future Space Vehicles.

  15. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  16. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  17. Stochastic Gauss equations

    Science.gov (United States)

    Pierret, Frédéric

    2016-02-01

    We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.

  18. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  19. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  20. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  1. Partial differential equations

    CERN Document Server

    Friedman, Avner

    2008-01-01

    This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we

  2. Introduction to functional equations

    CERN Document Server

    Sahoo, Prasanna K

    2011-01-01

    Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig

  3. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  4. Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers

    Energy Technology Data Exchange (ETDEWEB)

    Rastgoo, A. [University of Tehran, Tehran (Iran, Islamic Republic of); Ebrahimi, F. [lmam Khomeini International University, Qazvin (Iran, Islamic Republic of); Kargarnovin, M. H. [Sharif University of Technology, Tehran (Iran, Islamic Republic of)

    2008-06-15

    In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction, while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach

  5. Three-dimensional elasticity solution of simple-supported rectangular plate on point supports,line supports and elastic foundation

    Institute of Scientific and Technical Information of China (English)

    XU YePeng; ZHOU Ding

    2009-01-01

    This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in-termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer-cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.

  6. Three-dimensional elasticity solution of simple-supported rectangular plate on point supports, line supports and elastic foundation

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in- termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer- cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.

  7. A new strain based brick element for plate bending

    Directory of Open Access Journals (Sweden)

    L. Belounar

    2014-03-01

    Full Text Available This paper presents the development of a new three-dimensional brick finite element by the use of the strain based approach for the linear analysis of plate bending. The developed element has the three essential external degrees of freedom (U, V and W at each of the eight corner nodes as well as at the centroidal node. The displacement field of the developed element is based on assumed functions for the various strains satisfying the compatibility equations and the static condensation technique is used for the internal node. The performance of this element is evaluated on several problems related to thick and thin plate bending in linear analysis. The obtained results show the good performances and accuracy of the present element.

  8. APPROXIMATE SOLUTION FOR THIN PLATES CONSTRAINED AT ARBITRARY POINTS

    Institute of Scientific and Technical Information of China (English)

    1998-01-01

    The energy variational formula based on the principle of minimum potential energy is proposed for the plates constrained at arbitrary points. As an instance, the orthotropic large deflection rectangular thin plates with four free edges and transverse displacement constraints under uniform transverse load are discussed. The generalized Fourier series are used as the trial functions of the transverse displacement and the stress function to establish the essential equations, which are linearized by means of the incremental method of load and displacement constraint. In the end of the paper, several computational results are compared with the former literature. Moreover, one typical example is demonstrated through advanced experimental technique. The result shows the accuracy is satisfied well.

  9. Active cloaking for clusters of pins in thin plates

    CERN Document Server

    O'Neill, Jane; Haslinger, Stewart; Movchan, Natasha; Craster, Richard

    2016-01-01

    This paper considers active cloaking of a square array of evenly spaced pins in a Kirchhoff plate in the presence of flexural waves. Active sources are distributed exterior to the cluster and are represented by the non-singular Green's function for the biharmonic operator. The complex amplitudes of the active sources, which cancel out selected multipole orders of the scattered field, are found by solving an algebraic system of equations. For frequencies in the zero-frequency stop band, we find that a small number of active sources located on a grid is sufficient for cloaking. For higher frequencies, we achieve efficient cloaking with the active sources positioned on a circle surrounding the cluster. We demonstrate the cloaking efficiency with several numerical illustrations, considering key frequencies from band diagrams and dispersion surfaces for a Kirchhoff plate pinned in a doubly periodic fashion.

  10. Wave propagation in a magneto-electro- elastic plate

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    The wave propagation in a magneto-electro-elastic plate was studied. Some new characteristics were discovered: the guided waves are classified in the forms of the Quasi-P, Quasi-SV and Quasi-SH waves and arranged by the standing wavenumber; there are many patterns for the physical property of the magneto-electro-elastic dielectric medium influencing the stress wave propagation. We proposed a self-adjoint method, by which the guided-wave restriction condition was derived. After the corresponding orthogonal sets were found, the analytic dispersion equa-tion was obtained. In the end, an example was presented. The dispersive spectrum, the group velocity curved face and the steady-state response curve of a mag-neto-electro-elastic plate were plotted. Then the wave propagations affected by the induced electric and magnetic fields were analyzed.

  11. Thermodynamic optimization of fluid flow over an isothermal moving plate

    Directory of Open Access Journals (Sweden)

    A. Malvandi

    2013-09-01

    Full Text Available In this paper, entropy generation minimization (EGM was employed in order to achieve a thermodynamic optimization of fluid flow and heat transfer over a flat plate. The basic boundary layer equations including continuity, momentum, energy, and entropy generation have been reduced to a two-point boundary value problem via similarity variables and solved numerically via Runge–Kutta–Fehlberg scheme. The novelty of this study was to consider the effects of velocity ratio λ – which represents the ratio of the wall velocity to the free stream fluid velocity – in a thermodynamic system. Focusing on the velocity ratio as a pivotal parameter, in view of minimizing the entropy generation, the optimum value of λ=λo was achieved. Moreover, considering Bejan number, it was shown that the region, in which the maximum entropy generates, gets closer to the plate as λ increases.

  12. Plate Shape Control Theory and Experiment for 20-high Mill

    Institute of Scientific and Technical Information of China (English)

    Zheng-wen YUAN; Hong XIAO

    2015-01-01

    Roll lfattening theory is an important part of plate shape control theories for 20-high mill. In order to improve the ac-curacy of roll lfattening calculation for 20-high mill, a new and more accurate roll lfattening model was proposed. In this model, the roll barrel was considered as a ifnite length semi-inifnite body. Based on the boundary integral equation method, the numerical solution of the ifnite length semi-inifnite body under the distributed force was obtained and an accurate roll lfattening model was established. Coupled with roll bending model and strip plastic deformation, a new and more accurate plate control model for 20-high mill was established. Moreover, the effects of the ifrst intermediate roll taper angle and taper length were analyzed. The ten-sion distribution calculated by analytical model was consistent with the experimental results.

