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Sample records for karman-rostovstev plate equations

  1. Pullback attractors for a singularly nonautonomous plate equation

    Directory of Open Access Journals (Sweden)

    Vera Lucia Carbone

    2011-06-01

    Full Text Available We consider the family of singularly nonautonomous plate equations with structural damping $$ u_{tt} + a(t,xu_t - Delta u_t + (-Delta^2 u + lambda u = f(u, $$ in a bounded domain $Omega subset mathbb{R}^n$, with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in $H^2_0(Omega imes L^2(Omega$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

  2. Closed solutions to a differential-difference equation and an associated plate solidification problem.

    Science.gov (United States)

    Layeni, Olawanle P; Akinola, Adegbola P; Johnson, Jesse V

    2016-01-01

    Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some special cases of time-varying plate surface temperature.

  3. 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.

  4. Experimental study of the conventional equation to determine a plate's moment of inertia

    International Nuclear Information System (INIS)

    Pintao, Carlos A F; Filho, Moacir P de Souza; Grandini, Carlos R; Hessel, Roberto

    2004-01-01

    In this work, we describe an experimental setup in which an electric current is used to determine the angular velocity attained by a plate rotating around a shaft in response to a torque applied for a given period. Based on this information, we show how the moment of inertia of a plate can be determined using a procedure that differs considerably from the ones most commonly used, which generally involve time measurements. Some experimental results are also presented which allow one to determine parameters such as the exponents and constant of the conventional equation of a plate's moment of inertia

  5. 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.

  6. The solutions of Navier-Stokes equations in squeezing flow between parallel plates

    Czech Academy of Sciences Publication Activity Database

    Petrov, A. G.; Kharlamova, Irina

    2014-01-01

    Roč. 48, November–December (2014), s. 40-48 ISSN 0997-7546 Grant - others:Russian Foundation for Basic Research(RU) 14-01- 00818; Russian Foundation for Basic Research(RU) 14-01-00892 Institutional support: RVO:67985874 Keywords : closed form solution * Navier-Stokes equations * squeezing flow between plates * counterflow Subject RIV: BK - Fluid Dynamics Impact factor: 1.656, year: 2014

  7. Doubling inequalities for anisotropic plate equations and applications to size estimates of inclusions

    International Nuclear Information System (INIS)

    Di Cristo, M; Lin, C-L; Morassi, A; Rosset, E; Vessella, S; Wang, J-N

    2013-01-01

    We prove the upper and lower estimates of the area of an unknown elastic inclusion in a thin plate by one boundary measurement. The plate is made of non-homogeneous linearly elastic material belonging to a general class of anisotropy and the domain of the inclusion is a measurable subset of the plate. The size estimates are expressed in terms of the work exerted by a couple field applied at the boundary and of the induced transversal displacement and its normal derivative taken at the boundary of the plate. The main new mathematical tool is a doubling inequality for solutions to fourth-order elliptic equations whose principal part P(x, D) is the product of two second-order elliptic operators P 1 (x, D), P 2 (x, D) such that P 1 (0, D) = P 2 (0, D). The proof of the doubling inequality is based on the Carleman method, a sharp three-spheres inequality and a bootstrapping argument. (paper)

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

    International Nuclear Information System (INIS)

    Bucci, Francesca; Toundykov, Daniel

    2010-01-01

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

  9. 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...

  10. 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.

  11. PIV-based estimation of unsteady loads on a flat plate at high angle of attack using momentum equation approaches

    Science.gov (United States)

    Guissart, A.; Bernal, L. P.; Dimitriadis, G.; Terrapon, V. E.

    2017-05-01

    This work presents, compares and discusses results obtained with two indirect methods for the calculation of aerodynamic forces and pitching moment from 2D Particle Image Velocimetry (PIV) measurements. Both methodologies are based on the formulations of the momentum balance: the integral Navier-Stokes equations and the "flux equation" proposed by Noca et al. (J Fluids Struct 13(5):551-578, 1999), which has been extended to the computation of moments. The indirect methods are applied to spatio-temporal data for different separated flows around a plate with a 16:1 chord-to-thickness ratio. Experimental data are obtained in a water channel for both a plate undergoing a large amplitude imposed pitching motion and a static plate at high angle of attack. In addition to PIV data, direct measurements of aerodynamic loads are carried out to assess the quality of the indirect calculations. It is found that indirect methods are able to compute the mean and the temporal evolution of the loads for two-dimensional flows with a reasonable accuracy. Nonetheless, both methodologies are noise sensitive, and the parameters impacting the computation should thus be chosen carefully. It is also shown that results can be improved through the use of dynamic mode decomposition (DMD) as a pre-processing step.

  12. Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

    Science.gov (United States)

    Pipkins, Daniel Scott

    Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. plate. &The bending moments in the non-linear model are compared to those

  13. 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.

  14. Resolution of Laplace equation in a region containing plane and cylindrical charged plates

    International Nuclear Information System (INIS)

    Jesus Paes, A.C. de.

    1986-05-01

    A computational program to solve the Laplace equation, in two dimensions, was developed. Cylindrical coordinates were used and the electric potential was calculated in a region bounded by an eccentric circunference that is grounded and in this region there were electrodes at known potential. The iterative method of Gauss-Seidel was used to solve the equation and the matrix of the coefficients, a sparse matrix, was stored in a compacted form in three line matrices. The distribution of this electric field were obtained from the potential and a subroutine to draw was developed. (author) [pt

  15. 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

  16. Finite element modeling of penetration of rigid cylindrical bar impacting on a clamped circular plate, employing a strain rate dependent flow rate and a Gruneisen equation of state

    International Nuclear Information System (INIS)

    Tariq, M.; Khan, I.A.

    2003-01-01

    A time dependent Finite Element simulation of penetration of a rigid cylindrical bar impacting on a copper plate is conducted, to demonstrate how material behavior appears to change when Johnson-Cook plasticity rule is employed along with a Gruneisen, equation of state with cubic shock velocity-particle relationship, and defining pressure both for compressed and expanded materials, as compared to the behavior when only isotropic strain-hardening model is employed. The bar impacts the plate with a velocity of 1000 m/s, and penetrates the plate, a portion of it coming out of the other side. Results are obtained and compared taking both an isotropic strain-hardening model, and a model incorporating Johnson-Cook flow rule along with Gruneisen equation of state. (author)

  17. Using an equation based on flow stress to estimate structural integrity of annealed Type 304 stainless steel plate and pipes containing surface defects

    International Nuclear Information System (INIS)

    Reuter, W.G.; Place, T.A.

    1981-01-01

    An accurate assessment of the influence of defects on structural component integrity is needed. Generally accepted analytical techniques are not available for the very ductile materials used in many nuclear reactor components. Some results are presented from a test programme to obtain data by which to evaluate proposed models. Plate and pipe specimens containing surface flaws were fabricated from annealed Type 304 stainless steel and tested at room temperature. An evaluation of an empirical equation based on flow stress is presented. In essentially all instances the flow stress is not a constant but varies as a function of the size of the surface flaw. (author)

  18. 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

  19. FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

    African Journals Online (AJOL)

    eobe

    plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

  20. Cold plate

    Energy Technology Data Exchange (ETDEWEB)

    Marroquin, Christopher M.; O' Connell, Kevin M.; Schultz, Mark D.; Tian, Shurong

    2018-02-13

    A cold plate, an electronic assembly including a cold plate, and a method for forming a cold plate are provided. The cold plate includes an interface plate and an opposing plate that form a plenum. The cold plate includes a plurality of active areas arranged for alignment over respective heat generating portions of an electronic assembly, and non-active areas between the active areas. A cooling fluid flows through the plenum. The plenum, at the non-active areas, has a reduced width and/or reduced height relative to the plenum at the active areas. The reduced width and/or height of the plenum, and exterior dimensions of cold plate, at the non-active areas allow the non-active areas to flex to accommodate surface variations of the electronics assembly. The reduced width and/or height non-active areas can be specifically shaped to fit between physical features of the electronics assembly.

  1. Plating laboratory

    International Nuclear Information System (INIS)

    Seamster, A.G.; Weitkamp, W.G.

    1984-01-01

    The lead plating of the prototype resonator has been conducted entirely in the plating laboratory at SUNY Stony Brook. Because of the considerable cost and inconvenience in transporting personnel and materials to and from Stony Brook, it is clearly impractical to plate all the resonators there. Furthermore, the high-beta resonator cannot be accommodated at Stony Brook without modifying the set up there. Consequently the authors are constructing a plating lab in-house

  2. 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

  3. Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

    Science.gov (United States)

    Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

    1992-01-01

    Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

  4. 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.

  5. Natural Convective Heat Transfer from Narrow Plates

    CERN Document Server

    Oosthuizen, Patrick H

    2013-01-01

    Natural Convective Heat Transfer from Narrow Plates deals with a heat transfer situation that is of significant practical importance but which is not adequately dealt with in any existing textbooks or in any widely available review papers. The aim of the book is to introduce the reader to recent studies of natural convection from narrow plates including the effects of plate edge conditions, plate inclination, thermal conditions at the plate surface and interaction of the flows over adjacent plates. Both numerical and experimental studies are discussed and correlation equations based on the results of these studies are reviewed.

  6. The baffle influence on sound radiation characteristics of a plate

    Directory of Open Access Journals (Sweden)

    Bao Liu

    2017-01-01

    Full Text Available The acoustic radiation characteristics of the baffle plates and unbaffle plates are calculated and compared by single-layer potential and double-layer potential. Based on the boundary integral equation, the sound pressure integral equation of the baffle and the baffle are deduced respectively. According to the boundary compatibility condition, the sound pressure and the vibration velocity of the plates are obtained. Further, the dynamic equation of the structure is substituted into the vibration equation in the form of the baffle plate and the baffle plate. The sound pressure difference and the displacement of a plate surface are in the form of the vibration mode superposition and the acoustic radiation impedance of the double integral form is obtained, which determines vibration mode coefficient and sound radiation parameters. The effect of the baffle on the acoustic radiation characteristics of the thin plate is analyzed by comparing the acoustic radiation parameters with the simple and simple rectangular plate in water.

  7. Modeling particulate removal in plate-plate and wire-plate electrostatic precipitators

    Directory of Open Access Journals (Sweden)

    S Ramechecandane

    2016-09-01

    Full Text Available The present study is concerned with the modeling of electrically charged particles in a model plate-plate and a single wire-plate electrostatic precipitator (ESP. The particle concentration distributions for both a plate-plate and a wire-plate ESP are calculated using a modified drift flux model. Numerical investigations are performed using the modified drift flux model for particle number concentration, in addition to the RNG k - ε model for the mean turbulent flow field and the Poisson equation for the electric field. The proposed model and the outlined methodology for coupling the flow field, electric field, charging kinetics and particle concentration is applied to two model precipitators that are truly representative of a wide class of commercialized ESPs. The present investigation is quite different from the earlier studies as it does not make assumptions like a homogeneous electric field or an infinite turbulent diffusivity. The electric field calculated is a strong function of position and controls the migration velocity of particles. Hence, the proposed model can be implemented in a flow solver to obtain a full-fledged solution for any kind of ESP with no limitations on the particle number concentration, as encountered in a Lagrangian approach. The effect of turbulent diffusivity on particle number concentration in a plate-plate ESP is investigated in detail and the results obtained are compared with available experimental data. Similarly, the effect of particle size/diameter and applied electric potential on the accumulative collection performance in the case of a wire-plate ESP is studied and the results obtained are compared with available numerical data. The numerical results obtained using the modified drift flux model for both the plate-plate and wire-plate ESP are in close agreement with available experimental and numerical data.

  8. Analysis of hydraulic instability of ANS involute fuel plates

    International Nuclear Information System (INIS)

    Sartory, W.K.

    1991-11-01

    Curved shell equations for the involute Advanced Neutron Source (ANS) fuel plates are coupled to two-dimensional hydraulic channel flow equations that include fluid friction. A complete set of fluid and plate boundary conditions is applied at the entrance and exit and along the sides of the plate and the channel. The coupled system is linearized and solved to assess the hydraulic instability of the plates

  9. Plate tectonics

    Digital Repository Service at National Institute of Oceanography (India)

    Chaubey, A.K.

    's continental drift theory was later disproved, it was one of the first times that the idea of crustal movement had been introduced to the scientific community; and it has laid the groundwork for the development of modern plate tectonics. In the early... of the structure of the atom was to physical sciences and the theory of evolution was to the life sciences. Tectonics is the study of the forces within the Earth that give rise to continents, ocean basins, mountain ranges, earthquake belts and other large-scale...

  10. Create Your Plate

    Medline Plus

    Full Text Available ... Plate Share Create Your Plate ! Share: Seven Simple Steps to Create Your Plate It's simple and effective ... foods within each food category. Try these seven steps to get started: Using your dinner plate, put ...

  11. Application of generalized function to dynamic analysis of thick plates

    International Nuclear Information System (INIS)

    Zheng, D.; Weng, Z.

    1987-01-01

    The structures with thick plates have been used extensively in national defence, mechanical engineering, chemical engineering, nuclear engineering, civil engineering, etc.. Various theories have been established to deal with the problems of elastic plates, which include the classical theory of thin plates, the improved theory of thick plates, three-dimensional elastical theory. In this paper, the derivative of δ-function is handled by using the generalized function. The dynamic analysis of thick plates subjected the concentrated load is presented. The improved Donnell's equation of thick plates is deduced and employed as the basic equation. The generalized coordinates are solved by using the method of MWR. The general expressions for the dynamic response of elastic thick plates subjected the concentrated load are given. The numerical results for rectangular plates are given herein. The results are compared with those obtained from the improved theory and the classical theory of plates. (orig./GL)

  12. Semiclassical theory of plate vibrations

    International Nuclear Information System (INIS)

    Bogomolny, E.; Hugues, E.

    1996-11-01

    The bi-harmonic equation of flexural vibrations of elastic plates is studied by a semiclassical method which can easily be generalized for other models of wave propagation. The surface and perimeter terms of the asymptotic number of levels are derived exactly. The next constant term is also derived. A semiclassical approximation of the quantization condition is obtained. A Berry-Tabor formula and a Gutzwiller trace formula are deduced for the integrable and chaotic cases respectively. From 600 eigenvalues of a clamped stadium plate obtained by a specially developed numerical algorithm, the trace formula is assessed, looking at its Fourier transform compared with the membrane case. (author)

  13. Buckling Response of Thick Functionally Graded Plates

    Directory of Open Access Journals (Sweden)

    BOUAZZA MOKHTAR

    2014-11-01

    Full Text Available In this paper, the buckling of a functionally graded plate is studied by using first order shear deformation theory (FSDT. The material properties of the plate are assumed to be graded continuously in the direction of thickness. The variation of the material properties follows a simple power-law distribution in terms of the volume fractions of constituents. The von Karman strains are used to construct the equilibrium equations of the plates subjected to two types of thermal loading, linear temperature rise and gradient through the thickness are considered. The governing equations are reduced to linear differential equation with boundary conditions yielding a simple solution procedure. In addition, the effects of temperature field, volume fraction distributions, and system geometric parameters are investigated. The results are compared with the results of the no shear deformation theory (classic plate theory, CPT.

  14. 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...

  15. Dynamic coupled piezothermoelasticity of pyroelectric composite plate

    International Nuclear Information System (INIS)

    Heidary, F.; Reza Eslami, M.

    2005-01-01

    The equations governing the linear response of coupled piezothermolelastic composite plate, considering the pyroelectric effect, are outlined in this paper. The finite element method with linear shape functions for a first-order shear deformation theory of laminated plates is used to obtain the defections and temperature. The finite element equations are developed for piezothermoelectric sensor and actuator. The governing equations are solved using the time marching method. Numerical results are presented for the conventional active direct proportional control of the plate. Controlled and uncontrolled displacements and temperature responses are graphically illustrated. the corresponding temperature response with consideration of the pyroelectric effects is also presented. Dynamic case studies are carried out to observe the pyroelectric effects in the piezothermoelastic control systems. (authors)

  16. 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.

  17. 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...... calculations match perfectly with FEM while an isotropic approach causes up to 10% deviations in deflection profile. Furthermore, we show how commonly used analytic modelling methods such as static calculations of the pull-in voltage and dynamic modelling through an equivalent circuit representation can...

  18. equilibrium approach in thederivation of differential equations

    African Journals Online (AJOL)

    user

    DEPT OF CIVIL ENGINEERING, ENUGU STATE UNIVERSITY OF SCIENCE & TECHNOLOGY ... In this paper, the differential equations of Mindlin plates are derived from basic principles by ..... Journal of Applied Mechanics, pages 31-38.

  19. Radiation shielding plate

    International Nuclear Information System (INIS)

    Kobayashi, Torakichi; Sugawara, Takeo.

    1983-01-01

    Purpose: To reduce the weight and stabilize the configuration of a radiation shielding plate which is used in close contact with an object to be irradiated with radiation rays. Constitution: The radiation shielding plate comprises a substrate made of lead glass and a metallic lead coating on the surface of the substrate by means of plating, vapor deposition or the like. Apertures for permeating radiation rays are formed to the radiation shielding plate. Since the shielding plate is based on a lead glass plate, a sufficient mechanical strength can be obtained with a thinner structure as compared with the conventional plate made of metallic lead. Accordingly, if the shielding plate is disposed on a soft object to be irradiated with radiation rays, the object and the plate itself less deform to obtain a radiation irradiation pattern with distinct edges. (Moriyama, K.)

  20. 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......, and this introduces a weight function in the variations of the transverse normal and shear stresses. As a result the coupling between the two-dimensional differential equations is described in terms of a single difference operator. Special attention is given to a truncated system of equations for bending...... of transversely isotropic plates. This theory has three boundary conditions, like Reissner's, but includes the effect of transverse normal strain, essentially through a reinterpretation of the transverse displacement function. Full agreement with general integrals to the homogeneous three-dimensional equations...