  13. Trapped modes in 3D topographically varying plates

    Science.gov (United States)

    Postnova, J.; Craster, R. V.

    2008-12-01

    Trapped modes in 3D elastic plates are considered as a model of waves that are guided along, and localized to the vicinity of, welds. These waves propagate unattenuated along the weld and exponentially decay with distance transverse to it. In the direction of propagation (y), there is no change in geometry and we assume that waves have the form exp(i{beta}y). An asymptotic long-wave theory provides numerical values of the trapped mode frequencies and gives conditions at which trapping can occur; these depend on the components of the wave number in different directions and variations of the plate thickness. The results of this long-wave theory are compared with a numerical solution of the full governing equations.

  14. Unsteady Viscous Dissipative Dusty Nanofluid Flow Over a Vertical Plate

    Directory of Open Access Journals (Sweden)

    D.R.V.S.R.K. Sastry

    2016-10-01

    Full Text Available The flow past an infinite vertical isothermal plate started impulsively in its own plane in a viscous incompressible two-phase nanofluid has been considered by taking into account the viscous dissipative heat. Two nano particles Copper (Cu and Alumina (Al2O3 are submerged in a base fluid, Water (H20. The coupled non-linear partial differential equations which govern the flow are solved for nanofluid and dust particle phases by finite difference method. The velocity and temperature fields have been shown graphically for various parameters. Here Grashof number, (Gr being positive (cooling of the plate for dusty air. Also the effects of Eckert number on heat transfer and skin friction coefficient for various parameters are represented graphically. It is observed that dusty nanofluid enhances both skin friction and heat transfer rate in the case of cooling.

  15. A dynamic simulation of a flat-plate collector system

    Science.gov (United States)

    Annino, A.

    1983-04-01

    A numerical model for the performance of a flat plate solar collector array is presented, with account taken of thermal transients and calculation on a microcomputer. The system modeled consists of a flat plate array, the heat transfer fluid, an insulated storage tank, an exchange loop for heating a secondary fluid, and a load maintained by a pump. The one-dimensional analysis includes equations for the energy balances, with consideration given to heat losses to the outside. A function is defined for the total incident solar radiation, and behavior is simulated over the entire 24-hr day, weighted by the highest and lowest recorded temperatures. Good agreement has been found with experimental data.

  16. Optimal piezo-electro-mechanical coupling to control plate vibrations

    CERN Document Server

    Alessandroni, S; Frezza, F

    2010-01-01

    A new way of coupling electrical and mechanical waves, using piezoelectric effect, is presented here. Since the energy exchange between two systems supporting wave propagation is maximum when their evolution is governed by similar equations, hence, an optimal electromechanical coupling is obtained by designing an electric network which is "analog" to the mechanical structure to be controlled. In this paper, we exploit this idea to enhance the coupling, between a Kirchhoff-Love plate and one possible synthesis of its circuital analog, as obtained by means of a set of piezoelectric actuators uniformly distributed upon the plate. It is shown how this approach allows for an optimal energy exchange between the mechanic and the electric forms independent of the modal evolution of the structure. Moreover, we show how an efficient electric dissipation of the mechanical energy can be obtained adding dissipative elements in the electric network.

  17. A Comparison of IRT Equating and Beta 4 Equating.

    Science.gov (United States)

    Kim, Dong-In; Brennan, Robert; Kolen, Michael

    Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…

  18. Modelling and solution of contact problem for infinite plate and cross-shaped embedment

    Directory of Open Access Journals (Sweden)

    O.B. Kozin

    2016-09-01

    Full Text Available Development of efficient methods of determination of an intense-strained state of thin-walled constructional designs with inclusions, reinforcements and other stress raisers is an important problem both with theoretical, and from the practical point of view, considering their wide practical application. Aim: The aim of this research is to develop the analytical mathematical method of studying of an intense-strained state of infinite plate with cross-shaped embedment at a bend. Materials and Methods: The method of boundary elements is an efficient way of the boundary value problems solution for systems of differential equations. The methods based on boundary integral equations get wide application in many branches of science and technique, calculation of plates and shells. One of methods of solution of a numerous class of the integral equations and systems arising on the basis of a method of boundary integral equations is the analytical method of construction of these equations and systems to Riemann problems with their forthcoming decision. Results: The integral equation for the analysis of deflections and the analysis of an intense-strained state of a thin rigid plate with rigid cross-shaped embedment is received. The precise solution of this boundary value problem is received by reduction to a Riemann problem and its forthcoming solution. An asymptotical behavior of contact efforts at the ends of embedment is investigated.

  19. Asymptotic modelling of a thermopiezoelastic anisotropic smart plate

    Science.gov (United States)

    Long, Yufei

    Motivated by the requirement of modelling for space flexible reflectors as well as other applications of plate structures in engineering, a general anisotropic laminated thin plate model and a monoclinic Reissner-Mindlin plate model with thermal deformation, two-way coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method, without any ad hoc assumptions. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change. Three-dimensional strain field is built based on the concept of warping function and decomposition of the rotation tensor. The feature of small thickness and large in-plane dimension of plate structure helped to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. For the zeroth-order approximation, the asymptotically correct expression of energy is derived into the form of energetic equation in classical laminated plate theory, which will be enough to predict the behavior of plate structures as thin as a space flexible reflector. A through-the-thickness strain field can be expressed in terms of material constants and two-dimensional membrane and bending strains, while the transverse normal and shear stresses are not predictable yet. In the first-order approximation, the warping functions are further disturbed into a high order and an asymptotically correct energy expression with derivatives of the two-dimensional strains is acquired. For the convenience of practical use, the expression is transformed into a Reissner-Mindlin form with optimization implemented to minimize the error. Transverse stresses and strains are recovered using the in-plane strain variables. Several numerical examples of different laminations and shapes are studied with the help of analytical solutions or shell elements in finite element codes. The constitutive relation is

  20. EMPIRICAL STUDY OF CAR LICENSE PLATES RECOGNITION

    Directory of Open Access Journals (Sweden)