  1. 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.

  2. Vibration modes of a single plate with general boundary conditions

    Directory of Open Access Journals (Sweden)

    Phamová L.

    2016-06-01

    Full Text Available This paper deals with free flexural vibration modes and natural frequencies of a thin plate with general boundary conditions — a simply supported plate connected to its surroundings with torsional springs. Vibration modes were derived on the basis of the Rajalingham, Bhat and Xistris approach. This approach was originally used for a clamped thin plate, so its adaptation was needed. The plate vibration function was usually expressed as a single partial differential equation. This partial differential equation was transformed into two ordinary differential equations that can be solved in the simpler way. Theoretical background of the computations is briefly described. Vibration modes of the supported plate with torsional springs are presented graphically and numerically for three different values of stiffness of torsional springs.

  3. Create Your Plate

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  8. Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

    Directory of Open Access Journals (Sweden)

    Ding Zhou

    2012-01-01

    Full Text Available A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.

  9. 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...

  10. Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

    KAUST Repository

    Said-Houari, Belkacem

    2013-01-01

    In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent

  11. 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

    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 white light interferometer. Fitting...

  12. 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

  13. Theroretical modelling of the plate-tubes coupling in the hydroelasticity of the perforated plates

    International Nuclear Information System (INIS)

    Dzhupanov, V.A.; Manoach, E.S.

    1983-01-01

    In the previous investigations on the perforated plate hydroelasticity the problem of the plates-tubes-liquid interaction in the process of the general structural vibration is stated. But the interaction of the vibrating plates with the tubes, passing through them, is taken into account considering the tubes only as absolutely rigid supports. This is one of the possible technical realizations. In the present article the case when the tubes are taking part in the plate motion (vibration) is studied. Two circular perforated plates are supported by the absolutely rigid wall of the modelled roundcircular reactor barrel. The distance between the plates is given. They are connected by tubes, passing through, and clamped into the perforation holes. The plates and the tubes are made by any elastic HOOKIAN material. The volume between the two plates and outwardly to the tubes, but intrinsically of the barrel is filled by ideal, compressible and heavy liquid. Evidently the liquid volume is multiconnected one. The free vibration of the whole system is considered with the purposes: i) to give a theoretical model of the plates-tubes-liquid interaction including governing equations and boundary conditions; ii) to trace the solution of the eigen-value problem for the modelled structure; iii) to underline the engineering sides of the modelling process. (orig./GL)

  14. Vibration analysis of partially cracked plate submerged in fluid

    Science.gov (United States)

    Soni, Shashank; Jain, N. K.; Joshi, P. V.

    2018-01-01

    The present work proposes an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium. The governing equation of motion for the isotropic plate based on the classical plate theory is modified to accommodate a part through continuous line crack according to simplified line spring model. The influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations. Both partially and totally submerged plate configurations are considered. The governing equation also considers the in-plane stretching due to lateral deflection in the form of in-plane forces which introduces geometric non-linearity into the system. The fundamental frequencies are evaluated by expressing the lateral deflection in terms of modal functions. The assessment of the present results is carried out for intact submerged plate as to the best of the author's knowledge the literature lacks in analytical results for submerged cracked plates. New results for fundamental frequencies are presented as affected by crack length, fluid level, fluid density and immersed depth of plate. By employing the method of multiple scales, the frequency response and peak amplitude of the cracked structure is analyzed. The non-linear frequency response curves show the phenomenon of bending hardening or softening and the effect of fluid dynamic pressure on the response of the cracked plate.

  15. Paper microzone plates.

    Science.gov (United States)

    Carrilho, Emanuel; Phillips, Scott T; Vella, Sarah J; Martinez, Andres W; Whitesides, George M

    2009-08-01

    This paper describes 96- and 384-microzone plates fabricated in paper as alternatives to conventional multiwell plates fabricated in molded polymers. Paper-based plates are functionally related to plastic well plates, but they offer new capabilities. For example, paper-microzone plates are thin (approximately 180 microm), require small volumes of sample (5 microL per zone), and can be manufactured from inexpensive materials ($0.05 per plate). The paper-based plates are fabricated by patterning sheets of paper, using photolithography, into hydrophilic zones surrounded by hydrophobic polymeric barriers. This photolithography used an inexpensive formulation photoresist that allows rapid (approximately 15 min) prototyping of paper-based plates. These plates are compatible with conventional microplate readers for quantitative absorbance and fluorescence measurements. The limit of detection per zone loaded for fluorescence was 125 fmol for fluorescein isothiocyanate-labeled bovine serum albumin, and this level corresponds to 0.02 the quantity of analyte per well used to achieve comparable signal-to-noise in a 96-well plastic plate (using a solution of 25 nM labeled protein). The limits of detection for absorbance on paper was approximately 50 pmol per zone for both Coomassie Brilliant Blue and Amaranth dyes; these values were 0.4 that required for the plastic plate. Demonstration of quantitative colorimetric correlations using a scanner or camera to image the zones and to measure the intensity of color, makes it possible to conduct assays without a microplate reader.

  16. 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

  17. 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.

  18. Create Your Plate

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  19. Create Your Plate

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    Full Text Available ... Plate Gluten Free Diets Meal Planning for Vegetarian Diets Cook with Heart-Healthy Foods Holiday ... Carbohydrates Types of Carbohydrates Carbohydrate Counting Make Your Carbs ...

  20. The centre of mass of a triangular plate

    International Nuclear Information System (INIS)

    Sluesarenko, Viktor; Rojas, Roberto; Fuster, Gonzalo

    2008-01-01

    We present a derivation for the coordinates of the centre of mass-or centre of gravity-of a homogeneous triangular plate by using scaling and symmetry. We scale the triangular plate by a factor of 2 and divide its area into four plates identical to the original. By symmetry, we assert that the centre of mass of two identical masses lies at the midpoint of the line joining their centres of mass. By relating the centres of mass of the original to those of the scaled plates, we find the coordinates of the centre of mass as the solution of an algebraic equation

  1. 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.

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  4. Create Your Plate

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

  5. Create Your Plate

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    Full Text Available ... ready, you can try new foods within each food category. Try these seven steps to get started: Using your dinner plate, put a line down the middle of the plate. Then on one side, cut it ... and starchy foods. See this list of grains and starchy foods . ...

  6. Towards stacked zone plates

    International Nuclear Information System (INIS)

    Werner, S; Rehbein, S; Guttman, P; Heim, S; Schneider, G

    2009-01-01

    Fresnel zone plates are the key optical elements for soft and hard x-ray microscopy. For short exposure times and minimum radiation load of the specimen the diffraction efficiency of the zone plate objectives has to be maximized. As the efficiency strongly depends on the height of the diffracting zone structures the achievable aspect ratio of the nanostructures determines these limits. To reach aspect ratios ≥ 20:1 for high efficient optics we propose to superimpose zone plates on top of each other. With this multiplication approach the final aspect ratio is only limited by the number of stacked zone plate layers. For the stack process several nanostructuring process steps have to be developed and/or improved. Our results show for the first time two layers of zone plates stacked on top of each other.

  7. Bernoulli's Equation

    Indian Academy of Sciences (India)

    regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.

  8. Relativistic equations

    International Nuclear Information System (INIS)

    Gross, F.

    1986-01-01

    Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs

  9. 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

  10. High loading uranium plate

    International Nuclear Information System (INIS)

    Wiencek, T.C.; Domagala, R.F.; Thresh, H.R.

    1990-01-01

    Two embodiments of a high uranium fuel plate are disclosed which contain a meat comprising structured uranium compound confined between a pari of diffusion bonded ductile metal cladding plates uniformly covering the meat, the meat hiving a uniform high fuel loading comprising a content of uranium compound greater than about 45 Vol. % at a porosity not greater than about 10 Vol. %. In a first embodiment, the meat is a plurality of parallel wires of uranium compound. In a second embodiment, the meat is a dispersion compact containing uranium compound. The fuel plates are fabricated by a hot isostatic pressing process

  11. computational study of Couette flow between parallel plates for steady and unsteady cases

    International Nuclear Information System (INIS)

    Rihan, Y.

    2008-01-01

    Couette flow between parallel plates is a classical problem that has important applications in various industrial processing. In this investigation an analytical solution was obtained to predict the steady and unsteady Couette flow between parallel plates. One of the plates was stationary and the other plate moved with constant velocity. The governing partial differential equations were solved numerically using Crank-Nicolson implicit method to represent the flow behavior of the fluid

  12. Octanol reduces end-plate channel lifetime

    Science.gov (United States)

    Gage, Peter W.; McBurney, Robert N.; Van Helden, Dirk

    1978-01-01

    1. Post-synaptic effects of n-octanol at concentrations of 0·1-1 mM were examined in toad sartorius muscles by use of extracellular and voltage-clamp techniques. 2. Octanol depressed the amplitude and duration of miniature end-plate currents and hence depressed neuromuscular transmission. 3. The decay of miniature end-plate currents remained exponential in octanol solutions even when the time constant of decay (τD) was decreased by 80-90%. 4. The lifetime of end-plate channels, obtained by analysis of acetylcholine noise, was also decreased by octanol. The average lifetime measured from noise spectra agreed reasonably well with the time constant of decay of miniature end-plate currents, both in control solution and in octanol solutions. 5. Octanol caused a reduction in the conductance of end-plate channels. Single channel conductance was on average about 25 pS in control solution and 20 pS in octanol. 6. In most cells the normal voltage sensitivity of the decay of miniature end-plate currents was retained in octanol solutions. The lifetime of end-plate channels measured from acetylcholine noise also remained voltage-sensitive in octanol solutions. In some experiments in which channel lifetime was exceptionally reduced the voltage sensitivity was less than normal. 7. In octanol solutions, τD was still very sensitive to temperature changes in most cells although in some the temperature sensitivity of τD was clearly reduced. Changes in τD with temperature could generally be fitted by the Arrhenius equation suggesting that a single step reaction controlled the decay of currents both in control and in octanol solutions. In some cells in which τD became less than 0·3 ms, the relationship between τD and temperature became inconsistent with the Arrhenius equation. 8. As the decay of end-plate currents in octanol solutions remains exponential, and the voltage and temperature sensitivity can be unchanged even when τD is significantly reduced, it seems likely that

  13. Development of stress correction formulae for heat formed steel plates

    Directory of Open Access Journals (Sweden)

    Hyung Kyun Lim

    2018-03-01

    Full Text Available The heating process such as line heating, triangular heating and so on is widely used in plate forming of shell plates found in bow and stern area of outer shell in a ship. Local shrinkage during heating process is main physical phenomenon used in plate forming process. As it is well appreciated, the heated plate undergoes the change in material and mechanical properties around heated area due to the harsh thermal process. It is, therefore, important to investigate the changes of physical and mechanical properties due to heating process in order to use them plate the design stage of shell plates. This study is concerned with the development of formula of plastic hardening constitutive equation for steel plate on which line heating is applied. In this study the stress correction formula for the heated plate has been developed based on the numerical simulation of tension test with varying plate thickness and heating speed through the regression analysis of multiple variable case. It has been seen the developed formula shows very good agreement with results of numerical simulation. This paper ends with usefulness of the present formula in examining the structural characteristic of ship's hull. Keywords: Heat input, Heat transfer analysis, Line heating, Shell plate, Stress correction, Thermo-elasto-plastic analysis

  14. 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.

  15. Heat insulating plates

    Energy Technology Data Exchange (ETDEWEB)

    Allan, J.A.F.

    1976-10-28

    Micro-porous insulation plates are dealt with, for example, how they are used in the insulation of heat storage devices. Since one side of such plates is exposed to a temperature of over 700/sup 0/C, a shrinkage of the glass texture of the covering can occur, which can exceed the shrinkage of the inner micro-porous material, so that cracks and splits in the high temperature side of the covering can come about. The task of the invention is to design the plate in such a way as to prevent this from happening. For this purpose the plate is provided, according to invention specifications, with flutes, waves, ribs, waffle or grid patterns and the covering is set into the recesses originating from this.

  16. Create Your Plate

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  1. Create Your Plate

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  11. Humvee Armor Plate Drilling

    National Research Council Canada - National Science Library

    2004-01-01

    When drilling holes in hard steel plate used in up-armor kits for Humvee light trucks, the Anniston Army Depot, Anniston, Alabama, requested the assistance of the National Center for Defense Manufacturing and Machining (NCDMM...

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  15. BAO Plate Archive Project

    Science.gov (United States)

    Mickaelian, A. M.; Gigoyan, K. S.; Gyulzadyan, M. V.; Paronyan, G. M.; Abrahamyan, H. V.; Andreasyan, H. R.; Azatyan, N. M.; Kostandyan, G. R.; Samsonyan, A. L.; Mikayelyan, G. A.; Farmanyan, S. V.; Harutyunyan, V. L.

    2017-12-01

    We present the Byurakan Astrophysical Observatory (BAO) Plate Archive Project that is aimed at digitization, extraction and analysis of archival data and building an electronic database and interactive sky map. BAO Plate Archive consists of 37,500 photographic plates and films, obtained with 2.6m telescope, 1m and 0.5m Schmidt telescopes and other smaller ones during 1947-1991. The famous Markarian Survey (or the First Byurakan Survey, FBS) 2000 plates were digitized in 2002-2005 and the Digitized FBS (DFBS, www.aras.am/Dfbs/dfbs.html) was created. New science projects have been conducted based on this low-dispersion spectroscopic material. Several other smaller digitization projects have been carried out as well, such as part of Second Byurakan Survey (SBS) plates, photographic chain plates in Coma, where the blazar ON 231 is located and 2.6m film spectra of FBS Blue Stellar Objects. However, most of the plates and films are not digitized. In 2015, we have started a project on the whole BAO Plate Archive digitization, creation of electronic database and its scientific usage. Armenian Virtual Observatory (ArVO, www.aras.am/Arvo/arvo.htm) database will accommodate all new data. The project runs in collaboration with the Armenian Institute of Informatics and Automation Problems (IIAP) and will continues during 4 years in 2015-2018. The final result will be an Electronic Database and online Interactive Sky map to be used for further research projects. ArVO will provide all standards and tools for efficient usage of the scientific output and its integration in international databases.

  16. Neutron imaging plates

    International Nuclear Information System (INIS)

    Niimura, Nobuo

    1995-01-01

    Imaging plates have been used in the field of medical diagnosis since long ago, but their usefulness was verified as the two-dimensional detector for analyzing the X-ray crystalline structure of high bio molecules like protein, and they have contributed to the remarkable progress in this field. The great contribution is due to the excellent features, such as the detection efficiency of about 100%, the positional resolution smaller than 0.2 mm, the dynamic range of five digits, and the area of several hundreds mm square. The neutron imaging plates have not yet obtained the sufficient results. It was planned to construct the neutron diffractometer for biological matters, and to put imaging plate neutron detectors (IP-ND) to practical use as the detector. The research on the development of IP-NDs was carried out, and the IPp-NDs having the performance comparable with that for X-ray were able to be produced. Imaging plates are the integral type two-dimensional radiation detector using photostimulated luminescence matters, and their principle is explained. As to neutron imaging plates, the converter, neutron detection efficiency and the flight of secondary particles in photo-stimulated luminescence matters are described. As for the present state of development of neutron imaging plates, the IP-NDs made for trial, the dynamic range, the positional resolution, the detection efficiency and the kinds of converters, and the application of IP-NDs are reported. (K.I.)

  17. Modelling conjugation with stochastic differential equations

    DEFF Research Database (Denmark)

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

    2010-01-01

    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......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...

  18. Study of the electric field inside microchannel plate multipliers

    International Nuclear Information System (INIS)

    Gatti, E.; Oba, K.; Rehak, P.

    1982-01-01

    Electric field inside high gain microchannel plate multipliers was studied. The calculations were based directly on the solution of the Maxwell equations applied to the microchannel plate (MCP) rather than on the conventional lumped RC model. The results are important to explain the performance of MCP's, (1) under a pulsed bias tension and, (2) at high rate conditions. The results were tested experimentally and a new method of MCP operation free from the positive ion feedback was demonstrated

  19. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  20. Polar plate theory for orthogonal anisotropy

    Science.gov (United States)

    Bailey, Michelle D.

    1998-11-01

    The following paper discusses the derivation and evaluation of the plate equations for a circular composite disk with orthogonal anisotropy. The work will be on a macromechanical level and include buckling, static and dynamic load applications. Necessary to a complete examination of the circular disk is the conversion of the stiffness matrix to cylindrical coordinates. In the transformed state, these coefficients are no longer constant, adding to the complexity of the proposed differential equations. Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to weight and stiffness-to-weight ratios. However, because of the typical anisotropic behavior of composites, determining the material properties on a microscopic level and the mechanics on a macroscopic level is much more difficult. This difficulty manifests itself particularly well in the evaluation of material properties and governing differential equations of a circular disk with the fibers of the lamina oriented orthogonally. One could encounter such a situation in space structures that require a circular geometry. For example, determining fastener pull through in a circular composite plate would best be performed in a polar coordinate system. In order to calculate the strain (which is a function of the angle, θ) from the displacements, the stiffness matrix and boundary conditions would need to be expressed in cylindrical coordinates. Naturally the composite would be constructed with fibers in orthogonal directions, then the necessary geometry would be cut out, thus the required lengthy transformation of coordinate systems. To bypass this derivation, numerical methods have been used and finite element models have been attempted. FEM over predicts plate stiffness by 20% and underpredicts failure by 70%. Obviously there is a need to transform classical plate theory to a cylindrical coordinate system.

  1. Cadmium plating replacements

    Energy Technology Data Exchange (ETDEWEB)

    Nelson, M.J.; Groshart, E.C.