    Nasa Zata Dina

    2015-01-01

    Full Text Available The number of vehicles on the road has increased drastically in recent years. The license plate is an identity card for a vehicle. It can map to the owner and further information about vehicle. License plate information is useful to help traffic management systems. For example, traffic management systems can check for vehicles moving at speeds not permitted by law and can also be installed in parking areas to se-cure the entrance or exit way for vehicles. License plate recognition algorithms have been proposed by many researchers. License plate recognition requires license plate detection, segmentation, and charac-ters recognition. The algorithm detects the position of a license plate and extracts the characters. Various license plate recognition algorithms have been implemented, and each algorithm has its strengths and weaknesses. In this research, I implement three algorithms for detecting license plates, three algorithms for segmenting license plates, and two algorithms for recognizing license plate characters. I evaluate each of these algorithms on the same two datasets, one from Greece and one from Thailand. For detecting li-cense plates, the best result is obtained by a Haar cascade algorithm. After the best result of license plate detection is obtained, for the segmentation part a Laplacian based method has the highest accuracy. Last, the license plate recognition experiment shows that a neural network has better accuracy than other algo-rithm. I summarize and analyze the overall performance of each method for comparison.

  1. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  2. Stochastic Gauss Equations

    CERN Document Server

    Frédéric, Pierret

    2014-01-01

    The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.

  3. Kinetic equations: computation

    CERN Document Server

    Pareschi, Lorenzo

    2013-01-01

    Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.

  4. Modern nonlinear equations

    CERN Document Server

    Saaty, Thomas L

    1981-01-01

    Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.

  5. Geometry of differential equations

    CERN Document Server

    Khovanskiĭ, A; Vassiliev, V

    1998-01-01

    This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.

  6. Regularized Structural Equation Modeling.

    Science.gov (United States)

    Jacobucci, Ross; Grimm, Kevin J; McArdle, John J

    A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.

  7. Complex Maxwell's equations

    Institute of Scientific and Technical Information of China (English)

    A.I.Arbab

    2013-01-01

    A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.

  8. Applied partial differential equations

    CERN Document Server

    DuChateau, Paul

    2012-01-01

    Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.

  9. Singular Renormalization Group Equations

    OpenAIRE

    Minoru, HIRAYAMA; Department of Physics, Toyama University

    1984-01-01

    The possible behaviour of the effective charge is discussed in Oehme and Zimmermann's scheme of the renormalization group equation. The effective charge in an example considered oscillates so violently in the ultraviolet limit that the bare charge becomes indefinable.

  10. Problems in differential equations

    CERN Document Server

    Brenner, J L

    2013-01-01

    More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.

  11. Relativistic Guiding Center Equations

    Energy Technology Data Exchange (ETDEWEB)

    White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association

    2014-10-01

    In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.

  12. Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method

    Directory of Open Access Journals (Sweden)

    Luiz Carlos Facundo Sanches

    2007-01-01

    Full Text Available A direct version of the boundary element method (BEM is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs. Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane and for the out-of-plane state (bending. These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs. A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM.

  13. Bending of a uniformly loaded square plate resting on unilateral edge supports

    Directory of Open Access Journals (Sweden)

    Yos Sompornjaroensuk

    2008-10-01

    Full Text Available The objectives of this paper are to analyze the bending behaviors of unilaterally simply supported square plate subjected to the uniformly distributed load, and to examine the extent of receding contacts between the plate and the unilateral supports. In the present problem the mixed boundary conditions exist along the plate edges, which can be written in the form of dual series equations. These equations are further reduced to determine the solution of inhomogeneous Fredholmintegral equation of the second kind for an unknown auxiliary function by using the finite Hankel integral transform techniques.Numerical results concerning the extent of receding contact, deflection, bending moment, twisting moment, and support reaction of the plate are given and also compared with the results obtained by other available techniques. From investigations, the conclusions can be stated that (i the method used is found to be efficient for solving the problem considered, (ii the extent of contact is independent of the level of loading, but dependent on the values of Poisson’s ratio of the plate, and (iii the support reactions are proportional to the applied load.

  14. Bending analysis and control of rolled plate during snake hot rolling

    Institute of Scientific and Technical Information of China (English)

    张涛; 吴运新; 龚海; 郑细昭; 蒋绍松

    2015-01-01

    In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element (FE) models were established. Effects of different initial thicknesses, pass reductions, speed ratios and offset distances on the bending value of the plate were analyzed. ‘Quasi smooth plate’ and optimum offset distance were defined and quasi smooth plate could be acquired by adjusting offset distance, and then bending control equation was fitted. The results show that bending value of the plate as well as the extent of the increase grows with the increase of pass reduction and decrease of initial thickness; the bending value firstly increases and then keeps steady with the ascending speed ratio; the bending value can be reduced by enlarging the offset distance. The optimum offset distance varies for different rolling parameters and it is augmented with the increase of pass reduction and speed ratio and the decrease of initial thickness. A proper offset distance for different rolling parameters can be calculated by the bending control equation and this equation can be a guidance to acquire a quasi smooth plate. The FEM results agree well with experimental results.

  15. The Optimum Plate to Plate Spacing for Maximum Heat Transfer Rate from a Flat Plate Type Heat Exchanger

    Science.gov (United States)

    Ambarita, Himsar; Kishinami, Koki; Daimaruya, Mashashi; Tokura, Ikuo; Kawai, Hideki; Suzuki, Jun; Kobiyama, Mashayosi; Ginting, Armansyah

    The present paper is a study on the optimum plate to plate spacing for maximum heat transfer rate from a flat plate type heat exchanger. The heat exchanger consists of a number of parallel flat plates. The working fluids are flowed at the same operational conditions, either fixed pressure head or fixed fan power input. Parallel and counter flow directions of the working fluids were considered. While the volume of the heat exchanger is kept constant, plate number was varied. Hence, the spacing between plates as well as heat transfer rate will vary and there exists a maximum heat transfer rate. The objective of this paper is to seek the optimum plate to plate spacing for maximum heat transfer rate. In order to solve the problem, analytical and numerical solutions have been carried out. In the analytical solution, the correlations of the optimum plate to plate spacing as a function of the non-dimensional parameters were developed. Furthermore, the numerical simulation is carried out to evaluate the correlations. The results show that the optimum plate to plate spacing for a counter flow heat exchanger is smaller than parallel flow ones. On the other hand, the maximum heat transfer rate for a counter flow heat exchanger is bigger than parallel flow ones.

  16. Asymptotics for dissipative nonlinear equations

    CERN Document Server

    Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A

    2006-01-01

    Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

  17. Functional Equations and Fourier Analysis

    OpenAIRE

    2010-01-01

    By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.

  18. Linear Analytical Solutions of Mechanical Sensitivity in Large Deflection of Unsymmetrically Layered Piezoelectric Plate under Pretension

    Directory of Open Access Journals (Sweden)

    Chun-Fu Chen

    2014-03-01

    Full Text Available Linear analytical study on the mechanical sensitivity in large deflection of unsymmetrically layered and laterally loaded piezoelectric plate under pretension is conducted. von Karman plate theory for large deflection is utilized but extended to the case of an unsymmetrically layered plate embedded with a piezoelectric layer. The governing equations thus obtained are simplified by omitting the arising nonlinear terms, yielding a Bessel or modified Bessel equation for the lateral slope. Depending on the relative magnitude of the piezoelectric effect, for both cases, analytical solutions of various geometrical responses are developed and formulated via Bessel and modified Bessel functions. The associated ultimate radial stresses are further derived following lamina constitutive law to evaluate the mechanical sensitivity of the considered plate. For a nearly monolithic plate under a very low applied voltage, the results are in good agreement with those for a single-layered case due to pure mechanical load available in literature, and thus the present approach is checked. For a two-layered unsymmetric plate made of typical silicon-based materials, a sound piezoelectric effect is illustrated particularly in a low pretension condition.

  19. Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates

    Science.gov (United States)

    Destrade, Michel; Fu, Yibin; Nobili, Andrea

    2016-09-01

    The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.

  20. Thermal Effects on Vibration and Control of Piezocomposite Kirchhoff Plate Modeled by Finite Elements Method

    Directory of Open Access Journals (Sweden)

    M. Sanbi

    2015-01-01

    Full Text Available Theoretical and numerical results of the modeling of a smart plate are presented for optimal active vibration control. The smart plate consists of a rectangular aluminum piezocomposite plate modeled in cantilever configuration with surface bonded thermopiezoelectric patches. The patches are symmetrically bonded on top and bottom surfaces. A generic thermopiezoelastic theory for piezocomposite plate is derived, using linear thermopiezoelastic theory and Kirchhoff assumptions. Finite element equations for the thermopiezoelastic medium are obtained by using the linear constitutive equations in Hamilton’s principle together with the finite element approximations. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQG-Kalman filter is applied. By using this model, the study first gives the influences of the actuator/sensor pair placement and size on the response of the smart plate. Second, the effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. It is shown that the effectiveness of the control is not affected by the applied thermal gradient and can be applied with or without this gradient at any time of plate vibrations.

  1. Measurement procedure for optomechanical hole plate

    DEFF Research Database (Denmark)

    Larsen, Erik

    2003-01-01

    Measurement procedure for optomechanical hole plate in connection with CIRP interlaboratory comparison on measuring machines.......Measurement procedure for optomechanical hole plate in connection with CIRP interlaboratory comparison on measuring machines....

  2. Food Guide Pyramid Becomes a Plate

    Science.gov (United States)

    ... agency in charge of nutrition, created the colorful plate to help people remember to: Eat a variety ... of some foods and more of others. The plate features four sections — vegetables, fruits, grains, and protein — ...

  3. Earth's Decelerating Tectonic Plates

    Energy Technology Data Exchange (ETDEWEB)

    Forte, A M; Moucha, R; Rowley, D B; Quere, S; Mitrovica, J X; Simmons, N A; Grand, S P

    2008-08-22

    Space geodetic and oceanic magnetic anomaly constraints on tectonic plate motions are employed to determine a new global map of present-day rates of change of plate velocities. This map shows that Earth's largest plate, the Pacific, is presently decelerating along with several other plates in the Pacific and Indo-Atlantic hemispheres. These plate decelerations contribute to an overall, globally averaged slowdown in tectonic plate speeds. The map of plate decelerations provides new and unique constraints on the dynamics of time-dependent convection in Earth's mantle. We employ a recently developed convection model constrained by seismic, geodynamic and mineral physics data to show that time-dependent changes in mantle buoyancy forces can explain the deceleration of the major plates in the Pacific and Indo-Atlantic hemispheres.

  4. Earth's Decelerating Tectonic Plates

    Energy Technology Data Exchange (ETDEWEB)

    Forte, A M; Moucha, R; Rowley, D B; Quere, S; Mitrovica, J X; Simmons, N A; Grand, S P

    2008-08-22

    Space geodetic and oceanic magnetic anomaly constraints on tectonic plate motions are employed to determine a new global map of present-day rates of change of plate velocities. This map shows that Earth's largest plate, the Pacific, is presently decelerating along with several other plates in the Pacific and Indo-Atlantic hemispheres. These plate decelerations contribute to an overall, globally averaged slowdown in tectonic plate speeds. The map of plate decelerations provides new and unique constraints on the dynamics of time-dependent convection in Earth's mantle. We employ a recently developed convection model constrained by seismic, geodynamic and mineral physics data to show that time-dependent changes in mantle buoyancy forces can explain the deceleration of the major plates in the Pacific and Indo-Atlantic hemispheres.

  5. Thin flat plate with linear spring as mechanical stop. Final report

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, B.H.

    1997-06-01

    A mechanical device has been developed which dissipates mechanical energy simply and reliably, without generating debris. The device basically consists of a stack of thin flat metal layers, forming a flexible plate, and a mechanical spring to buffer the impact of the moving object. Equations have been developed which allow the design of such devices for particular applications.

  6. Analytical Solution of Forced-Convective Boundary-Layer Flow over a Flat Plate

    DEFF Research Database (Denmark)

    Mirgolbabaei, H.; Barari, Amin; Ibsen, Lars Bo

    2010-01-01

    In this letter, the problem of forced convection heat transfer over a horizontal flat plate is investigated by employing the Adomian Decomposition Method (ADM). The series solution of the nonlinear differential equations governing on the problem is developed. Comparison between results obtained...