    1995-03-01

    The Boeing Company has been searching for replacements to cadmium plate. Two alloy plating systems seem close to meeting the needs of a cadmium replacement. The two alloys, zinc-nickel and tin-zinc are from alloy plating baths; both baths are neutral pH. The alloys meet the requirements for salt fog corrosion resistance, and both alloys excel as a paint base. Currently, tests are being performed on standard fasteners to compare zinc-nickel and tin-zinc on threaded hardware where cadmium is heavily used. The Hydrogen embrittlement propensity of the zinc-nickel bath has been tested, and just beginning for the tin-zinc bath. Another area of interest is the electrical properties on aluminum for tin-zinc and will be discussed. The zinc-nickel alloy plating bath is in production in Boeing Commercial Airplane Group for non-critical low strength steels. The outlook is promising that these two coatings will help The Boeing Company significantly reduce its dependence on cadmium plating.

  2. Plating on Zircaloy-2

    International Nuclear Information System (INIS)

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

    1979-03-01

    Zircaloy-2 is a difficult alloy to coat with an adherent electroplate because it easily forms a tenacious oxide film in air and aqueous solutions. Procedures reported in the literature and those developed at SLL for surmounting this problem were investigated. The best results were obtained when specimens were first etched in either an ammonium bifluoride/sulfuric acid or an ammonium bifluoride solution, plated, and then heated at 700 0 C for 1 hour in a constrained condition. Machining threads in the Zircaloy-2 for the purpose of providing sites for mechanical interlocking of the plating also proved satisfactory

  3. NICKEL PLATING PROCESS

    Science.gov (United States)

    Hoover, T.B.; Zava, T.E.

    1959-05-12

    A simplified process is presented for plating nickel by the vapor decomposition of nickel carbonyl. In a preferred form of the invention a solid surface is nickel plated by subjecting the surface to contact with a mixture containing by volume approximately 20% nickel carbonyl vapor, 2% hydrogen sulfide and .l% water vapor or 1% oxygen and the remainder carbon dioxide at room temperature until the desired thickness of nickel is obtained. The advantage of this composition over others is that the normally explosive nickel carbonyl is greatly stabilized.

  4. Hydrodynamics of a flexible plate between pitching rigid plates

    Science.gov (United States)

    Kim, Junyoung; Kim, Daegyoum

    2017-11-01

    The dynamics of a flexible plate have been studied as a model problem in swimming and flying of animals and fluid-structure interaction of plants and flags. Motivated by fish schooling and an array of sea grasses, we investigate the dynamics of a flexible plate closely placed between two pitching rigid plates. In most studies on passive deformation of the flexible plate, the plate is immersed in a uniform flow or a wavy flow. However, in this study, the flexible plate experiences periodic deformation by the oscillatory flow generated by the prescribed pitching motion of the rigid plates. In our model, the pitching axes of the rigid plates and the clamping position of the flexible plate are aligned on the same line. The flexible plate shows various responses depending on length and pitching frequency of rigid plates, thickness of a flexible plate, and free-stream velocity. To find the effect of each variable on the response of the flexible plate, amplitude of a trailing edge and modal contribution of a flapping motion are compared, and flow structure around the flexible plate is examined.

  5. Analytical results for post-buckling behaviour of plates in compression and in shear

    Science.gov (United States)

    Stein, M.

    1985-01-01

    The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

  6. Create Your Plate

    Medline Plus

    Full Text Available ... meal-planning, . In this section Food Planning Meals Diabetes Meal Plans and a Healthy Diet Create Your Plate Meal Planning for Vegetarian Diets Gluten Free Diets Holiday Meal Planning Cook with Heart-Healthy Foods donate en -- A Future Without Diabetes - a-future-without-diabetes-2.html A Future ...

  7. Create Your Plate

    Medline Plus

    Full Text Available ... tool is not to scale because of the differences in types of vegetables. When creating your plate ... function (data) { $('#survey-errors').remove(); $('.survey-form .form-group .survey-alert-wrap').remove(); if (data.submitSurveyResponse.success == ' ...

  8. Create Your Plate

    Medline Plus

    Full Text Available ... Your Plate Meal Planning for Vegetarian Diets Gluten Free Diets Holiday Meal Planning Cook with Heart-Healthy Foods donate en -- A Future Without Diabetes - a-future-without-diabetes-2.html A Future Without Diabetes Donate towards research today and your gift will be matched. Donate ...

  9. 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 ... Type 2 Education Series Hear audio clips and full recordings of past Q&A events at your ...

  10. 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 ...

  11. 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 ... effective way to manage your blood glucose levels and lose weight. With this method, you fill your plate with more non-starchy ...

  12. Microchannel plate photodetectors

    International Nuclear Information System (INIS)

    Majka, R.

    1977-01-01

    A review is given the status of development work on photodetectors using microchannel plates (MCP) as the electron gain element. Projections are made and opinions are presented on what might be available in the next few years. Several uses for these devices at ISABELLE are mentioned

  13. Parallel plate detectors

    International Nuclear Information System (INIS)

    Gardes, D.; Volkov, P.

    1981-01-01

    A 5x3cm 2 (timing only) and a 15x5cm 2 (timing and position) parallel plate avalanche counters (PPAC) are considered. The theory of operation and timing resolution is given. The measurement set-up and the curves of experimental results illustrate the possibilities of the two counters [fr

  14. Flat plate collector. Solarflachkollektor

    Energy Technology Data Exchange (ETDEWEB)

    Raab, N

    1979-03-29

    The invention refers to a flat solar collector with an absorber plate, which is arranged on a support and is covered by a transparent window, between which and the plate there is an air space. The previously known structures of this type had the disadvantage that the thermal expansion of the enclosed air caused considerable difficulties. The purpose of the invention is therefore to create a collector, which can be used on the modular system, retains its properties and is safe in spite of the great temperature variations. According to the invention this problem is solved by providing a compensating space in the collector, which is separated by a diaphragm from the airspace between the plate and the covering window. The airspace therefore remains sealed against the atmosphere, so that no dirt, corrosion of the inside and no condensation can reduce the efficiency of the collector. A rise in pressure due to an increase in temperature is immediately reduced by expansion of the diaphragm, which enters the compensation space. In order to increase the pressure in the airspace above the plate for increases in temperature, the compensation space is connected to the atmosphere. The diaphragm can be mirrored on the side towards the absorber, which makes the diaphragm into an insulating element, as it reflects radiated heat from the absorber.

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

    International Nuclear Information System (INIS)

    Rao, T V

    2005-01-01

    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 O(τ -(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 O(τ -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 O(τ -9 ) approximation predicts the capacity extremely well for any τ ≥ 2 and an O(τ -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 O(τ -6 ) for τ ≥ 2

  16. Global collapse and J integral analysis for inner-diameter defected curved plates in tension

    International Nuclear Information System (INIS)

    Hertelé, Stijn; Verstraete, Matthias; Denys, Rudi; De Waele, Wim

    2013-01-01

    Reference stress equations are widely used to predict both the limit load and the J integral response of defected structures. Their validity is key to performing a safe assessment of structural integrity (plastic collapse and fracture). An analytical reference stress equation based upon global collapse has recently been developed for curved plates with a part-through defect located at the inner diameter surface. This equation predicts decreasing reference stress values as plate curvature increases. To qualify the predictions, the authors have performed a series of finite element analyses covering a wide range of possible geometries. This paper compares the numerically obtained limit loads and J integral responses with the analytical predictions of the reference stress equation. The finite element results generally confirm the decrease of reference stress with increasing plate curvature. Highly pronounced differences may occur between flat plates and slightly curved plates. Overall, the analytically predicted decrease in reference stress is overestimated for small defects but is representative for larger defects. -- Highlights: • A reference stress equation for inner-diameter defected curved plates in tension was developed earlier. • The equation predicts a lower reference stress as plate curvature increases. • The analytical predictions are validated through finite element analysis. • Collapse and J integral are insensitive to curvature for small defects. • For large defects, the analytically predicted trend is confirmed

  17. an elasticity solution for simply suported rectangular plates

    African Journals Online (AJOL)

    MIS

    1983-09-01

    Sep 1, 1983 ... σx, σy, σz. = direct stresses ξxy, ξxz, ξyz. = shear stresses εy, εy, εz. = direct strains rxy, rxz ryz. = shear strains μ. = Poisson's ratio α = rm /Pb. = nπ/2b. R = 2 ... based on Donnell's5 thick plate theory are examined. 2. BASIC EQUATIONS. The general solution of the equations of elasticity can be expressed in.

  18. 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.

  19. Instability of a cantilevered flexible plate in viscous channel flow

    Science.gov (United States)

    Balint, T. S.; Lucey, A. D.

    2005-10-01

    The stability of a flexible cantilevered plate in viscous channel flow is studied as a representation of the dynamics of the human upper airway. The focus is on instability mechanisms of the soft palate (flexible plate) that cause airway blockage during sleep. We solve the Navier Stokes equations for flow with Reynolds numbers up to 1500 fully coupled with the dynamics of the plate motion solved using finite-differences. The study is 2-D and based upon linearized plate mechanics. When both upper and lower airways are open, the plate is found to lose its stability through a flutter mechanism and a critical Reynolds number exists. When one airway is closed, the plate principally loses its stability through a divergence mechanism and a critical flow speed exists. However, below the divergence-onset flow speed, flutter can exist for low levels of structural damping in the flexible plate. Our results serve to extend understanding of flow-induced instability of cantilevered flexible plates and will ultimately improve the diagnosis and treatment of upper-airway disorders.

  20. 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.

  1. Sound insulation performance of plates with interconnected distributed piezoelectric patches

    Directory of Open Access Journals (Sweden)

    Yi Kaijun

    2017-02-01

    Full Text Available This paper deals with the sound insulation performance of a thin plate with interconnected distributed piezoelectric patches. Piezoelectric patches are periodically bonded on the surfaces of the plate in a collocated fashion, and are interconnected via an inductive circuit network. This piezoelectric system is termed as piezo-electromechanical (PEM plate in the paper. Homogenization methods are involved under a sub-wavelength assumption to analytically develop the dynamical equations for the PEM plate. The dispersion relationships and energy densities of the wave modes propagating in the PEM plate are studied; the sub-wavelength assumption is verified for the simulations in this paper. The coincidence frequency of the PEM plate is researched, and results show that the coincidence frequency of the PEM plate will disappear at certain circumstances; mathematical and physical explanations are made for this phenomenon. The disappearance of the coincidence frequency is used to optimize the value of inductance, for the purpose of improving the sound transmission loss of the PEM plate.

  2. Extended rate equations

    International Nuclear Information System (INIS)

    Shore, B.W.

    1981-01-01

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

  3. Equilibrium approach in the derivation of differential equations for ...

    African Journals Online (AJOL)

    In this paper, the differential equations of Mindlin plates are derived from basic principles by simultaneous satisfaction of the differential equations of equilibrium, the stress-strain laws and the strain-displacement relations for isotropic, homogenous linear elastic materials. Equilibrium method was adopted in the derivation.

  4. 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.

  5. Plate Full of Color

    Centers for Disease Control (CDC) Podcasts

    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.

  6. Nonlinear analysis of piezoelectric nanocomposite energy harvesting plates

    International Nuclear Information System (INIS)

    Rafiee, M; He, X Q; Liew, K M

    2014-01-01

    This paper investigates the nonlinear analysis of energy harvesting from piezoelectric functionally graded carbon nanotube reinforced composite plates under combined thermal and mechanical loadings. The excitation, which derives from harmonically varying mechanical in-plane loading, results in parametric excitation. The governing equations of the piezoelectric functionally graded carbon nanotube reinforced composite plates are derived based on classical plate theory and von Kármán geometric nonlinearity. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned, straight and have a uniform layout. The linear buckling and vibration behavior of the nanocomposite plates is obtained in the first step. Then, Galerkin’s method is employed to derive the nonlinear governing equations of the problem with cubic nonlinearities associated with mid-plane stretching. Periodic solutions are determined by using the Poincaré–Lindstedt perturbation scheme with movable simply supported boundary conditions. The effects of temperature change, the volume fraction and the distribution pattern of the SWCNTs on the parametric resonance, in particular the amplitude of vibration and the average harvested power of the smart functionally graded carbon nanotube reinforced composite plates, are investigated through a detailed parametric study. (paper)

  7. Bifurcation of cubic nonlinear parallel plate-type structure in axial flow

    International Nuclear Information System (INIS)

    Lu Li; Yang Yiren

    2005-01-01

    The Hopf bifurcation of plate-type beams with cubic nonlinear stiffness in axial flow was studied. By assuming that all the plates have the same deflections at any instant, the nonlinear model of plate-type beam in axial flow was established. The partial differential equation was turned into an ordinary differential equation by using Galerkin method. A new algebraic criterion of Hopf bifurcation was utilized to in our analysis. The results show that there's no Hopf bifurcation for simply supported plate-type beams while the cantilevered plate-type beams has. At last, the analytic expression of critical flow velocity of cantilevered plate-type beams in axial flow and the purely imaginary eigenvalues of the corresponding linear system were gotten. (authors)

  8. Effect of plate shapes in orifice plate type flowmeters

    International Nuclear Information System (INIS)

    Moeller, S.V.

    1984-01-01

    The study of unusual plate shapes in orifice plate type flowmeters is presented, with a view to providing data for the substitution of the plate with one centered circular orifice in those applications where its use is not possible. For this purpose, six pairs of plates with different forms, with and without chamfered edges, were made and tested in a closed water loop. Results show that, generally, the use of chamfers improves the results and, in the case of perforated and slotlike orificed plates, the narrow-ness of the fluid passage tends to make unnecessary its use. (Author) [pt

  9. 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. Copyright © 2015 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

  10. 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...... as for the out-of-plane reaction force....

  11. Normal and abnormal growth plate

    International Nuclear Information System (INIS)

    Kumar, R.; Madewell, J.E.; Swischuk, L.E.

    1987-01-01

    Skeletal growth is a dynamic process. A knowledge of the structure and function of the normal growth plate is essential in order to understand the pathophysiology of abnormal skeletal growth in various diseases. In this well-illustrated article, the authors provide a radiographic classification of abnormal growth plates and discuss mechanisms that lead to growth plate abnormalities

  12. thermoelastic waves without energy dissipation in an elastic plate ...

    African Journals Online (AJOL)

    cistvr

    The first generalization, for isotropic bodies, is due to Lord & Shulman (1967) who obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier's law. ...... In this paper we have studied the thermoelastic interactions due to the punching of a cylindrical hole in an elastic plate ...

  13. An Irrotational Flow Field That Approximates Flat Plate Boundary Conditions

    OpenAIRE

    Ruffa, Anthony A.

    2004-01-01

    An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow, with severe numerical difficulties in some regions.

  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. 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...

  16. Pyrolysis and Boundary Layer Combustion of a Non-Charring Solid Plate Under Forced Flow

    National Research Council Canada - National Science Library

    Ananth, Ramagopal

    2003-01-01

    Solutions of Navier-Stokes (NS) equations were obtained for burning rate Nu and temperature distributions for a flat PMMA plate using an iterative method to impose steady-state, pyrolysis kinetics at the surface...

  17. 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...

  18. 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

  19. Study of uranium plating measurement

    International Nuclear Information System (INIS)

    Lin Jufang; Wen Zhongwei; Wang Mei; Wang Dalun; Liu Rong; Jiang Li; Lu Xinxin

    2007-06-01

    In neutron physics experiments, the measurement for plate-thickness of uranium can directly affect uncertainties of experiment results. To measure the plate-thickness of transform target (enriched uranium plating and depleted uranium plating), the back to back ionization chamber, small solid angle device and Au-Si surface barrier semi-conductor, were used in the experiment study. Also, the uncertainties in the experiment were analyzed. Because the inhomo-geneous of uranium lay of plate can quantitively affect the result, the homogeneity of uranium lay is checked, the experiment result reflects the homogeneity of uranium lay is good. (authors)

  20. Fuel cell end plate structure

    Science.gov (United States)

    Guthrie, Robin J.; Katz, Murray; Schroll, Craig R.

    1991-04-23

    The end plates (16) of a fuel cell stack (12) are formed of a thin membrane. Pressure plates (20) exert compressive load through insulation layers (22, 26) to the membrane. Electrical contact between the end plates (16) and electrodes (50, 58) is maintained without deleterious making and breaking of electrical contacts during thermal transients. The thin end plate (16) under compressive load will not distort with a temperature difference across its thickness. Pressure plate (20) experiences a low thermal transient because it is insulated from the cell. The impact on the end plate of any slight deflection created in the pressure plate by temperature difference is minimized by the resilient pressure pad, in the form of insulation, therebetween.

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

    International Nuclear Information System (INIS)

    Anjomshoa, Amin; Tahani, Masoud

    2016-01-01

    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.

  2. [Conventional plate osteosynthesis].

    Science.gov (United States)

    Klaue, K

    2010-02-01

    Consolidation of bone is an essential clinical problem when treating fractures, fixing osteotomies and fusing joints. In most cases, the means of fixation are plates and screws. The goal is functional postoperative therapy by moving the adjacent joints and thus avoiding the deleterious disadvantages of long-lasting articular immobilization. Pre-operative planning, surgical approach, a good understanding of the precise mechanics of the structure and the biological answer for the various tissues are prerequisites of successful osteosynthesis. The choice of implants and the application of their versatility, as well as their adaptation to individual cases are the key to good results.

  3. 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.

  4. 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.

  5. Equating error in observed-score equating

    NARCIS (Netherlands)

    van der Linden, Willem J.

    2006-01-01

    Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

  6. Multipactor saturation in parallel-plate waveguides

    International Nuclear Information System (INIS)

    Sorolla, E.; Mattes, M.

    2012-01-01

    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.