  7. Exact controllability of the Euler-Bernoulli plate with variable coefficients and simply supported boundary condition

    Directory of Open Access Journals (Sweden)

    Fengyan Yang

    2016-09-01

    Full Text Available This article studies the exact controllability of an Euler-Bernoulli plate equation with variable coefficients, subject to the simply supported boundary condition. By the Riemannian geometry approach, the duality method, the multiplier technique, and the compactness-uniqueness argument, we establish the corresponding observability inequality and obtain the exact controllability results.

  8. LOCALIZED BUCKLING OF THE SEMI-INFINITE ISOTROPIC PLATE NEAR ELASTICALLY FASTENED EDGE

    Directory of Open Access Journals (Sweden)

    Sharifian R.

    2012-06-01

    Full Text Available Localized buckling of a semi-infinite isotropic plate near elastically fastened edge has been investigated. Mathematical model is of structure is provided and characteristic equation of the problem is derived. The existence conditions of localized buckling are derived analytically. For the cases when localized buckling exists numerical solutions and plots for the critical loads are provided.

  9. Analytical Solution of Forced-Convective Boundary-Layer Flow over a Flat Plate

    DEFF Research Database (Denmark)

    Mirgolbabaei, H.; Barari, Amin; Ibsen, Lars Bo;

    2010-01-01

    In this letter, the problem of forced convection heat transfer over a horizontal flat plate is investigated by employing the Adomian Decomposition Method (ADM). The series solution of the nonlinear differential equations governing on the problem is developed. Comparison between results obtained...

  10. MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate

    Institute of Scientific and Technical Information of China (English)

    Krishnendu Bhattacharyya; Swati Mukhopadhyay; G.C.Layek

    2011-01-01

    An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.%@@ An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented.A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method.In the boundary slip condition no local similarity occurs.Velocity and temperature distributions within the boundary layer are presented.Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.

  11. On the flexural vibration of an elastic plate carrying a concentrated mass

    Energy Technology Data Exchange (ETDEWEB)

    Sadiku, S. (Federal Univ. of Technology, Minna (Nigeria). Dept. of Civil Engineering)

    1989-12-01

    The dynamic response of an elastic plate carrying a concentrated mass is analysed. Despite the presence of a singular mass distribtion function, a rigorous analysis leading to a closed-form solution in the form of an infinite series has been made. By developing Green's function for the associated partial differential equation, any form of dynamic excitation is easily considered. (orig.).

  12. Embedded adhesive connection for laminated glass plates

    DEFF Research Database (Denmark)

    Hansen, Jens Zangenberg; Poulsen, S.H.; Bagger, A.

    2012-01-01

    The structural behavior of a new connection design, the embedded adhesive connection, used for laminated glass plates is investigated. The connection consists of an aluminum plate encapsulated in-between two adjacent triple layered laminated glass plates. Fastening between glass and aluminum...... usage in a design situation. The embedded connection shows promising potential as a future fastening system for load-carrying laminated glass plates....

  13. Electrochemical Assay of Gold-Plating Solutions

    Science.gov (United States)

    Chiodo, R.

    1982-01-01

    Gold content of plating solution is assayed by simple method that required only ordinary electrochemical laboratory equipment and materials. Technique involves electrodeposition of gold from solution onto electrode, the weight gain of which is measured. Suitable fast assay methods are economically and practically necessary in electronics and decorative-plating industries. If gold content in plating bath is too low, poor plating may result, with consequent economic loss to user.

  14. Practical automatic Arabic license plate recognition system

    Science.gov (United States)

    Mohammad, Khader; Agaian, Sos; Saleh, Hani

    2011-02-01

    Since 1970's, the need of an automatic license plate recognition system, sometimes referred as Automatic License Plate Recognition system, has been increasing. A license plate recognition system is an automatic system that is able to recognize a license plate number, extracted from image sensors. In specific, Automatic License Plate Recognition systems are being used in conjunction with various transportation systems in application areas such as law enforcement (e.g. speed limit enforcement) and commercial usages such as parking enforcement and automatic toll payment private and public entrances, border control, theft and vandalism control. Vehicle license plate recognition has been intensively studied in many countries. Due to the different types of license plates being used, the requirement of an automatic license plate recognition system is different for each country. [License plate detection using cluster run length smoothing algorithm ].Generally, an automatic license plate localization and recognition system is made up of three modules; license plate localization, character segmentation and optical character recognition modules. This paper presents an Arabic license plate recognition system that is insensitive to character size, font, shape and orientation with extremely high accuracy rate. The proposed system is based on a combination of enhancement, license plate localization, morphological processing, and feature vector extraction using the Haar transform. The performance of the system is fast due to classification of alphabet and numerals based on the license plate organization. Experimental results for license plates of two different Arab countries show an average of 99 % successful license plate localization and recognition in a total of more than 20 different images captured from a complex outdoor environment. The results run times takes less time compared to conventional and many states of art methods.

  15. Modeling the hydrodynamics of Phloem sieve plates

    DEFF Research Database (Denmark)

    Jensen, Kaare Hartvig; Mullendore, Daniel Leroy; Holbrook, Noel Michele;

    2012-01-01

    Sieve plates have an enormous impact on the efficiency of the phloem vascular system of plants, responsible for the distribution of photosynthetic products. These thin plates, which separate neighboring phloem cells, are perforated by a large number of tiny sieve pores and are believed to play...... are investigated. We find that the sieve plate resistance is correlated to the cell lumen resistance, and that the sieve plate and the lumen contribute almost equally to the total hydraulic resistance of the phloem translocation pathway....