  7. Rate effects in resistive plate chambers

    International Nuclear Information System (INIS)

    Lippmann, C.; Riegler, W.; Kalweit, A.

    2006-01-01

    The resistive plates in RPCs cause a drop of the electric field in the gas gap at high particle rates or large gas gain, which affects efficiency and time resolution. This effect is typically estimated by assuming the particle flux to be a DC current that causes a voltage drop when it passes through the resistive plate. In an improved model by Abbrescia (Nucl. Instr. Meth. A 533 (2004) 7), the fluctuation of the field in the gas gap is modelled by assuming that the avalanche partially discharges a small capacitor which gets recharged with a time constant characteristic for the given RPC. In our approach, the effect is calculated by using the exact analytic solution for the time dependent electric field of a point charge sitting on the surface of a resistive plate in an RPC. This is, by definition, the best possible approximation to reality. The solution is obtained using the quasi-static approximation of Maxwell's equations. The formulas are presented as integral representations with 'cured' integrands, which allow easy numerical evaluation for Monte Carlo simulations. The solutions show that the charges in RPCs are 'destroyed' with a continuous distribution of time constants which are related in a very intuitive way to some limiting cases. Using these formulas we present a Monte Carlo simulation of rate effects, proving the applicability of this approach. Finally, we compare the Monte Carlo results to analytical calculations, similar to the ones proposed by Gonzalez-Diaz et al. (see proceedings of this conference)

  8. The Interaction between the Plane Wave and the Plate with Limited Height in Soil

    Directory of Open Access Journals (Sweden)

    N.A. Lokteva

    2017-03-01

    Full Text Available A solution of the two-dimensional task on interaction between the harmonic wave and the plate with the limited height in soil has been provided. The plate surrounded on both sides with the half-spaces filled with soil medium has been used as a vibro-absorbing obstacle. The mechanical behavior of the plate has been described by S.P. Timoshenko's shift model and the mechanical behavior of soil by a linear elasticity theory equation. The main purpose of the paper is to determine the total acceleration vector field inducted by the penetrated and radiated waves in the second half-space. The mathematical formulation of the task includes a model of upcoming wave, soil medium and plate movement equation, infinity conditions, and conditions of soil contact with obstacle. Conditions of free slip have been taken as the contact conditions between the soil and the obstacle. We have considered a closed system of equations, which includes wave equations for scalar and vector potentials, elasticity theory equations for soil mediums, Koshi's relations, physical law, and plate movement equation. The boundary conditions for the plate correspond to a hinged support. To solve this task, all functions have been expanded in trigonometric series that allowed to obtain potential values in the coefficients of the series. To define the integrations constants, the contact conditions between the obstacle and soil have been used. On the basis of the revealed potentials, we have defined displacements on the boundary between the plate and soil and in other points of the second half-space. The vibro-absorbing properties of the plate have been investigated depending on the frequency of the harmonic wave falling on the plate. From the practical point of view, this task is related to protection of buildings from vibrations formed at a distance from underground railways.

  9. Plating on difficult-to-plate metals: what's new

    International Nuclear Information System (INIS)

    Wiesner, H.J.

    1980-01-01

    Some of the changes since 1970 in procedures for plating on such materials as titanium, molybdenum, silicon, aluminum, and gallium arsenide are summarized. While basic procedures for plating some of these materials were developed as many as 30 to 40 years ago, changes in the end uses of the plated products have necessitated new plating processes. In some cases, vacuum techniques - such as ion bombardment, ion implantation, and vacuum metallization - have been introduced to improve the adhesion of electrodeposits. In other cases, these techniques have been used to deposit materials upon which electrodeposits are required

  10. Model to Analyze Micro Circular Plate Subjected to Electrostatic Force

    Directory of Open Access Journals (Sweden)

    Cao Tian-Jie

    2013-06-01

    Full Text Available In this paper a distributed model with three possible static modes was presented to investigate the behavior of the plate subjected to electrostatic force and uniform hydrostatic pressure both before pull in and beyond pull in. The differential governing equation of the micro circular plate specifically used for numerical solution of the three modes, in which the singularity at the center of the micro plate did not occur, was presented based on the classical thin plate theory, Taylor's series expansion and Saint-Venant's principle. The numerical solution to the differential governing equation for the different mode was mainly attributed to solve for one unknown boundary condition and the applied voltage, which could be obtained by using a two-fold method of bisection based on the shooting method. The voltage ranges over which the three modes could exist and the points where transitions occurred between the modes were computed. Incorporating the above numerical solution to the applied voltage at the normal mode with some constrained optimization method, pull-in voltage and the corresponding pull-in position can automatically be obtained. In examples, the entire mechanical behavior of the circular plate over the operational voltage ranges was investigated and the effects of different parameters on pull-in voltage were studied. The obtained results were compared with the existing results and good agreement has been achieved.

  11. Magneto-elastic dynamics and bifurcation of rotating annular plate*

    International Nuclear Information System (INIS)

    Hu Yu-Da; Piao Jiang-Min; Li Wen-Qiang

    2017-01-01

    In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton’s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos. (paper)

  12. Static Analysis of Laminated Composite Plate using New Higher Order Shear Deformation Plate Theory

    Directory of Open Access Journals (Sweden)

    Ibtehal Abbas Sadiq

    2017-02-01

    Full Text Available In the present work a theoretical analysis depending on the new higher order . element in shear deformation theory for simply supported cross-ply laminated plate is developed. The new displacement field of the middle surface expanded as a combination of exponential and trigonometric function of thickness coordinate with the transverse displacement taken to be constant through the thickness. The governing equations are derived using Hamilton’s principle and solved using Navier solution method to obtain the deflection and stresses under uniform sinusoidal load. The effect of many design parameters such as number of laminates, aspect ratio and thickness ratio on static behavior of the laminated composite plate has been studied. The modal of the present work has been verified by comparing the results of shape functions with that were obtained by other workers. Result shows the good agreement with 3D elasticity solution and that published by other researchers.

  13. 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...... as for the out-of-plane reaction force. (C) 1998 Elsevier Science Ltd. All rights reserved....

  14. Bipolar Plates for PEM Systems

    OpenAIRE

    Lædre, Sigrid

    2016-01-01

    Summary of thesis: The Bipolar Plate (BPP) is an important component in both Proton Exchange Membrane Fuel Cells (PEMFCs) and Proton Exchange Membrane Water Electrolyzers (PEMWEs). Bipolar plate material and processing constitutes for a large fraction of the cost and weight of a PEM cell stack. The main tasks for the bipolar plates in both systems are to separate single cell in a stack, conduct current between single cells and remove heat from active areas. In addition, the BPPs distribu...

  15. Scintillator plate calorimetry

    International Nuclear Information System (INIS)

    Price, L.E.

    1990-01-01

    Calorimetry using scintillator plates or tiles alternated with sheets of (usually heavy) passive absorber has been proven over multiple generations of collider detectors. Recent detectors including UA1, CDF, and ZEUS have shown good results from such calorimeters. The advantages offered by scintillator calorimetry for the SSC environment, in particular, are speed (<10 nsec), excellent energy resolution, low noise, and ease of achieving compensation and hence linearity. On the negative side of the ledger can be placed the historical sensitivity of plastic scintillators to radiation damage, the possibility of nonuniform response because of light attenuation, and the presence of cracks for light collection via wavelength shifting plastic (traditionally in sheet form). This approach to calorimetry is being investigated for SSC use by a collaboration of Ames Laboratory/Iowa State University, Argonne National Laboratory, Bicron Corporation, Florida State University, Louisiana State University, University of Mississippi, Oak Ridge National Laboratory, Virginia Polytechnic Institute and State University, Westinghouse Electric Corporation, and University of Wisconsin

  16. Reviewing metallic PEMFC bipolar plates

    Energy Technology Data Exchange (ETDEWEB)

    Wang, H.; Turner, J.A. [National Renewable Energy Laboratory, Golden, CO (United States)

    2010-08-15

    A bipolar plate is one of the most important components in a polymer exchange membrane fuel cell (PEMFC) stack and has multiple functions. Metallic bipolar plate candidates have advantages over composite rivals in excellent electrical and thermal conductivity, good mechanical strength, high chemical stability, very wide alloy choices, low cost and, most importantly, existing pathways for high-volume, high-speed mass production. The challenges with metallic bipolar plates are the higher contact resistance and possible corrosion products, which may contaminate the membrane electrode assembly. This review evaluates the candidate metallic and coating materials for bipolar plates and gives the perspective of the research trends. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

  17. Experimental and numerical study of the wave run-up along a vertical plate

    DEFF Research Database (Denmark)

    Molin, Bernard; Kimmoun, O.; Liu, Y.

    2010-01-01

    Results from experiments on wave interaction with a rigid vertical plate are reported. The 5m long plate is set against the wall of a 30m wide basin, at 100m from the wavemaker. This set-up is equivalent to a 10m plate in the middle of a 60m wide basin. Regular waves are produced, with wavelength...... on extended Boussinesq equations. In most of the experimental tests, despite the large distance from the wavemaker to the plate and the small amplitude of the incident wave, no steady state is attained by the end of the exploitable part of the records....

  18. Natural Frequency of F.G. Rectangular Plate by Shear Deformation Theory

    International Nuclear Information System (INIS)

    Shahrjerdi, Ali; Sapuan, S M; Shahzamanian, M M; Mustapha, F; Zahari, R; Bayat, M

    2011-01-01

    Natural frequency of functionally graded (F.G.) rectangular plate is carried out by using second-order shear deformation theory (SSDT). The material properties of functionally graded rectangular plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution. The equations of motion are obtained by energy method. Numerical results for functionally graded plates are given in dimensionless graphical forms and the effects of material properties on natural frequency are determined.

  19. Axisymmetric buckling analysis of laterally restrained thick annular plates using a hybrid numerical method

    Energy Technology Data Exchange (ETDEWEB)

    Malekzadeh, P. [Department of Mechanical Engineering, Persian Gulf University, Bushehr 75168 (Iran, Islamic Republic of); Center of Excellence for Computational Mechanics, Shiraz University, Shiraz (Iran, Islamic Republic of)], E-mail: malekzadeh@pgu.ac.ir; Ouji, A. [Department of Civil Engineering, Persian Gulf University, Bushehr 75168 (Iran, Islamic Republic of); Islamic Azad University, Larestan Branch, Larestan (Iran, Islamic Republic of)

    2008-11-15

    The buckling analysis of annular thick plates with lateral supports such as two-parameter elastic foundations or ring supports is investigated using an elasticity based hybrid numerical method. For this purpose, firstly, the displacement components are perturbed around the pre-buckling state, which is located using the elasticity theory. Then, by decomposing the plate into a set of sub-domain in the form of co-axial annular plates, the buckling equations are discretized through the radial direction using global interpolation functions in conjunction with the principle of virtual work. The resulting differential equations are solved using the differential quadrature method. The method has the capability of modeling the arbitrary boundary conditions either at the inner and outer edges of thin-to-thick plates and with different types of lateral restraints. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its accuracy and versatility for thin-to-thick plates.

  20. The solution of certain loss of contact between a plate and unilateral supports

    Directory of Open Access Journals (Sweden)

    Sompornjaroensuk Yos

    2007-01-01

    Full Text Available This paper examines the loss of contact between a square plate and the unilateral supports under uniformly distributed load. Since the plate is rested on the unilateral supports, it will have the regions of lost contact between a plate and the supports due to the absence of restraining corner force at the plate corners. This leads to the mixed boundary conditions and these conditions are then written in the form of dual-series equations which can further be reduced to a Fredholm integral equation by taking advantage of finite Hankel transform technique. Numerical results are given for the deflections of free edge and deflections along the middle line of the plate with deferent values of the Poisson’s ratio. In addition, the deflection surface is also presented. From the investigation, it can be indicated that the loss of contact is decreased upon the increasing Poisson’s ratio.

  1. Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory

    Directory of Open Access Journals (Sweden)

    Alireza Shooshtari

    Full Text Available Abstract Free vibration of a magnetoelectroelastic rectangular plate is investigated based on the Reddy's third-order shear deformation theory. The plate rests on an elastic foundation and it is considered to have different boundary conditions. Gauss's laws for electrostatics and magnetostatics are used to model the electric and magnetic behavior. The partial differential equations of motion are reduced to a single partial differential equation and then by using the Galerkin method, the ordinary differential equation of motion as well as an analytical relation for the natural frequency of the plate is obtained. Some numerical examples are presented to validate the proposed model and to investigate the effects of several parameters on the vibration frequency of the considered smart plate.

  2. Chemical Equation Balancing.

    Science.gov (United States)

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  3. Stress-intensity factor equations for cracks in three-dimensional finite bodies

    Science.gov (United States)

    Newman, J. C., Jr.; Raju, I. S.

    1981-01-01

    Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

  4. Handbook of integral equations

    CERN Document Server

    Polyanin, Andrei D

    2008-01-01

    This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

  5. 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.

  6. Laterally Loaded Nail-Plates

    DEFF Research Database (Denmark)

    Nielsen, Jacob; Rathkjen, Arne

    Load-displacement curves from about 200 short-term and laterally loaded nail-plate joints are analysed. The nail-plates are from Gang-Nail Systems, type GNA 20 S. The test specimens and the measuring systems are described. The tests are divided into 32 different series. The influence of the number...

  7. MyPlate Food Guide

    Science.gov (United States)

    ... Safe Videos for Educators Search English Español MyPlate Food Guide KidsHealth / For Teens / MyPlate Food Guide What's ... and other sugary drinks. Avoid large portions . Five Food Groups Different food groups have different nutrients and ...

  8. Scintillating plate calorimeter optical design

    International Nuclear Information System (INIS)

    McNeil, R.; Fazely, A.; Gunasingha, R.; Imlay, R.; Lim, J.

    1990-01-01

    A major technical challenge facing the builder of a general purpose detector for the SSC is to achieve an optimum design for the calorimeter. Because of its fast response and good energy resolution, scintillating plate sampling calorimeters should be considered as a possible technology option. The work of the Scintillating Plate Calorimeter Collaboration is focused on compensating plate calorimeters. Based on experimental and simulation studies, it is expected that a sampling calorimeter with alternating layers of high-Z absorber (Pb, W, DU, etc.) and plastic scintillator can be made compensating (e/h = 1.00) by suitable choice of the ratio of absorber/scintillator thickness. Two conceptual designs have been pursued by this subsystem collaboration. One is based on lead as the absorber, with read/out of the scintillator plates via wavelength shifter fibers. The other design is based on depleted uranium as the absorber with wavelength shifter (WLS) plate readout. Progress on designs for the optical readout of a compensating scintillator plate calorimeter are presented. These designs include readout of the scintillator plates via wavelength shifter plates or fiber readout. Results from radiation damage studies of the optical components are presented

  9. Equivalent properties for perforated plates. An analytical approach

    International Nuclear Information System (INIS)

    Cepkauskas, M.M.; Yang Jianfeng

    2005-01-01

    Structures that contain perforated plates have been a subject of interest in the Nuclear Industry. Steam generators, condensers and reactor internals utilize plates containing holes which act as flow holes or separate structures from flow by using a 'tube bank' design. The equivalent plate method has been beneficial in analyzing perforate plates. Details are found in various papers found in the bibliography. In addition the ASME code addresses perforated plates in Appendix A-8000, but is limited to a triangular hole pattern. This early work performed in this field utilized test data and analytical approaches. This paper is an examination of an analytical approach for determining equivalent plate mechanical and thermal properties. First a patch of the real plate is identified that provides a model for the necessary physical behavior of the plate. The average strain of this patch is obtained by first applying simplified one dimensional mechanical load to the patch, determining stress as a function of position, converting the stress to strain and then integrating the strain over the patch length. This average strain is then equated to the average strain of an equivalent fictitious rectangular patch. This results in obtaining equivalent Young's Modulus and Poison's Ratio for the equivalent plate in all three orthogonal directions. The corresponding equivalent shear modulus in all three directions is then determined. An orthotropic material stress strain matrix relationship is provided for the fictitious properties. By equating the real average strain with the fictitious average strain in matrix form, a stress multiplier is found to convert average fictitious stress to average real stress. This same type of process is repeated for heat conduction coefficients and coefficients of thermal expansion. Results are provided for both a square and triangular hole pattern. Reasonable results are obtained when comparing the effective Young's Modulus and Poison's Ratio with ASME

  10. Fundamental processes in ion plating

    International Nuclear Information System (INIS)

    Mattox, D.M.

    1980-01-01

    Ion plating is a generic term applied to film deposition processes in which the substrate surface and/or the depositing film is subjected to a flux of high energy particles sufficient to cause changes in the interfacial region of film properties compared to a nonbombarded deposition. Ion plating is being accepted as an alternative coating technique to sputter deposition, vacuum evaporation and electroplating. In order to intelligently choose between the various deposition techniques, the fundamental mechanisms, relating to ion plating, must be understood. This paper reviews the effects of low energy ion bombardment on surfaces, interface formation and film development as they apply to ion plating and the implementation and applications of the ion plating process

  11. Calculation of similarity solutions of partial differential equations

    International Nuclear Information System (INIS)

    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/

  12. Parallel double-plate capacitive proximity sensor modelling based on effective theory

    International Nuclear Information System (INIS)

    Li, Nan; Zhu, Haiye; Wang, Wenyu; Gong, Yu

    2014-01-01

    A semi-analytical model for a double-plate capacitive proximity sensor is presented according to the effective theory. Three physical models are established to derive the final equation of the sensor. Measured data are used to determine the coefficients. The final equation is verified by using measured data. The average relative error of the calculated and the measured sensor capacitance is less than 7.5%. The equation can be used to provide guidance to engineering design of the proximity sensors

  13. Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Zhaoting; Wang, Rong Hui; Chen, Li; Dong, Chung Uang [School of Civil Engineering and Transportation, South China University of Technology, Guangzhou (China)

    2016-08-15

    This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.