  16. FUNDAMENTAL RESONANCE AND BIFURCATION OF LARGE GENERATOR END WINDING WHEN ITS CLAMPING PLATES ARE LOOSE

    Institute of Scientific and Technical Information of China (English)

    HU Yu-da; QIU Jia-jun; TA Na

    2005-01-01

    Vibration problems of a segment of winding between two clamping plates are studied when the clamping plates, which are used to fix stator end winding, are loose. First,magnetic induction expressions of the winding while the generator was running were given by using separation of variables method. Also, the expressions of the winding electromagnetic force and dry friction force between loosing clamping plates were gotten. Secondly, a mechanical model, which was used to study nonlinear vibration problem of the winding, was set up. Fundamental resonance was analyzed by using multiple scales method, and a resonance equation of amplitude and frequency in steady state was given. Then stability,bifurcation and singularity of the steady solution were studied. Criterions of stability and transition set of the bifurcation equation were obtained. At last, through numerical calculations, resonance curves were obtained. The results are helpful for analysis and protection of generator accidents.

  17. EXPERIMENTAL STUDY ON TOTAL UPLIFT FORCES OF WAVES ON HORIZONTAL PLATES

    Institute of Scientific and Technical Information of China (English)

    ZHOU Yi-ren; CHEN Guo-ping; WANG Deng-ting

    2004-01-01

    The total uplift forces of waves acting on hori zontal plates are the important basis for the design of maritime hollow-trussed structures. In this paper, an experimental study on the total uplift forces of waves on horizontal plates was conducted by a series of model tests. The results show that the maximum total uplift forces do not necessarily occur with the maximum impact pressure intensity synchronously.On the basis of the test results, formation mechanism of the total uplift forces of waves as well as its influencing factors were analyzed in detail, and an equation for calculation of the maximum total uplift forces of waves on plates was put forward. Lots of test data shows the present equation is in good agreement with the test results.

  18. Frequency dependence of magnetic shielding performance of HTS plates in mixed states

    Energy Technology Data Exchange (ETDEWEB)

    Kamitani, Atsushi; Yokono, Takafumi [Yamagata Univ., Yonezawa (Japan). Faculty of Engineering; Yokono, Takafumi [Tsukuba Univ., Ibaraki (Japan). Inst. of Information Sciences and Electronics

    2000-06-01

    The magnetic shielding performance of the high-Tc superconducting (HTS) plate is investigated numerically. The behavior of the shielding current density in the HTS plate is expressed as the integral-differential equation with a normal component of the current vector potential as a dependent variable. The numerical code for solving the equation has been developed by using the combination of the Newton-Raphson method and the successive substitution method and, by use of the code, damping coefficients and shielding factors are evaluated for the various values of the frequency {omega}. The results of computations show that the HTS plate has a possibility of shielding the high-frequency magnetic field with {omega} > or approx. 1 kHz. (author)

  19. Nonlinear morphoelastic plates I: Genesis of residual stress

    KAUST Repository

    McMahon, J.

    2011-04-28

    Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established. © SAGE Publications 2011.

  20. Numerical modeling of parallel-plate based AMR

    DEFF Research Database (Denmark)

    In this work we present an improved 2-dimensional numerical model of a parallel-plate based AMR. The model includes heat transfer in fluid and magnetocaloric domains respectively. The domains are coupled via inner thermal boundaries. The MCE is modeled either as an instantaneous change between high...... and low field or as a magnetic field profile including the actual physical movement of the regenerator block in and out of field, i.e. as a source term in the thermal equation for the magnetocaloric material (MCM). The model is further developed to include parasitic thermal losses throughout the bed...

  1. Calculating the Solar Energy of a Flat Plate Collector

    Directory of Open Access Journals (Sweden)

    Ariane Rosario

    2014-09-01

    Full Text Available The amount of solar energy that could be obtained by a flat plate solar collector of one square meter dimension is calculated in three different locations: Tampa FL, Fairbanks AL, and Pontianak Indonesia, considering the varying sunset time for each day of the year. The results show that if the collectors are placed near the equator, more total energy could be obtained. In fact, by placing a solar collector in Pontianak, Indonesia 12.42% more solar energy can be obtained than by placing it in Tampa and 96.9% more solar energy than Alaska.

  2. Thermo elastic waves with thermal relaxation in isotropic micropolar plate

    Indian Academy of Sciences (India)

    Soumen Shaw; Basudeb Mukhopadhyay

    2011-04-01

    In the present investigation, we have discussed about the features of waves in different modes of wave propagation in an infinitely long thermoelastic, isotropic micropolar plate, when the generalized theory of Lord–Shulman (L–S) is considered. A more general dispersion equation is obtained. The different analytic expressions in symmetric and anti-symmetric vibration for short as well as long waves are obtained in different regions of phase velocities. It is found that results agree with that of the existing results predicted by Sharma and Eringen in the context of various theories of classical as well as micropolar thermoelasticity.

  3. Transfinite thin plate spline interpolation

    CERN Document Server

    Bejancu, Aurelian

    2009-01-01

    Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves or hypersurfaces, Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo Levi type to construct a semi-cardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying Beppo Levi boundary conditions is in fact a thin plate spline, i.e. it minimizes a Duchon type functional.

  4. Silicon-micromachined microchannel plates

    CERN Document Server

    Beetz, C P; Steinbeck, J; Lemieux, B; Winn, D R

    2000-01-01

    Microchannel plates (MCP) fabricated from standard silicon wafer substrates using a novel silicon micromachining process, together with standard silicon photolithographic process steps, are described. The resulting SiMCP microchannels have dimensions of approx 0.5 to approx 25 mu m, with aspect ratios up to 300, and have the dimensional precision and absence of interstitial defects characteristic of photolithographic processing, compatible with positional matching to silicon electronics readouts. The open channel areal fraction and detection efficiency may exceed 90% on plates up to 300 mm in diameter. The resulting silicon substrates can be converted entirely to amorphous quartz (qMCP). The strip resistance and secondary emission are developed by controlled depositions of thin films, at temperatures up to 1200 deg. C, also compatible with high-temperature brazing, and can be essentially hydrogen, water and radionuclide-free. Novel secondary emitters and cesiated photocathodes can be high-temperature deposite...