  14. Vibration of functionally graded plate resting on viscoelastic elastic foundation subjected to moving loads

    Science.gov (United States)

    Duy Hien, Ta; Lam, Nguyen Ngoc

    2018-04-01

    The dynamics of plates subjected to a moving load must be considered by engineering mechanics and design structures. This paper deals with the dynamic responses of functionally graded (FG) rectangular plates resting on a viscoelastic foundation under moving loads. It is assumed that material properties of the plate vary continuously in the thickness direction according to the power-law. The governing equations are derived by using Hamilton’s principle, which considers the effect of the higher-order shear deformation in the plate. Transient responses of simply supported FG rectangular plates are employed by using state-space methods. Several examples are given for displacement and stresses in the plates with various structural parameters, and the effects of these parameters are discussed.

  15. Vibroacoustic study of a point-constrained plate mounted in a duct

    Science.gov (United States)

    Sapkale, Swapnil L.; Sucheendran, Mahesh M.; Gupta, Shakti S.; Kanade, Shantanu V.

    2018-04-01

    The vibroacoustic study of the interaction of sound with a point-constrained, simply-supported square plate is considered in this paper. The plate is mounted flush on one of the walls of an infinite duct of rectangular cross section and is backed by a cavity. The plate response and the acoustic field is predicted by solving the coupled governing equations using modal expansion with the relevant eigenmodes of the plate dynamics and acoustic fields in the duct and cavity. By varying the location of the point constraint, the frequency characteristics of the transmission loss in the duct can be tuned. The point constraint can also alter the amplitude and spectral characteristics of the plate's response. Interestingly, some new peaks are observed in the response because of the excitation of unsymmetric modes which are otherwise dormant. Mode-localization phenomenon, which is the localization of vibration in specific regions of the plate, is observed for selected constrained points.

  16. 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.

  17. 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.

  18. Finite thickness effect of a zone plate on focusing hard x-rays

    International Nuclear Information System (INIS)

    Yun, W.B.; Chrzas, J.; Viccaro, P.J.

    1992-01-01

    Spatial resolution and focusing efficiency are two important properties of a zone plate in x-ray focusing applications. A general expression of the zone plate equation describing its zone registration is derived from the interference of spherical waves emited from two mutually coherent point sources. An analytical expression of the focusing efficiency in terms of the zone plate thickness and x-ray refractive indices of the zones is also derived. Validity condition for using this expression is considered. Thickness required for obtaining adequate focusing efficiency is calculated as a function of x-ray energy for several representative materials. The spatial resolution of a finite thickness zone plate is worse than that of an infinetly thin zone plate. which is approximately equal to the smallest zone width of the zone plate. The effect of the finite thickness on the spatial resolution is considered

  19. Mathematical model of temperature field distribution in thin plates during polishing with a free abrasive

    Directory of Open Access Journals (Sweden)

    Avilov Alex

    2017-01-01

    Full Text Available The purpose of this paper is to estimate the dynamic characteristics of the heating process of thin plates during polishing with a free abrasive. A mathematical model of the temperature field distribution in space and time according to the plate thickness is based on Lagrange equation of the second kind in the thermodynamics of irreversible processes (variation principle Bio. The research results of thermo elasticity of thin plates (membranes will allow to correct the modes of polishing with a free abrasive to receive the exact reflecting surfaces of satellites reflector, to increase temperature stability and the ability of radio signal reflection, satellite precision guidance. Calculations of temperature fields in thin plates of different thicknesses (membranes is held in the Excel, a graphical characteristics of temperature fields in thin plates (membranes show non-linearity of temperature distribution according to the thickness of thin plates (membranes.

  20. The Golosyiv plate archive digitisation

    Science.gov (United States)

    Sergeeva, T. P.; Sergeev, A. V.; Pakuliak, L. K.; Yatsenko, A. I.

    2007-08-01

    The plate archive of the Main Astronomical Observatory of the National Academy of Sciences of Ukraine (Golosyiv, Kyiv) includes about 85 000 plates which have been taken in various observational projects during 1950-2005. Among them are about 25 000 of direct northern sky area plates and more than 600 000 plates containing stellar, planetary and active solar formations spectra. Direct plates have a limiting magnitude of 14.0-16.0 mag. Since 2002 we have been organising the storage, safeguarding, cataloguing and digitization of the plate archive. The very initial task was to create the automated system for detection of astronomical objects and phenomena, search of optical counterparts in the directions of gamma-ray bursts, research of long period, flare and other variable stars, search and rediscovery of asteroids, comets and other Solar System bodies to improve the elements of their orbits, informational support of CCD observations and space projects, etc. To provide higher efficiency of this work we have prepared computer readable catalogues and database for 250 000 direct wide field plates. Now the catalogues have been adapted to Wide Field Plate Database (WFPDB) format and integrated into this world database. The next step will be adaptation of our catalogues, database and images to standards of the IVOA. Some magnitude and positional accuracy estimations for Golosyiv archive plates have been done. The photometric characteristics of the images of NGC 6913 cluster stars on two plates of the Golosyiv's double wide angle astrograph have been determined. Very good conformity of the photometric characteristics obtained with external accuracies of 0.13 and 0.15 mag. has been found. The investigation of positional accuracy have been made with A3± format fixed bed scanner (Microtek ScanMaker 9800XL TMA). It shows that the scanner has non-detectable systematic errors on the X-axis, and errors of ± 15 μm on the Y-axis. The final positional errors are about ± 2 μm (

  1. 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

  2. Mass transfer effects on vertical oscillating plate with heat flux

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2007-01-01

    Full Text Available Theoretical solution of unsteady viscous incompressible flow past an infinite vertical oscillating plate with uniform heat flux and mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. The temperature from the plate to the fluid at an uniform rate and the mass is diffused uniformly. The dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity and concentration are studied for different parameters like phase angle chemical reaction parameter, thermal Grashof number, mass Grashof number Schmidt number and time are studied. The so­lutions are valid only for small values of time t. It is observed that the velocity increases with decreasing phase angle ωt or chemical reaction parameter.

  3. 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

  4. 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.

  5. Wettability measurements of irregular shapes with Wilhelmy plate method

    Science.gov (United States)

    Park, Jaehyung; Pasaogullari, Ugur; Bonville, Leonard

    2018-01-01

    One of the most accurate methods for measuring the dynamic contact angle of liquids on solid surfaces is the Wilhelmy plate method. This method generally requires the use of rectangular samples having a constant perimeter in the liquid during advancing and receding cycles. A new formulation based on the Wilhelmy force balance equation to determine the contact angle for plate samples with irregular shapes has been developed. This method employs a profile plot obtained from an optical image to determine the perimeter (i.e. wetted length) of the sample as a function of the immersion depth. The raw force data measured by the force tensiometer is manipulated using the profile plot and the Wilhelmy equation to determine the wetting force and consequently advancing and the receding contact angle. This method is verified with both triangular and irregular PTFE samples in water, and measured contact angles are in good agreement with results from conventional regular shaped samples with a constant perimeter.

  6. Numerical simulation of droplet evaporation between two circular plates

    International Nuclear Information System (INIS)

    Bam, Hang Jin; Son, Gi Hun

    2015-01-01

    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.

  7. 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

  8. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  9. Group analysis for natural convection from a vertical plate

    Science.gov (United States)

    Rashed, A. S.; Kassem, M. M.

    2008-12-01

    The steady laminar natural convection of a fluid having chemical reaction of order n past a semi-infinite vertical plate is considered. The solution of the problem by means of one-parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations. Two different similarity transformations are found. In each case the set of differential equations are solved numerically using Runge-Kutta and the shooting method. For each transformation different Schmidt numbers and chemical reaction orders are tested.

  10. Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution

    International Nuclear Information System (INIS)

    Baltacioglu, A.K.; Civalek, O.; Akgoez, B.; Demir, F.

    2011-01-01

    This paper presents nonlinear static analysis of a rectangular laminated composite thick plate resting on nonlinear two-parameter elastic foundation with cubic nonlinearity. The plate formulation is based on first-order shear deformation theory (FSDT). The governing equation of motion for a rectangular laminated composite thick plate is derived by using the von Karman equation. The nonlinear static deflections of laminated plates on elastic foundation are investigated using the discrete singular convolution method. The effects of foundation and geometric parameters of plates on nonlinear deflections are investigated. The validity of the present method is demonstrated by comparing the present results with those available in the literature. - Highlights: → Large deflection analysis of laminated composite plates are investigated. → As foundation, nonlinear elastic models have been used firstly. → The effects of three-parameter foundation are investigated in detail.

  11. Computation of the homogeneous and forced solutions of a finite length, line-driven, submerged plate.

    Science.gov (United States)

    DiPerna, Daniel T; Blake, William K; DiPerna, Xingguang Z

    2006-12-01

    A formulation is developed to predict the vibration response of a finite length, submerged plate due to a line drive. The formulation starts by describing the fluid in terms of elliptic cylinder coordinates, which allows the fluid loading term to be expressed in terms of Mathieu functions. By moving the fluid loading term to the right-hand side of the equation, it is considered to be a force. The operator that remains on the left-hand side is the same as that of the in vacuo plate: a fourth-order, constant coefficient, ordinary differential equation. Therefore, the problem appears to be an inhomogeneous ordinary differential equation. The solution that results has the same form as that of the in vacuo plate: the sum of a forced solution, and four homogeneous solutions, each of which is multiplied by an arbitrary constant. These constants are then chosen to satisfy the structural boundary conditions on the two ends of the plate. Results for the finite plate are compared to the infinite plate in both the wave number and spatial domains. The theoretical predictions of the plate velocity response are also compared to results from finite element analysis and show reasonable agreement over a large frequency range.

  12. THERMAL PERFORMANCE OF FLAT PLATE SOLAR COLLECTOR

    Directory of Open Access Journals (Sweden)

    TABET I.

    2017-06-01

    Full Text Available In this paper, a theoretical and experimental studyof flat platesolar water collector with reflectors.A mathematical model based on energy balance equations saw the thermal behavior of the collector is investigated. The experimental test was made at the unit research applies in renewable energy (URAER located in southern Algeria.An increase of 23% for solar radiation incident on the collector surface with the addition of the planers reflectors in the day of May, this increase causes an improvement of the performance of the collector,the fluid temperature increases with an average of 5%. Thetests conducted on the flat plate solar water collector in open circuit enabled the determination of thermal performance of the collector by estimating the daily output The thermal efficiency of the collector ranges from 1% -63% during the day, a mean value of 36%obtained.

  13. 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....

  14. Plating on stainless steel alloys

    International Nuclear Information System (INIS)

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

    1981-01-01

    Quantitative adhesion data are presented for a variety of electroplated stainless steel type alloys. Results show that excellent adhesion can be obtained by using a Wood's nickel strike or a sulfamate nickel strike prior to final plating. Specimens plated after Wood's nickel striking failed in the deposit rather than at the interface between the substrate and the coating. Flyer plate quantitative tests showed that use of anodic treatment in sulfuric acid prior to Wood's nickel striking even further improved adhesion. In contrast activation of stainless steels by immersion or cathodic treatment in hydrochloric acid resulted in very reduced bond strengths with failure always occurring at the interface between the coating and substrate

  15. Postbuckling Analysis Of A Rectangular Plate Loaded In Compression

    Directory of Open Access Journals (Sweden)

    Havran Jozef

    2015-12-01

    Full Text Available The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied.

  16. 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...

  17. Benney's long wave equations

    International Nuclear Information System (INIS)

    Lebedev, D.R.

    1979-01-01

    Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

  18. Investigation of Three-Dimensional Axisymmetric Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

    OpenAIRE

    ali shokrgozar abbasi; Asghar Baradaran Rahimi; Hamidreza Mozayeni

    2016-01-01

    General formulation and solution of Navier-Stokes and energy equations are sought in the study of threedimensional axisymmetric unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration towards the main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z - directi...

  19. Solution of the Bagley Torvik equation by fractional DTM

    Science.gov (United States)

    Arora, Geeta; Pratiksha

    2017-07-01

    In this paper, fractional differential transform method(DTM) is implemented on the Bagley Torvik equation. This equation models the viscoelastic behavior of geological strata, metals, glasses etc. It explains the motion of a rigid plate immersed in a Newtonian fluid. DTM is a simple, reliable and efficient method that gives a series solution. Caputo fractional derivative is considered throughout this work. Two examples are given to demonstrate the validity and applicability of the method and comparison is made with the existing results.

  20. Fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Laskin, Nick

    2002-01-01

    Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

  1. 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

  2. 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

  3. Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method

    Directory of Open Access Journals (Sweden)

    WANG Minhao

    2017-08-01

    Full Text Available Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.

  4. MyPlate Daily Checklist

    Science.gov (United States)

    ... Price Tag Read the Food Label Kitchen Timesavers Cooking for Your Family Tasty & Low-Cost Recipes Sample 2-Week Menus Resources for Professionals MyPlate Tip Sheets Print Materials Infographics 5 Ways ...

  5. License plate recognition (phase B).

    Science.gov (United States)

    2010-06-01

    License Plate Recognition (LPR) technology has been used for off-line automobile enforcement purposes. The technology has seen mixed success with correct reading rate as high as 60 to 80% depending on the specific application and environment. This li...

  6. Armor Plate Surface Roughness Measurements

    National Research Council Canada - National Science Library

    Stanton, Brian; Coburn, William; Pizzillo, Thomas J

    2005-01-01

    ...., surface texture and coatings) that could become important at high frequency. We measure waviness and roughness of various plates to know the parameter range for smooth aluminum and rolled homogenous armor (RHA...

  7. Averaged RMHD equations

    International Nuclear Information System (INIS)

    Ichiguchi, Katsuji

    1998-01-01

    A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)

  8. Rhodium platings – experimental study

    OpenAIRE

    Rudolf, R.; Budić, B.; Stamenković, D.; Čolić, M.; Ivanič, A.; Kosec, B.

    2013-01-01

    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.

  9. 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.

  10. 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.

  11. 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.

  12. Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

    Science.gov (United States)

    Newman, J. C., Jr.; Raju, I. S.

    1984-01-01

    Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.

  13. Local and global nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate

    International Nuclear Information System (INIS)

    Ye Min; Lu Jing; Zhang Wei; Ding Qian

    2005-01-01

    The present investigation deals with nonlinear dynamic behavior of a parametrically excited simply supported rectangular symmetric cross-ply laminated composite thin plate for the first time. The governing equation of motion for rectangular symmetric cross-ply laminated composite thin plate is derived by using von Karman equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. The Galerkin approach is used to obtain a two-degree-of-freedom nonlinear system under parametric excitation. The method of multiple scales is utilized to transform the second-order non-autonomous differential equations to the first-order averaged equations. Using numerical method, the averaged equations are analyzed to obtain the steady state bifurcation responses. The analysis of stability for steady state bifurcation responses in laminated composite thin plate is also given. Under certain conditions laminated composite thin plate may have two or multiple steady state bifurcation solutions. Jumping phenomenon occurs in the steady state bifurcation solutions. The chaotic motions of rectangular symmetric cross-ply laminated composite thin plate are also found by using numerical simulation. The results obtained here demonstrate that the periodic, quasi-periodic and chaotic motions coexist for a parametrically excited fore-edge simply supported rectangular symmetric cross-ply laminated composite thin plate under certain conditions

  14. 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.

  15. 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

  16. Properties of local equations for a separation column

    International Nuclear Information System (INIS)

    Hodor, I.

    1992-01-01

    An overall theory of column separation is developed. A general expression for fully-developed concentration fields is found. For close-separation processes, a simple method to derive the theoretical plate height and the stage efficiency from local equations are given. Application of separation-of-variables to linearized systems is discussed and a partial range completeness of the eigenfunctions is found. (author)

  17. The Nonlinear Dynamic Response of an Elastic-Plastic Thin Plate under Impulsive Loading,

    Science.gov (United States)

    1987-06-11

    Among those numerical methods, the finite element method is the most effective one. The method presented in this paper is an " influence function " numerical...computational time is much less than the finite element method. Its precision is higher also. II. Basic Assumption and the Influence Function of a Simple...calculation. Fig. 1 3 2. The Influence function of a Simple Supported Plate The motion differential equation of a thin plate can be written as DV’w+ _.eluq() (1

  18. Heat transfer effects on flow past an exponentially accelerated vertical plate with variable temperature

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2008-01-01

    Full Text Available An exact solution to the problem of flow past an exponentially accelerated infinite vertical plate with variable temperature is analyzed. The temperature of the plate is raised linearly with time t. The dimensionless governing equations are solved using Laplace-transform technique. The velocity and temperature profiles are studied for different physical parameters like thermal Grashof number Gr, time and an accelerating parameter a. It is observed that the velocity increases with increasing values of a or Gr.

  19. Quasi-estatic and dynamic elasto/viscoplastic analysis of plates and shells

    International Nuclear Information System (INIS)

    Dinis, L.M.S.

    1981-01-01

    The non-linear quasi-static and dynamic analysis of plates and shells is presented using the finite - element method for spatial discretization and the Central Finite Differences for the integration of the transient dynamic equation. The behaviour of the material is represented by the elasto/viscoplastic model of Perzyna together with approximations of the Von Mises yield surfaces for plates and shells. (Author) [pt

  20. Time dependent shear stress and temperature distribution over an insulated flat plate moving at hypersonic speed.

    Science.gov (United States)

    Rodkiewicz, C. M.; Gupta, R. N.

    1971-01-01

    The laminar two-dimensional flow over a stepwise accelerated flat plate moving with hypersonic speed at zero angle of attack is analysed. The governing equations in the self-similar form are linearized and solved numerically for small times. The solutions obtained are the deviations of the velocity and the temperature profiles from those of steady state. The presented results may be used to find the first order boundary layer induced pressure on the plate.

  1. Resonant frequency function of thickness-shear vibrations of rectangular crystal plates.

    Science.gov (United States)

    Wang, Ji; Yang, Lijun; Pan, Qiaoqiao; Chao, Min-Chiang; Du, Jianke

    2011-05-01

    The resonant frequencies of thickness-shear vibrations of quartz crystal plates in rectangular and circular shapes are always required in the design and manufacturing of quartz crystal resonators. As the size of quartz crystal resonators shrinks, for rectangular plates we must consider effects of both length and width for the precise calculation of resonant frequency. Starting from the three-dimensional equations of wave propagation in finite crystal plates and the general expression of vibration modes, we obtained the relations between frequency and wavenumbers. By satisfying the major boundary conditions of the dominant thickness-shear mode, three wavenumber solutions are obtained and the frequency equation is constructed. It is shown the resonant frequency of thickness-shear mode is a second-order polynomial of aspect ratios. This conforms to known results in the simplest form and is applicable to further analytical and experimental studies of the frequency equation of quartz crystal resonators.

  2. On separable Pauli equations

    International Nuclear Information System (INIS)

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  3. Functional equations with causal operators

    CERN Document Server

    Corduneanu, C

    2003-01-01

    Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

  4. Modeling RERTR experimental fuel plates using the PLATE code

    International Nuclear Information System (INIS)

    Hayes, S.L.; Meyer, M.K.; Hofman, G.L.; Snelgrove, J.L.; Brazener, R.A.

    2003-01-01

    Modeling results using the PLATE dispersion fuel performance code are presented for the U-Mo/Al experimental fuel plates from the RERTR-1, -2, -3 and -5 irradiation tests. Agreement of the calculations with experimental data obtained in post-irradiation examinations of these fuels, where available, is shown to be good. Use of the code to perform a series of parametric evaluations highlights the sensitivity of U-Mo dispersion fuel performance to fabrication variables, especially fuel particle shape and size distributions. (author)

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

    International Nuclear Information System (INIS)

    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

  6. Electroless metal plating of plastics

    International Nuclear Information System (INIS)

    Krause, L.J.

    1986-01-01

    The product of an electroless plating process is described for plating at least one main group metal directly on a surface of a polymeric substrate comprising the steps of forming a nonaqueous solution containing a metallic salt of an alkali metal in a positive valence state and at least one main group metal in a negative valence state, the main group metal being selected from the group consisting of Ge, Sn, Pb, As, Sb, Bi, Si and Te, selecting an aromatic polymeric substrate reducible by the solublized salt and resistant to degration during the reaction, and carrying out a redox reaction between the salt in solution and the substrate by contacting the solution with the substrate for a sufficient time to oxidize and deposit the main group metal in elemental form to produce a plated substrate. The product is characterized by the plated metal being directly on the surface of the polymeric substrate and the alkali metal being retained in the plated substrate with the substrate being negatively charged with electrons transferred from the main group metal during the redox reaction

  7. 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...

  8. 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.

  9. 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.

  10. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  11. Surface effects on the electroelastic responses of a thin piezoelectric plate with nanoscale thickness

    International Nuclear Information System (INIS)

    Yan Zhi; Jiang Liying

    2012-01-01

    This work aims to investigate the electroelastic responses of a thin piezoelectric plate under mechanical and electrical loads with the consideration of surface effects. Surface effects, including surface elasticity, residual surface stress and surface piezoelectricity, are incorporated into the conventional Kirchhoff plate theory for a piezoelectric plate via the surface piezoelectricity model and the generalized Young-Laplace equations. Different from the results predicted by the conventional plate theory ignoring the surface effects, the proposed model predicts size-dependent behaviours of the piezoelectric thin plate with nanoscale thickness. It is found that surface effects have significant influence on the electroelastic responses of the piezoelectric nanoplate. This work is expected to provide more accurate predictions on characterizing nanofilm or nanoribbon based piezoelectric devices in nanoelectromechanical systems. (paper)

  12. Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

    Science.gov (United States)

    Cheng, Yong; Ji, Chun-yan; Zhai, Gang-jun; Oleg, Gaidai

    2018-03-01

    This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy's law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.

  13. 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.

  14. 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.

  15. Solving Ordinary Differential Equations

    Science.gov (United States)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  16. Reactimeter dispersion equation

    OpenAIRE

    A.G. Yuferov

    2016-01-01

    The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

  17. 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.

  18. Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

    Science.gov (United States)

    Chiang, C. K.; Xue, David Y.; Mei, Chuh

    1993-04-01

    A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

  19. An Experimental and Analytical Study of a Radiative Cooling System with Unglazed Flat Plate Collectors

    DEFF Research Database (Denmark)

    Hosseinzadeh, Elham; Taherian, Hessam

    2012-01-01

    plate solar collectors in a humid area, Babol, Iran, is assessed both experimentally and numerically. Different methods available in the literature are reviewed and by using a widely accepted model, the sky temperature is determined. The mathematical model for a flat plate solar collector is used...... as a guideline to derive the governing equations of a night sky radiator. Then, a cooling loop, including a storage tank, pump, connecting pipes, and a radiator has been studied experimentally. The water is circulated through the unglazed flat-plate radiator having 4 m2 of collector area at night to be cooled...

  20. Study of flow past an exponentially accelerated isothermal vertical plate in the presence of chemical reaction

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2010-01-01

    Full Text Available Theoretical study of unsteady flow past an exponentially accelerated infinite isothermal vertical plate with variable mass diffusion has been presented in the presence of homogeneous chemical reaction of first order. The plate temperature is raised to Tw and species concentration level near the plate is made to rise linearly with time. The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles are studied for different physical parameters like chemical reaction parameter, thermal Grashof number, mass Grashof number, a and time. It is observed that the velocity increases with increasing values of a or t. But the trend is just reversed with respect to K.

  1. Heat and mass transfer effects on moving vertical plate in the presence of thermal radiation

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2004-01-01

    Full Text Available Thermal radiation effects on moving infinite vertical plate in the presence variable temperature and mass diffusion is considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature and the concentration level near the plate are raised linearly with time. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity and skin-friction are studied for different parameters like thermal Grashof number, mass Grashof number, time and radiation parameter. It is observed that the velocity slightly decreases with increasing value of the radiation parameter.

  2. Soft Plate and Impact Tectonics

    Science.gov (United States)

    Tikoff, Basil

    In the field of tectonics, most of our ideas are published in journals. This is not true of other fields, such as history, in which ideas are primarily published in books. Within my own field of structural geology, I can recall only one book, Strain Fades by E. Hansen (Springer-Verlag, 1971), which presents a new idea in book form. However, even this book is more useful for its philosophical approach and particular methodology of determining directions of folding, than for its overarching idea.Enter Soft Plate and Impact Tectonics, a new book with an interesting hypothesis that has been informally discussed in the geoscience community: A fundamental tenet of plate tectonics is incorrect—namely, that the plates are rigid. This assertion is evident when looking at any mountain range, and is perhaps most clearly stated in Molnar [1988].

  3. A new evolution equation

    International Nuclear Information System (INIS)

    Laenen, E.

    1995-01-01

    We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)

  4. Gentilly 2 divider plate replacement

    International Nuclear Information System (INIS)

    Forest, J.; Klisel, E.; McClellan, G.; Schnelder, W.

    1995-01-01

    The steam generators at the Gentilly 2 Nuclear Plant in operation since 1983 were built with primary divider plates of a bolted panel configuration. During a routine outage inspection, it was noted that two bolts had dislodged from the divider and were located lying in the primary head. Subsequent inspections revealed erosion damage to a substantial number of divider plate bolts and to a lesser extent, to the divider plate itself. After further inspection and repair the units were returned to operation, however, it was determined that a permanent replacement of the primary divider plates was going to be necessary. After evaluation of various options, it was decided that the panel type dividers would be replaced with a single piece floating design. The divider itself was to be of a one piece all-welded arrangement to be constructed from individual panels to be brought in through the manways. In view of the strength limitations of the bolted attachment of the upper seat bar to the tubesheet, a new welded seat bar was provided. To counteract erosion concerns, the new divider is fitted with erosion resistant inserts or weld buildup and with improved sealing features in order to minimize leakage and erosion. At an advanced stage in the design and manufacture of the components, the issue of divider strength during LOCA conditions came into focus. Analysis was performed to determine the strength and/or failure characteristics of the divider to a variety of small and large LOCA conditions. The paper describes the diagnosis of the original divider plates and the design, manufacture, field mobilization, installation and subsequent operation of the replacement divider plates. (author)

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

    International Nuclear Information System (INIS)

    Bhattacharyya, Krishnendu; Mukhopadhyay, Swati; Layek, G. C.

    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. (fundamental areas of phenomenology(including applications))

  6. 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.

  7. Equational type logic

    NARCIS (Netherlands)

    Manca, V.; Salibra, A.; Scollo, Giuseppe

    1990-01-01

    Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either

  8. Alternative equations of gravitation

    International Nuclear Information System (INIS)

    Pinto Neto, N.

    1983-01-01

    It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt

  9. Reduced Braginskii equations

    Energy Technology Data Exchange (ETDEWEB)

    Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.

  10. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0

  11. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1994-01-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation

  12. Model Compaction Equation

    African Journals Online (AJOL)

    The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...

  13. The Wouthuysen equation

    NARCIS (Netherlands)

    M. Hazewinkel (Michiel)

    1995-01-01

    textabstractDedication: 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

  14. The generalized Fermat equation

    NARCIS (Netherlands)

    Beukers, F.

    2006-01-01

    This article will be devoted to generalisations of Fermat’s equation xn + yn = zn. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would

  15. The tectonic plates are moving!

    CERN Document Server

    Livermore, Roy

    2018-01-01

    Written in a witty and informal style, this book explains modern plate tectonics in a non-technical manner, showing not only how it accounts for phenomena such as great earthquakes, tsunamis, and volcanic eruptions, but also how it controls conditions at the Earth’s surface, including global geography and climate, making it suitable for life. The book presents the advances that have been made since the establishment of plate tectonics in the 1960s, highlighting, on the fiftieth anniversary of the theory, the contributions of a small number of scientists who have never been widely recognized for their discoveries. Beginning with the publication of a short article in Nature by Vine and Matthews, the book traces the development of plate tectonics through two generations of the theory. First-generation plate tectonics covers the exciting scientific revolution of the 1960s, its heroes, and its villains. The second generation includes the rapid expansions in sonar, satellite, and seismic technologies during the 1...

  16. 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

  17. 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...

  18. Stress state in perforated plates

    International Nuclear Information System (INIS)

    Visner, J.

    1977-01-01

    The method is described of photoelastic measurement of stress concentration factors (s.c.f) in plates perforated by a square, triangular and diagonal grid of circular holes and loaded by uniaxial or biaxial tensile stress. A loading equipment which was developed and its modifications are described. Stress concentration factors found are compared with theoretical and experimental results given in references. (author)

  19. Regulators of growth plate maturation

    NARCIS (Netherlands)

    Emons, Joyce Adriana Mathilde

    2010-01-01

    Estrogen is known to play an important role in longitudinal bone growth and growth plate maturation, but the mechanism by which estrogens exert their effect is not fully understood. In this thesis this role is further explored. Chapter 1 contains a general introduction to longitudinal bone growth

  20. 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...

  1. Elastic stability of thick auxetic plates

    International Nuclear Information System (INIS)

    Lim, Teik-Cheng

    2014-01-01

    Auxetic materials and structures exhibit a negative Poisson’s ratio while thick plates encounter shear deformation, which is not accounted for in classical plate theory. This paper investigates the effect of a negative Poisson’s ratio on thick plates that are subjected to buckling loads, taking into consideration the shear deformation using Mindlin plate theory. Using a highly accurate shear correction factor that allows for the effect of Poisson’s ratio, the elastic stability of circular and square plates are evaluated in terms of dimensionless parameters, namely the Mindlin-to-Kirchhoff critical buckling load ratio and Mindlin critical buckling load factors. Results for thick square plates reveal that both parameters increase as the Poisson’s ratio becomes more negative. In the case of thick circular plates, the Mindlin-to-Kirchhoff critical buckling load ratios and the Mindlin critical buckling load factors increase and decrease, respectively, as the Poisson’s ratio becomes more negative. The results obtained herein show that thick auxetic plates behave as thin conventional plates, and therefore suggest that the classical plate theory can be used to evaluate the elastic stability of thick plates if the Poisson’s ratio of the plate material is sufficiently negative. The results also suggest that materials with highly negative Poisson’s ratios are recommended for square plates, but not circular plates, that are subjected to buckling loads. (paper)

  2. 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.

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

    International Nuclear Information System (INIS)

    Bo, Z; Chen, J H

    2010-01-01

    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.

  4. Microstructure and Mechanical Property of Aluminum Alloy Plate AA 7055

    Directory of Open Access Journals (Sweden)

    CHEN Junzhou

    2017-10-01

    Full Text Available Through-thickness microstructure and mechanical property of AA 7055-T7751 aluminum alloy plate were investigated by using electron backscattered diffraction (EBSD, transmission electron microscope (TEM and small angle X-ray scattering(SAXS. The results indicate an inhomogeneous distribution of microstructure through the thickness. The degree of recrystallization decreases gradually from 69% to 19.1%, as deepening from the surface to the center of the plate. The size of subgrains decreases from 10 μm at the surface to around 2 μm at the center. Strong texture of rolling type is observed near the center but the intensity decreases gradually as nearing the surface and the shear texture becomes the dominant. High density of plate-like η' phases are observed in the alloy, indicating the sufficient precipitation. η' precipitates of this condition are around 3.7 nm in radius, 1-3 nm in thickness and are found coherent with the Al matrix with a coherent strain of 0.0133, showing a strong strengthening effect. The heterogeneity in grain scale does not influence the distribution and the morphology of precipitates. The yield strength (L direction varies linearly along the thickness direction of the plate, fitting an equation of σy=-38.7S+604.8 (0≤S≤1. The variation of yield strength is related to the heterogeneity of grain structure.

  5. Development of novel segmented-plate linearly tunable MEMS capacitors

    International Nuclear Information System (INIS)

    Shavezipur, M; Khajepour, A; Hashemi, S M

    2008-01-01

    In this paper, novel MEMS capacitors with flexible moving electrodes and high linearity and tunability are presented. The moving plate is divided into small and rigid segments connected to one another by connecting beams at their end nodes. Under each node there is a rigid step which selectively limits the vertical displacement of the node. A lumped model is developed to analytically solve the governing equations of coupled structural-electrostatic physics with mechanical contact. Using the analytical solver, an optimization program finds the best set of step heights that provides the highest linearity. Analytical and finite element analyses of two capacitors with three-segmented- and six-segmented-plate confirm that the segmentation technique considerably improves the linearity while the tunability remains as high as that of a conventional parallel-plate capacitor. Moreover, since the new designs require customized fabrication processes, to demonstrate the applicability of the proposed technique for standard processes, a modified capacitor with flexible steps designed for PolyMUMPs is introduced. Dimensional optimization of the modified design results in a combination of high linearity and tunability. Constraining the displacement of the moving plate can be extended to more complex geometries to obtain smooth and highly linear responses

  6. Modal radiation patterns of baffled circular plates and membranes.

    Science.gov (United States)

    Christiansen, Thomas Lehrmann; Hansen, Ole; Thomsen, Erik Vilain; Jensen, Jørgen Arendt

    2014-05-01

    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 force, which is used as a sound receiver in any medium or as a sound transmitter in a gaseous medium. A general, concise expression is given for the radiation pattern of any mode of the membrane and the plate with arbitrary boundary conditions. Specific solutions are given for the four special cases of a plate with clamped, simply supported, and free edge boundary conditions as well as for the membrane. For all non-axisymmetric modes, the velocity potential along the axis of the radiator is found to be strictly zero. In the long wavelength limit, the radiation pattern of all axisymmetric modes approaches 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.

  7. 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)

  8. Critical impact energy for the perforation of metallic plates

    International Nuclear Information System (INIS)

    Aly, S.Y.; Li, Q.M.

    2008-01-01

    This paper investigates the empirical formulae used in engineering practice to predict the critical perforation energy of metallic plates struck by rigid projectiles in the sub-ordnance regime. Main factors affecting the critical perforation energy are identified and valid conditions for each empirical formula are compared. Dimensional analysis is conducted to show the dependence of the non-dimensional critical impact energy on other influential non-dimensional numbers. Available empirical formulae are re-expressed in non-dimensional forms. A modified Jowett/AEA equation is proposed to predict the critical perforation energy of a flat-ended short projectile. The present work increases the confidence of using these empirical formulae and can be regarded as a quick guide for ballistic protection design of metallic shields and steel armour plates

  9. Optimization Design of Bipolar Plate Flow Field in PEM Stack

    Science.gov (United States)

    Wen, Ming; He, Kanghao; Li, Peilong; Yang, Lei; Deng, Li; Jiang, Fei; Yao, Yong

    2017-12-01

    A new design of bipolar plate flow field in proton exchange membrane (PEM) stack was presented to develop a high-performance transfer efficiency of the two-phase flow. Two different flow fields were studied by using numerical simulations and the performance of the flow fields was presented. the hydrodynamic properties include pressure gap between inlet and outlet, the Reynold’s number of the two types were compared based on the Navier-Stokes equations. Computer aided optimization software was implemented in the design of experiments of the preferable flow field. The design of experiments (DOE) for the favorable concept was carried out to study the hydrodynamic properties when changing the design parameters of the bipolar plate.

  10. 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.

  11. Dynamic nonlinear interaction of elastic plates on discrete supports

    International Nuclear Information System (INIS)

    Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

    1984-01-01

    A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

  12. Active damping of multiferroic composite plates using 1-3 piezoelectric composites

    Science.gov (United States)

    Kattimani, S. C.