  5. Vehicle License Plate Character Segmentation

    Institute of Scientific and Technical Information of China (English)

    Mei-Sen Pan; Jun-Biao Yan; Zheng-Hong Xiao

    2008-01-01

    Vehicle license plate (VLP) character segmentation is an important part of the vehicle license plate recognition system (VLPRS). This paper proposes a least square method (LSM) to treat horizontal tilt and vertical tilt in VLP images. Auxiliary lines are added into the image (or the tilt-corrected image) to make the separated parts of each Chinese character to be an interconnected region. The noise regions will be eliminated after two fusing images are merged according to the minimum principle of gray values.Then, the characters are segmented by projection method (PM) and the final character images are obtained. The experimental results show that this method features fast processing and good performance in segmentation.

  6. Electroless metal plating of plastics

    Science.gov (United States)

    Krause, Lawrence J.

    1984-01-01

    Process for plating main group metals on aromatic polymers is carried out by the use of a nonaqueous solution of a salt of an alkali metal in a positive valence state and a main group metal in a negative valence state with contact between the solution and polymer providing a redox reaction causing the deposition of the main group metal and the reduction of the polymer. Products from the process exhibit useful decorative and electrical properties.

  7. 49 CFR 236.779 - Plate, top.

    Science.gov (United States)

    2010-10-01

    ... 49 Transportation 4 2010-10-01 2010-10-01 false Plate, top. 236.779 Section 236.779 Transportation... OF SIGNAL AND TRAIN CONTROL SYSTEMS, DEVICES, AND APPLIANCES Definitions § 236.779 Plate, top. A metal plate secured to a locking bracket to prevent the cross locking from being forced out of the...

  8. 30 CFR 22.10 - Approval plate.

    Science.gov (United States)

    2010-07-01

    ... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Approval plate. 22.10 Section 22.10 Mineral... MINING PRODUCTS PORTABLE METHANE DETECTORS § 22.10 Approval plate. (a) Attachment to be made by manufacturers. (1) Manufacturers shall attach, stamp, or mold an approval plate on each permissible methane...

  9. 24 CFR 3280.5 - Data plate.

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Data plate. 3280.5 Section 3280.5... MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.5 Data plate. Each manufactured home shall bear a data plate affixed in a permanent manner near the main electrical panel or other readily...

  10. 30 CFR 20.13 - Approval plate.

    Science.gov (United States)

    2010-07-01

    ... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Approval plate. 20.13 Section 20.13 Mineral... MINING PRODUCTS ELECTRIC MINE LAMPS OTHER THAN STANDARD CAP LAMPS § 20.13 Approval plate. The manufacturer shall attach, stamp, or mold an approval plate on the battery container or housing of each...

  11. Moving Divertor Plates in a Tokamak

    Energy Technology Data Exchange (ETDEWEB)

    S.J. Zweben, H. Zhang

    2009-02-12

    Moving divertor plates could help solve some of the problems of the tokamak divertor through mechanical ingenuity rather than plasma physics. These plates would be passively heated on each pass through the tokamak and cooled and reprocessed outside the tokamak. There are many design options using varying plate shapes, orientations, motions, coatings, and compositions.

  12. Secure matching of Dutch car license plates

    NARCIS (Netherlands)

    Sunil, A.B.; Erkiny, Z.; Veugenyz, T.

    2016-01-01

    License plate matching plays an important role in applications like law enforcement, traffic management and road pricing, where the plate is first recognized and then compared to a database of authorized vehicle registration plates. Unfortunately, there are several privacy related issues that should

  13. Designing a licence plate for memorability

    NARCIS (Netherlands)

    Schraagen, J.M.C.; Dongen, C.J.G. van

    2005-01-01

    Good memorability of licence plates is important in those cases where licence plates are viewed for a brief period of time and the information is essential for police investigations. The purpose of the current study was to design a new Dutch licence plate that could be remembered well. A memory expe

  14. Episodic plate tectonics on Venus

    Science.gov (United States)

    Turcotte, Donald

    1992-01-01

    Studies of impact craters on Venus from the Magellan images have placed important constraints on surface volcanism. Some 840 impact craters have been identified with diameters ranging from 2 to 280 km. Correlations of this impact flux with craters on the Moon, Earth, and Mars indicate a mean surface age of 0.5 +/- 0.3 Ga. Another important observation is that 52 percent of the craters are slightly fractured and only 4.5 percent are embayed by lava flows. These observations led researchers to hypothesize that a pervasive resurfacing event occurred about 500 m.y. ago and that relatively little surface volcanism has occurred since. Other researchers have pointed out that a global resurfacing event that ceased about 500 MYBP is consistent with the results given by a recent study. These authors carried out a series of numerical calculations of mantle convection in Venus yielding thermal evolution results. Their model considered crustal recycling and gave rapid planetary cooling. They, in fact, suggested that prior to 500 MYBP plate tectonics was active in Venus and since 500 MYBP the lithosphere has stabilized and only hot-spot volcanism has reached the surface. We propose an alternative hypothesis for the inferred cessation of surface volcanism on Venus. We hypothesize that plate tectonics on Venus is episodic. Periods of rapid plate tectonics result in high rates of subduction that cool the interior resulting in more sluggish mantle convection.

  15. Modified tubularized incised plate urethroplasty

    Directory of Open Access Journals (Sweden)

    Shivaji Mane

    2013-01-01

    Full Text Available Aim: To share our experience of doing tubularized incised plate urethroplasty with modifications. Materials and Methods: This is a single surgeon personal series from 2004 to 2009. One hundred patients of distal hypospadias were subjected for Snodgrass urethroplasty with preputioplasty. The age range was 1 to 5 year with mean age of 2.7 years. Selection criteria were good urethral plate, without chordee and torsion needing complete degloving. Main technical modification from original Snodgrass procedure was spongioplasty, preputioplasty, and dorsal slit when inability to retract prepuce during surgery. Results: Average follow-up period is 23 months. Seven (7% patients developed fistula and one patient had complete preputial dehiscence. Phimosis developed in three (3% patients and required circumcision. Dorsal slit was required in seven patients. One patient developed meatal stenosis in postoperative period. All other patients are passing single urinary stream and have cosmesis that is acceptable. Conclusions: Modified tubularized incised plate urethroplasty with preputioplasty effectively gives cosmetically normal looking penis with low complications.