    2017-12-01

    A layer-wise shear deformation theory is used to analyze the smart damping of multiferroic composite or magneto-electro-elastic (MEE) plates. The intent of this analysis is to investigate the need for incorporating additional smart elements for controlling the vibrations of multiferroic composite plates. Active constrained layer damping (ACLD) treatment has been incorporated to alleviate the vibration of MEE plate. A layer of viscoelastic material is used as constrained layer for the ACLD treatment. The coupled constitutive equations of multiferroic (ferroelectric and ferromagnetic) composite materials along with the total potential energy principle are used to derive the finite element formulation for the overall multiferroic or MEE plate. Maxwell’s electrostatic and electromagnetic relations are used to compute the electric and magnetic potential distribution. Influence of obliquely reinforced piezoelectric fibers in the piezoelectric layer of the ACLD treatment has also been investigated. In order to investigate the importance of using ACLD treatment for an active damping of multiferroic or MEE plate, an active control of MEE plate has also been analyzed by providing the control voltage directly to the piezoelectric layers of the MEE substrate plate without using the ACLD treatment. The present study suggests that for an optimal control of MEE plates, the smartness element such as the ACLD treatment is essentially required.

  13. 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.

  14. Subduction Drive of Plate Tectonics

    Science.gov (United States)

    Hamilton, W. B.

    2003-12-01

    Don Anderson emphasizes that plate tectonics is self-organizing and is driven by subduction, which rights the density inversion generated as oceanic lithosphere forms by cooling of asthenosphere from the top. The following synthesis owes much to many discussions with him. Hinge rollback is the key to kinematics, and, like the rest of actual plate behavior, is incompatible with bottom-up convection drive. Subduction hinges (which are under, not in front of, thin leading parts of arcs and overriding plates) roll back into subducting plates. The Pacific shrinks because bounding hinges roll back into it. Colliding arcs, increasing arc curvatures, back-arc spreading, and advance of small arcs into large plates also require rollback. Forearcs of overriding plates commonly bear basins which preclude shortening of thin plate fronts throughout periods recorded by basin strata (100 Ma for Cretaceous and Paleogene California). This requires subequal rates of advance and rollback, and control of both by subduction. Convergence rate is equal to rates of rollback and advance in many systems but is greater in others. Plate-related circulation probably is closed above 650 km. Despite the popularity of concepts of plumes from, and subduction into, lower mantle, there is no convincing evidence for, and much evidence against, penetration of the 650 in either direction. That barrier not only has a crossing-inhibiting negative Clapeyron slope but also is a compositional boundary between fractionated (not "primitive"), sluggish lower mantle and fertile, mobile upper mantle. Slabs sink more steeply than they dip. Slabs older than about 60 Ma when their subduction began sink to, and lie down on and depress, the 650-km discontinuity, and are overpassed, whereas younger slabs become neutrally buoyant in mid-upper mantle, into which they are mixed as they too are overpassed. Broadside-sinking old slabs push all upper mantle, from base of oceanic lithosphere down to the 650, back under

  15. 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.

  16. 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

  17. 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

  18. 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

  19. Supersymmetric quasipotential equations

    International Nuclear Information System (INIS)

    Zaikov, R.P.

    1981-01-01

    A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

  20. Local instant conservation equations

    International Nuclear Information System (INIS)

    Delaje, Dzh.

    1984-01-01

    Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface

  1. 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

  2. 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,

  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. 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.

  5. Non-linear analysis of skew thin plate by finite difference method

    International Nuclear Information System (INIS)

    Kim, Chi Kyung; Hwang, Myung Hwan

    2012-01-01

    This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed

  6. Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state

    Science.gov (United States)

    Wang, Yan Qing

    2018-02-01

    To provide reference for aerospace structural design, electro-mechanical vibrations of functionally graded piezoelectric material (FGPM) plates carrying porosities in the translation state are investigated. A modified power law formulation is employed to depict the material properties of the plates in the thickness direction. Three terms of inertial forces are taken into account due to the translation of plates. The geometrical nonlinearity is considered by adopting the von Kármán non-linear relations. Using the d'Alembert's principle, the nonlinear governing equation of the out-of-plane motion of the plates is derived. The equation is further discretized to a system of ordinary differential equations using the Galerkin method, which are subsequently solved via the harmonic balance method. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge-Kutta technique. Additionally, the stability of the steady state responses is examined by means of the perturbation technique. Linear and nonlinear vibration analyses are both carried out and results display some interesting dynamic phenomenon for translational porous FGPM plates. Parametric study shows that the vibration characteristics of the present inhomogeneous structure depend on several key physical parameters.

  7. 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.

  8. 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...

  9. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  10. On Dust Charging Equation

    OpenAIRE

    Tsintsadze, Nodar L.; Tsintsadze, Levan N.

    2008-01-01

    A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.

  11. Equations For Rotary Transformers

    Science.gov (United States)

    Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.

    1988-01-01

    Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.

  12. 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.

  13. 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.

  14. Nonlinear differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  15. 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.

  16. Mathematical modeling of impact of two metal plates using two-fluid approach

    Science.gov (United States)

    Utkin, P. S.; Fortova, S. V.

    2018-01-01

    The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

  17. 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...

  18. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    Science.gov (United States)

    Collier, D.M.; Meeks, L.A.; Palmer, J.P.

    1960-05-10

    A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

  19. Structural Equations and Causation

    OpenAIRE

    Hall, Ned

    2007-01-01

    Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

  20. 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...... of academic teaching and lecturing into account....

  1. Electroless metal plating of plastics

    Science.gov (United States)

    Krause, L.J.

    1982-09-20

    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.

  2. A tandem parallel plate analyzer

    International Nuclear Information System (INIS)

    Hamada, Y.; Fujisawa, A.; Iguchi, H.; Nishizawa, A.; Kawasumi, Y.

    1996-11-01

    By a new modification of a parallel plate analyzer the second-order focus is obtained in an arbitrary injection angle. This kind of an analyzer with a small injection angle will have an advantage of small operational voltage, compared to the Proca and Green analyzer where the injection angle is 30 degrees. Thus, the newly proposed analyzer will be very useful for the precise energy measurement of high energy particles in MeV range. (author)

  3. Curved Folded Plate Timber Structures

    OpenAIRE

    Buri, Hans Ulrich; Stotz, Ivo; Weinand, Yves

    2011-01-01

    This work investigates the development of a Curved Origami Prototype made with timber panels. In the last fifteen years the timber industry has developed new, large size, timber panels. Composition and dimensions of these panels and the possibility of milling them with Computer Numerical Controlled machines shows great potential for folded plate structures. To generate the form of these structures we were inspired by Origami, the Japanese art of paper folding. Common paper tessellations are c...

  4. PRETREATING URANIUM FOR METAL PLATING

    Science.gov (United States)

    Wehrmann, R.F.

    1961-05-01

    A process is given for anodically treating the surface of uranium articles, prior to metal plating. The metal is electrolyzed in an aqueous solution of about 10% polycarboxylic acid, preferably oxalic acid, from 1 to 5% by weight of glycerine and from 1 to 5% by weight of hydrochloric acid at from 20 to 75 deg C for from 30 seconds to 15 minutes. A current density of from 60 to 100 amperes per square foot is used.

  5. 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....

  6. Equations of radiation hydrodynamics

    International Nuclear Information System (INIS)

    Mihalas, D.

    1982-01-01

    The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented

  7. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  8. Dynamic temperature field in the ferromagnetic plate induced by moving high frequency inductor

    Directory of Open Access Journals (Sweden)

    Milošević-Mitić Vesna

    2014-01-01

    Full Text Available The subject of the paper is the temperature distribution in the thin metallic ferromagnetic plate influenced by moving linear high frequency induction heater. As a result of high frequency electromagnetic field, conducting currents appear in the part of the plate. Distribution of the eddy-current power across the plate thickness is obtained by use of complex analysis. The influences of the heater frequency, magnetic field intensity and plate thickness on the heat power density were discussed. By treating this power as a moving heat source, differential equations governing distribution of the temperature field are formulated. Temperature across the plate thickness is assumed to be in linear form. Differential equations are analytically solved by using integral-transform technique, Fourier finite-sine and finite-cosine transform and Laplace transform. The influence of the heater velocity to the plate temperature is presented on numerical examples based on theoretically obtained results. [Projekat Ministarstva nauke Republike Srbije, br. TR 35040 i br. TR 35011

  9. 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.

  10. Experimental and numerical simulation the effect of distribution plates in a mobile electrostatic precipitator

    International Nuclear Information System (INIS)

    Noorpoor, A. R.; Sadeghi, M.

    2003-01-01

    In this investigation, behaviour of airflow inside an electrostatic precipitator with three different distribution plates has been considered by means of numerical and experimental methods and results have been compared together. This device has been designed and produced in this center for the first time in Iran, and its ability to absorb particles, haze and soot is good. But for increasing the efficiency there must be some changes to an miscellaneous sections. Therefore, here we consider the effect of distribution plates to increase performance, because when distribution flow at cross sections of precipitator is uniform, the efficiency will increase. To have a numerical simulation, fluent software version 5.3 was and for modeling turbulence the RNG k-Σ turbulent model applied. This program after discretization governing equations on a body fitted coordinate system, that is produced in preprocessor, integrates this equations on control volumes and determines the rate of quantities on control volume faces using order two (upwind)approximations. Finally by means of a pitot tube velocity magnitude of fluid in two sections of domain was measured and compared with numerical results which shows a good agreement. After simulation the three model, e.g. without distribution plate, with a distribution plate after inlet duct and with two distribution plates (one after inlet duct and before outlet duct), and taking some results and by comparing them, we conclude that use of combined distribution plate can give a good result

  11. Covariant field equations in supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

    2017-12-15

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  12. Covariant field equations in supergravity

    International Nuclear Information System (INIS)

    Vanhecke, Bram; Proeyen, Antoine van

    2017-01-01

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  13. 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.

  14. Divertor plate for thermonuclear reactor

    International Nuclear Information System (INIS)

    Yamazaki, Seiichiro; Sato, Keisuke; Nishio, Satoshi.

    1993-01-01

    In a divertor plate for a thermonuclear reactor, adjacent cooling pipes are electrically insulated from each other and pipes made of a gradient functional material prepared by compositing ceramics having an insulation property and metals are metallurgically joined to at least one portion of each of the cooling pipes. Electric current caused upon occurrence of plasma disruption is interrupted by the insulation portion, so that a large circuit is not formed and electromagnetic force is decreased to such a extent that the divertor plate is not ruptured. Since a header of the cooling pipes can be installed at any optional position, the installation space can be reduced. Further, since inlet and exit collection headers can be disposed on both ends of the cooling pipes, it is possible to shorten the length of the cooling pipe of the divertor plate corresponded to high heat fluxes and reduce the pressure loss on the side of coolants to about 1/2. Further, turn back portions of small radius of curvature of the cooling pipes are eliminated to reduce the cost and extend the lifetime and, in addition, protection tiles can be attached easily. (N.H.)

  15. Nonlinear dynamics and control of a vibrating rectangular plate

    Science.gov (United States)

    Shebalin, J. V.

    1983-01-01

    The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

  16. 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.

  17. Nonlinear morphoelastic plates I: Genesis of residual stress

    KAUST Repository

    McMahon, J.; Goriely, A.; Tabor, M.

    2011-01-01

    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.

  18. Vortex molecule in a nanoscopic square superconducting plate

    International Nuclear Information System (INIS)

    Suematsu, Hisataka; Kato, Masaru; Ishida, Takekazu; Koyama, Tomio; Machida, Masahiko

    2010-01-01

    Using the finite element method and solving the Bogoliubov-de Gennes equation, we have investigated magnetic field dependence of the stable vortex structures in a mesoscopic superconducting plate at low temperature (T = 0.1T c ). Because of the compactness of vortex configuration, there is interference between bound states around vortices and such quasi-particle structure affects the vortex configuration. Especially in two-vortices state, vortices form a molecule-like state, where bound states of each vortex form molecular orbital like bonding and anti-bonding states. The vortex configuration is different from that, which is expected from the repulsive interaction between vortices. (author)

  19. Differential Equation over Banach Algebra

    OpenAIRE

    Kleyn, Aleks

    2018-01-01

    In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

  20. 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

  1. Moving Divertor Plates in a Tokamak

    International Nuclear Information System (INIS)

    Zweben, S.J.; Zhang, H.

    2009-01-01

    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

  2. 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

  3. Strength of Ship Plates under Combined Loading

    DEFF Research Database (Denmark)

    Cui, W.; Wang, Y.; Pedersen, Preben Terndrup

    2002-01-01

    Strength of ship plates plays a significant role in the ultimate strength analysis of ship structures. In recent years several authors have proposed simplified analytical methods to calculate the ultimate strength of unstiffened plates. The majority of these investigations deal with plates subjec...

  4. Strength of ship plates under combined loading

    DEFF Research Database (Denmark)

    Cui, Weiching; Wang, Yongjun; Pedersen, Preben Terndrup

    2000-01-01

    Strength of ship plates plays a significant role for the ultimate strength analysis of ship structures. In recent years several authors have proposed simplified methods to calculate the ultimate strength of unstiffened plates. The majority of these investigations deal with plates subjected to lon...

  5. Operational test of bonded magnetocaloric plates

    DEFF Research Database (Denmark)

    Bahl, Christian; Navickaité, Kristina; Neves Bez, Henrique

    2017-01-01

    Bonded plates made by hot pressing La0.85Ce0.15Fe11.25Mn0.25Si1.5Hy particles and resin have been tested as active magnetic regenerators in a small scale magnetocaloric device. Firstly the plates were carefully characterised magnetically and thermally. The plates were prepared with 5 wt% resin...

  6. 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.

  7. Forced and free convection hydromagnetic flow past a vertical flat plate

    International Nuclear Information System (INIS)

    Abdelkhalek, M.M.

    2004-01-01

    The effects of magnetic field and temperature heat source on the free and forced convection flow past an infinite vertical plate is studied analytically. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using perturbation technique. The expression for the velocity field, skin friction and Nusselt number have been obtained

  8. Vibrations And Deformations Of Moderately Thick Plates In Stochastic Finite Element Method

    Directory of Open Access Journals (Sweden)

    Grzywiński Maksym

    2015-12-01

    Full Text Available The paper deals with some chosen aspects of stochastic dynamical analysis of moderately thick plates. The discretization of the governing equations is described by the finite element method. The main aim of the study is to provide the generalized stochastic perturbation technique based on classical Taylor expansion with a single random variable.

  9. Laminar dispersion in parallel plate sections of flowing systems used in analytical chemistry and chemical engineering

    NARCIS (Netherlands)

    Kolev, S.D.; Kolev, Spas D.; van der Linden, W.E.

    1991-01-01

    An exact solution of the convective-diffusion equation for fully developed parallel plate laminar flow was obtained. It allows the derivation of theoretical relationships for calculating the Peclet number in the axially dispersed plug flow model and the concentration distribution perpendicular to

  10. Asymmetric Vibrations of a Circular Elastic Plate on an Elastic Half Space

    DEFF Research Database (Denmark)

    Schmidt, H.; Krenk, Steen

    1982-01-01

    The asymmetric problem of a vibrating circular elastic plate in frictionless contact with an elastic half space is solved by an integral equation method, where the contact stress appears as the unknown function. By a trigonometric expansion, the problem is reduced to a number of uncoupled two...

  11. FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

    OpenAIRE

    Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

    2014-01-01

    Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

  12. FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

    Directory of Open Access Journals (Sweden)

    Bazhenov V.A.

    2014-06-01

    Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

  13. MHD free convection flow past an oscillating plate in the presence of ...

    African Journals Online (AJOL)

    The study of unsteady magnetohydrodynamic heat and mass transfer in MHD flow past an infinite vertical oscillating plate through porous medium, taking account of the presence of free convection and mass transfer. The energy and chemical species equations are solved in closed form by Laplace-transform technique and ...

  14. Auto-ignition of methane-air mixtures flowing along an array of thin catalytic plates

    Science.gov (United States)

    Treviño, C.

    2010-12-01

    In this paper, the heterogeneous ignition of a methane-air mixture flowing along an infinite array of catalytic parallel plates has been studied by inclusion of gas expansion effects and the finite heat conduction on the plates. The system of equations considers the full compressible Navier-Stokes equations coupled with the energy equations of the plates. The gas expansion effects which arise from temperature changes have been considered. The heterogeneous kinetics considers the adsorption and desorption reactions for both reactants. The limits of large and small longitudinal thermal conductance of the plate material are analyzed and the critical conditions for ignition are obtained in closed form. The governing equations are solved numerically using finite differences. The results show that ignition is more easily produced as the longitudinal wall thermal conductance increases, and the effects of the gas expansion on the catalytic ignition process are rather small due to the large value of the activation energy of the desorption reaction of adsorbed oxygen atoms.

  15. Numerical solution of the problems for plates on partial internal supports of complicated configurations

    International Nuclear Information System (INIS)

    Quang A, Dang; Hai, Truong Ha

    2014-01-01

    Very recently in the work S imple Iterative Method for Solving Problems for Plates with Partial Internal Supports, Journal of Engineering Mathematics, DOI: 10.1007/s10665-013-9652-7 (in press) , we proposed a numerical method for solving some problems of plates on one and two line partial internal supports (LPIS). In the essence they are problems with strongly mixed boundary conditions for biharmonic equation. Using this method we reduced the problems to a sequence of boundary value problems for the Poisson equation with weakly mixed boundary conditions, which are easily solved numerically. The advantages of the method over other ones were shown. In this paper we apply the method to plates on internal supports of more complicated configurations. Namely, we consider the case of three LPIS and the case of the cross support. The convergence of the method is established theoretically and its efficiency is confirmed on numerical experiments

  16. Damage of plates due to impact, dynamic pressure and explosive loads

    Directory of Open Access Journals (Sweden)

    Norman Jones

    Full Text Available It is the purpose of this article to present design equations which can be used to predict the damage of ductile plating when subjected to mass impact, dynamic pressure or impulsive loadings. The external loadings are sufficiently severe to produce inelastic material behaviour and produce finite transverse displacement, or geometry change, effects. The damage is characterised as the final or permanent transverse displacement of a plate. The theoretical method predicts values for the maximum permanent transverse displacements which agree reasonably well with the corresponding experimental results generated on aluminium alloy circular, square and rectangular plates. Thus, the equations presented in this article are valuable for preliminary design purposes and for forensic studies, while the experimental data can be used for validating numerical schemes.