  16. Plating of proximal humeral fractures.

    Science.gov (United States)

    Martetschläger, Frank; Siebenlist, Sebastian; Weier, Michael; Sandmann, Gunther; Ahrens, Philipp; Braun, Karl; Elser, Florian; Stöckle, Ulrich; Freude, Thomas

    2012-11-01

    The optimal treatment for proximal humeral fractures is controversial. Few data exist concerning the influence of the surgical approach on the outcome. The purpose of this study was to evaluate the clinical and radiological outcomes of proximal humeral fractures treated with locking plate fixation through a deltopectoral vs an anterolateral deltoid-splitting approach. Of 86 patients who met the inclusion criteria, 70 were available for follow-up examination. Thirty-three patients were treated through a deltopectoral approach and 37 through an anterolateral deltoid-splitting approach. In all cases, open reduction and internal fixation with a PHILOS locking plate (Synthes, Umkirch, Germany) was performed. Clinical follow-up included evaluation of pain, shoulder mobility, and strength. Constant score and Disabilities of the Arm, Shoulder and Hand (DASH) score were assessed. A clinical neurological examination of the axillary nerve was also performed. Consolidation, reduction, and appearance of head necrosis were evaluated radiographically. After a mean follow-up of 33 months, Constant scores, DASH scores, and American Shoulder and Elbow Surgeons scores showed no significant differences between the groups. Clinical neurologic examination of the axillary nerve revealed no obvious damage to the nerve in either group. Deltopectoral and anterolateral detoid-splitting approaches for plate fixation of proximal humeral fractures are safe and provide similar clinical outcomes. The results of this study suggest that the approach can be chosen according to surgeon preference.

  17. On the free vibrations of a rectangular plate with two opposite sides simply supported and the other sides attached to linear springs

    NARCIS (Netherlands)

    Zarubinskaya, M.A.; van Horssen, W.T.

    2003-01-01

    In this paper an initial-boundary value problem for a plate equation will be studied. This initialboundary value problem can be regarded as a rather simple model describing free oscillations of a suspension bridge. The suspension bridge is modeled as a rectangular plate with two opposite sides simpl

  18. Scaling Equation for Invariant Measure

    Institute of Scientific and Technical Information of China (English)

    LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui

    2003-01-01

    An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.

  19. Multi-frequency excitation of stiffened triangular plates for large amplitude oscillations

    Science.gov (United States)

    Askari, H.; Saadatnia, Z.; Esmailzadeh, E.; Younesian, D.

    2014-10-01

    Free and forced vibrations of triangular plate are investigated. Diverse types of stiffeners were attached onto the plate to suppress the undesirable large-amplitude oscillations. The governing equation of motion for a triangular plate, based on the von Kármán theory, is developed and the nonlinear ordinary differential equation of the system using Galerkin approach is obtained. Closed-form expressions for the free undamped and large-amplitude vibration of an orthotropic triangular elastic plate are presented using the two well-known analytical methods, namely, the energy balance method and the variational approach. The frequency responses in the closed-form are presented and their sensitivities with respect to the initial amplitudes are studied. An error analysis is performed and the vibration behavior, as well as the accuracy of the solution methods, is evaluated. Different types of the stiffened triangular plates are considered in order to cover a wide range of practical applications. Numerical simulations are carried out and the validity of the solution procedure is explored. It is demonstrated that the two methods of energy balance and variational approach have been quite straightforward and reliable techniques to solve those nonlinear differential equations. Subsequently, due to the importance of multiple resonant responses in engineering design, multi-frequency excitations are considered. It is assumed that three periodic forces are applied to the plate in three specific positions. The multiple time scaling method is utilized to obtain approximate solutions for the frequency resonance cases. Influences of different parameters, namely, the position of applied forces, geometry and the number of stiffeners on the frequency response of the triangular plates are examined.

  20. Vortex distribution in small star-shaped Mo{sub 80}Ge{sub 20} plate

    Energy Technology Data Exchange (ETDEWEB)

    Vu, The Dang, E-mail: vu-dang@pe.osakafu-u.ac.jp [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Department of Physics and Electronics, University of Sciences, Vietnam National University HCMC (Viet Nam); Matsumoto, Hitoshi; Miyoshi, Hiroki [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Huy, Ho Thanh [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Department of Physics and Electronics, University of Sciences, Vietnam National University HCMC (Viet Nam); Shishido, Hiroaki [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Institute for Nanofabrication Research, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Kato, Masaru [Institute for Nanofabrication Research, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Department of Mathematical Science, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Ishida, Takekazu [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Institute for Nanofabrication Research, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan)

    2017-02-15

    Highlights: • We found the general feature of vortex configuration in small star-shaped Mo{sub 80}Ge{sub 20} plates such as the appearance of symmetric line, the rule of shell filling and the existence of a magic number in both theoretical predictions and experimental results. • We found that the vortex distribution in a concave decagon tends to adapt to one of the five symmetric axes of the star-shaped plate expected in confining vortices in a restricted sample geometry. • The numerical results of Ginzburg–Landau equation confirmed that the filling rules for a vortex configuration and the existence of a magic number for small star-shaped plates are in good agreement with experiment results. - Abstract: We investigated vortex states in small star-shaped Mo{sub 80}Ge{sub 20} plates both theoretically and experimentally. The numerical calculations of the Ginzburg–Landau equation have been carried out with the aid of the finite element method, which is convenient to treat an arbitrarily shaped superconductor. The experimental results were observed by using a scanning SQUID microscope. Through systematic measurements, we figured out how vortices form symmetric configuration with increasing the magnetic field. The vortex distribution tends to adapt to one of five mirror symmetric lines when vortices were located at the five triangular horns of a star-shaped plate. The crystalline homogeneity of a sample was confirmed by the X-ray diffraction and the superconducting properties so that vortices are easily able to move for accommodating vortices in the geometric symmetry of the star-shaped plate. The experimental vortex configurations obtained for a star-shaped plate are in good agreement with theoretical predictions from the nonlinear Ginzburg–Landau equation.