  17. 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)

  18. Frequency dependence of magnetic shielding performance of HTS plates in mixed states

    International Nuclear Information System (INIS)

    Kamitani, Atsushi; Yokono, Takafumi; Yokono, Takafumi

    2000-01-01

    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 ω. The results of computations show that the HTS plate has a possibility of shielding the high-frequency magnetic field with ω > or approx. 1 kHz. (author)

  19. Modeling and analysis of waves in a heat conducting thermo-elastic plate of elliptical shape

    Directory of Open Access Journals (Sweden)

    R. Selvamani

    Full Text Available Wave propagation in heat conducting thermo elastic plate of elliptical cross-section is studied using the Fourier expansion collocation method based on Suhubi's generalized theory. The equations of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermo elastic plate of elliptical cross-sections composed of homogeneous isotropic material. The frequency equations are obtained by using the boundary conditions along outer and inner surface of elliptical cross-sectional plate using Fourier expansion collocation method. The computed non-dimensional frequency, velocity and quality factor are plotted in dispersion curves for longitudinal and flexural (symmetric and antisymmetric modes of vibrations.

  20. Plate tectonics, habitability and life

    Science.gov (United States)

    Spohn, Tilman; Breuer, Doris

    2016-04-01

    The role of plate tectonics in defining habitability of terrestrial planets is being increasingly discussed (e.g., Elkins-Tanton, 2015). Plate tectonics is a significantly evolved concept with a large variety of aspects. In the present context, cycling of material between near surface and mantle reservoirs is most important. But increased heat transport through mixing of cold lithosphere with the deep interior and formation of continental crust may also matter. An alternative mechanism of material cycling between these reservoirs is hot-spot volcanism combined with crust delamination. Hot-spot volcanism will transport volatiles to the atmosphere while delamination will mix crust, possibly altered by sedimentation and chemical reactions, with the mantle. The mechanism works as long as the stagnant lithosphere plate has not grown thicker than the crust and as long as volcanic material is added onto the crust. Thermal evolution studies suggest that the mechanism could work for the first 1-2 Ga of planetary evolution. The efficiency of the mechanism is limited by the ratio of extrusive to intrusive volcanism, which is thought to be less than 0.25. Plate tectonics would certainly have an advantage by working even for more evolved planets. A simple, most-used concept of habitability requires the thermodynamic stability of liquid water on the surface of a planet. Cycling of CO2between the atmosphere, oceans and interior through subduction and surface volcanism is an important element of the carbonate-silicate cycle, a thermostat feedback cycle that will keep the atmosphere from entering into a runaway greenhouse. Calculations for a model Earth lacking plate tectonics but degassing CO2, N, and H2O to form a surface ocean and a secondary atmosphere (Tosi et al, 2016) suggest that liquid water can be maintained on the surface for 4.5Ga. The model planet would then qualify as habitable. It is conceivable that the CO2 buffering capability of its ocean together with silicate

  1. 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.

  2. Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

    Science.gov (United States)

    Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

    2018-04-01

    In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.

  3. Entropy Generation on Nanofluid Flow through a Horizontal Riga Plate

    Directory of Open Access Journals (Sweden)

    Tehseen Abbas

    2016-06-01

    Full Text Available In this article, entropy generation on viscous nanofluid through a horizontal Riga plate has been examined. The present flow problem consists of continuity, linear momentum, thermal energy, and nanoparticle concentration equation which are simplified with the help of Oberbeck-Boussinesq approximation. The resulting highly nonlinear coupled partial differential equations are solved numerically by means of the shooting method (SM. The expression of local Nusselt number and local Sherwood number are also taken into account and discussed with the help of table. The physical influence of all the emerging parameters such as Brownian motion parameter, thermophoresis parameter, Brinkmann number, Richardson number, nanoparticle flux parameter, Lewis number and suction parameter are demonstrated graphically. In particular, we conferred their influence on velocity profile, temperature profile, nanoparticle concentration profile and Entropy profile.

  4. Modelling of plate-out under gas-cooled reactor (GCR) accident conditions

    International Nuclear Information System (INIS)

    Taig, A.R.

    1981-01-01

    The importance of plate-out in mitigating consequences of gas-cooled reactor accidents, and its place in assessing these consequences, are discussed. The data requirements of a plate-out modelling program are discussed, and a brief description is given of parallel work programs on thermal/hydraulic reactor behaviour and fuel modelling, both of which will provide inputs to the plate-out program under development. The representation of a GCR system used in SRD studies is presented, and the equations governing iodine adsorption, desorption and transport round the circuit are derived. The status of SRD's plate-out program is described, and the type of sensitivity studies to be undertaken with the partially-developed computer program in order to identify the most useful lines for future research is discussed. (author)

  5. Calibration of a laboratory spectrophotometer for specular light by means of stacked glass plates.

    Science.gov (United States)

    Allen, W. A.; Richardson, A. J.

    1971-01-01

    Stacked glass plates have been used to calibrate a laboratory spectrophotometer, over the spectral range 0.5-2.5 microns, for specular light. The uncalibrated instrument was characterized by systematic errors when used to measure the reflectance and transmittance of stacked glass plates. Calibration included first, a determination of the reflectance of a standard composed of barium sulfate paint deposited on an aluminum plate; second, the approximation of the reflectance and transmittance residuals between observed and computed values by means of cubic equations; and, finally, the removal of the systematic errors by a computer. The instrument, after calibration, was accurate to 1% when used to measure the reflectance and transmittance of stacked glass plates.

  6. Magnetohydrodynamic unsteady flow of a Maxwell fluid past a flat plate

    International Nuclear Information System (INIS)

    Khandpur, S.L.; Ravi Kant

    1979-01-01

    A study of the equations describing the flow pattern set up in a linear electrically conducting viscoelastic fluid past an infinite flat plate in the presence of a transverse magnetic field has been made, when the plate is moving parallel to itself with an arbitrary time dependent velocity. The pressure is assumed to be uniform with initial velocity distribution in an exponential form. Operational methods are used to obtain the exact solutions for the velocity profiles. The effects of relaxation parameter of the fluid and magnetic field have been studied. Several particular cases are easily deduced of which two cases: (i) when the plate is moving in its own plane harmonically with time, and (ii) when the velocity of the plate is decaying exponentially with time, are discussed. (auth.)

  7. Theoretical study of chemical reaction effects on vertical oscillating plate with variable temperature

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2006-01-01

    Full Text Available An exact solution to the flow of a viscous incompressible unsteady flow past an infinite vertical oscillating plate with variable temperature and mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. Both the plate temperature and the concentration level near the plate are raised linearly with respect to time. The dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity and concentration are studied for different parameters like phase angle, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time are studied. The solutions are valid only for small values of time t. It is observed that the velocity increases with decreasing phase angle ωt or chemical reaction parameter. .

  8. The interaction of thermal radiation on vertical oscillating plate with variable temperature and mass diffusion

    Directory of Open Access Journals (Sweden)

    Muthucumaraswamy R.

    2006-01-01

    Full Text Available Thermal radiation effects on unsteady free convective flow of a viscous incompressible flow past an infinite vertical oscillating plate with variable temperature and mass diffusion has been studied. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised linearly with respect to time and the concentration level near the plate is also raised linearly with respect to time. An exact solution to the dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity, temperature and concentration are studied for different parameters like phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time are studied. It is observed that the velocity increases with decreasing phase angle ωt. .

  9. Modeling of damage evaluation in thin composite plate loaded by pressure loading

    Directory of Open Access Journals (Sweden)

    Dudinský M.

    2012-12-01

    Full Text Available This article presents the results of numerical analysis of elastic damage of thin laminated long fiber-reinforced composite plate consisting of unidirectional layers which is loaded by uniformly distributed pressure. The analysis has been performed by means of the finite element method (FEM. The numerical implementation uses layered plate finite elements based on the Kirchhoff plate theory. System of nonlinear equations has been solved by means of the Newton- Raphson procedure. Evolution of damage has been solved using the return-mapping algorithm based on the continuum damage mechanics (CDM. The analysis was performed using own program created in MATLAB. Problem of laminated fiber-reinforced composite plate fixed on edges for two different materials and three different laminate stacking sequences (LSS was simulated. Evolution of stresses vs. strains and also evolution of damage variables in critical points of the structure are shown.

  10. The influence of retention on the plate height in ion-exchange chromatography

    DEFF Research Database (Denmark)

    Hansen, Ernst; Mollerup, Jørgen

    2004-01-01

    The plate heights for the amino acid tyrosine (anion exchange) and the polypeptide aprotinin (cation exchange) were determined on a porous media (Resource 15) and a get filled media (HyperD 20) at salt concentrations ranging from weak to strong retention. At a constant velocity, measurements showed....... In this article, the rate of mass transfer in the particles is described by three different rate mechanisms, pore diffusion, solid diffusion, and parallel diffusion. The van Deemter equation was used to model the data to determine the mass-transfer properties. The development of the plate height with increasing...... retention revealed a characteristic behavior for each rate mechanism. In the pore diffusion model, the plate height increased toward a constant value at strong retention, while the plate height in the solid diffusion model decreased, approaching a constant value at strong retention. In the parallel...

  11. Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory

    Directory of Open Access Journals (Sweden)

    Yuwaraj Marotrao Ghugal

    Full Text Available Thermal stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to nonlinear thermal load through the thickness of laminated plates are presented by using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The validity of present theory is verified by comparing the results with those of classical plate theory and first order shear deformation theory and higher order shear deformation theory.

  12. Transport equation solving methods

    International Nuclear Information System (INIS)

    Granjean, P.M.

    1984-06-01

    This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

  13. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  14. Free vibration analysis of corroded steel plates

    Energy Technology Data Exchange (ETDEWEB)

    Eslami-Majd, Alireza; Rahbar-Ranji, Ahmad [AmirKabir University of Technology, Tehran (Iran, Islamic Republic of)

    2014-06-15

    Vibration analysis of unstiffened/stiffened plates has long been studied due to its importance in the design and condition assessments of ship and offshore structures. Corrosion is inevitable in steel structures and has been so far considered in strength analysis of structures. We studied the free vibration of pitted corroded plates with simply supported boundary conditions. Finite element analysis, with ABAQUS, was used to determine the natural frequencies and mode shapes of corroded plates. Influential parameters including plate aspect ratio, degree of pit, one-sided/both-sided corroded plate, and different corrosion patterns were investigated. By increasing the degree of corrosion, reduction of natural frequency increases. Plate aspect ratio and plate dimensions have no influence on reduction of natural frequency. Different corrosion patterns on the surface of one-sided corroded plates have little influence on reduction of natural frequency. Ratio of pit depth over plate thickness has no influence on the reduction of natural frequency. The reduction of natural frequency in both-sided corroded plates is higher than one-sided corroded plates with the same amount of total corrosion loss. Mode shapes of vibration would change due to corrosion, except square mode shapes.

  15. Bottom nozzle for nuclear reactor fuel assembly having an adaptor plate and a coupled filtration plate

    International Nuclear Information System (INIS)

    Verdier, M.; Mortgat, R.

    1992-01-01

    The bottom nozzle includes an adaptor plate with openings to allow the passage of water and a filtration plate with small holes. The openings in the adaptor plate are symmetrical with regard to medians and diagonals. Within each zone, some of the openings are rectangular and some may be circular. The small holes in the filtration plate coincide with the rectangular openings in the adaptor plate

  16. METHOD OF MAKING AND PLATE CONNECTION

    Science.gov (United States)

    Patriarca, P.; Shubert, C.E.; Slaughter, G.M.

    1963-02-26

    This invention relates to a method of joining, by welding or brazing, a tube to a plate, particularly where the tube and the plate are of different thickness or have different thermal conductivities and are subject to high temperatures. In this method the tube is inserted in the core of a plate containing an annular groove in its back face concentric with the bore and in communication with the bore. One end of the tube is welded substantially flush with the front end of the plate. Brazing alloy is placed in the groove on the back face of the plate and heat is applied to the plate and tube to melt the brazing alloy to permit the alloy to flow into the bore and bond the tube to the plate. (AEC)

  17. PWR integral tie plate and locking mechanism

    International Nuclear Information System (INIS)

    Flora, B.S.; Osborne, J.L.

    1980-01-01

    A locking mechanism for securing an upper tie plate to the tie rods of a nuclear fuel bundle is described. The mechanism includes an upper tie plate assembly and locking sleeves fixed to the ends of the tie rods. The tie plate is part of the upper tie plate assembly and is secured to the fuel bundle by securing the entire upper tie plate assembly to the locking sleeves fixed to the tie rods. The assembly includes, in addition to the tie plate, locking nuts for engaging the locking sleeves, retaining sleeves to operably connect the locking nuts to the assembly, a spring biased reaction plate to restrain the locking nuts in the locked position and a means to facilitate the removal of the entire assembly as a unit from the fuel bundle

  18. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  19. Stochastic porous media equations

    CERN Document Server

    Barbu, Viorel; Röckner, Michael

    2016-01-01

    Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

  20. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

  1. Optimum Energy Extraction from Coherent Vortex Rings Passing Tangentially Over Flexible Plates

    Science.gov (United States)

    Pirnia, Alireza; Browning, Emily A.; Peterson, Sean D.; Erath, Byron D.

    2017-11-01

    Coherent vortical structures can incite self-sustained oscillations in flexible membranes. This concept has recently gained interest for energy extraction from ambient environments. In this study the special case of a vortex ring passing tangentially over a cantilevered flexible plate is investigated. This problem is governed by the Kirchhoff-Love plate equation, which can be expressed in terms of a non-dimensional mass parameter of the plate, non-dimensional pressure loading induced by the vortex ring, and a Strouhal (St) number which expresses the duration of pressure loading relative to the period of plate oscillation. For a plate with a fixed mass parameter immersed in a fluid environment, the St number specifies the beam dynamics and the energy exchange process. The aim of this study is to identify the St number corresponding to maximum energy exchange between plates and vortex rings. The energy exchange process between the vortex ring and the plate is investigated over a range of 0.3 transfer is reported in each case and an empirical correlation is provided for predictive purposes. Supported by the National Science Foundation (NSF) under Grant No. CBET-1511761, and the Natural Sciences and Engineering Research Council of Canada (NSERC), under Grant No. 05778-2015.

  2. Free vibration response of a multilayer smart hybrid composite plate with embedded SMA wires

    Directory of Open Access Journals (Sweden)

    K. Malekzadeh

    Full Text Available In this paper, free vibration response of a hybrid composite plate was studied. Effects of some geometrical, physical and material parameters on response of the composite plates embedded with shape memory alloy (SMA wires were investigated, which have not been reported in the literature thus far. Some of these parameters included important factors affecting free vibration response of the smart hybrid composite plates. The SMA wires were embedded within the layers of the composite laminate. First-order shear deformation theory (FSDT was utilized to obtain the governing equations of hybrid composite plates. Transverse shear and rotary inertia effects of the plate were taken into consideration. For simply-supported boundary conditions, systematic closed form solutions were obtained by Navier's technique. It was established that dynamic behavior of the smart hybrid composite plate depended on various parameters such as volume fraction, temperature dependent recovery stress and tensile pre-strain of SMA wires and aspect ratio of the laminated hybrid plate.

  3. Compounded natural convection enhancement in a vertical parallel-plate channel

    Energy Technology Data Exchange (ETDEWEB)

    Andreozzi, Assunta [Dipartimento di Energetica, Termofluidodinamica Applicata e Condizionamenti Ambientali, Universita degli Studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Campo, Antonio [Department of Mechanical Engineering, The University of Vermont, 33 Colchester Ave., Burlington, VT 05405 (United States); Manca, Oronzio [Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Universita degli Studi di Napoli, via Roma 29, Aversa (CE) 81031 (Italy)

    2008-06-15

    This paper addresses the natural convection behavior of air when heated in single vertical, parallel-plate channels. To enhance the heat transfer two passive schemes are combined: (1) an equidistant short plate is inserted at the inlet and (2) two parallel, colinear insulated plates are appended at the exit. The channel plates are symmetrically heated with a uniform heat flux. The computational procedure is made by solving the full elliptic Navier-Stokes and energy equations with the finite-volume methodology in an I-type computational domain that is much larger than the physical domain. Within the framework of a ''proof-of-concept'' the controlling Grashof number based on the heated plate height ranges between 10{sup 3} and 10{sup 6}. The numerical velocity, pressure and temperature fields are post-processed to compute the quantities of engineering interest such as the induced mass flow rate, the pressure at the channel mid-plane and the temperature along the plates. In addition, the Nusselt number and the average Nusselt number, both based on the heated plate height, are presented in graphical form. At the end, optimal channel configurations expressed in terms of the highest average Nusselt number are obtained for the pair of pre-assigned Grashof numbers. (author)

  4. Equations of mathematical physics

    CERN Document Server

    Tikhonov, A N

    2011-01-01

    Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

  5. Iteration of adjoint equations

    International Nuclear Information System (INIS)

    Lewins, J.D.

    1994-01-01

    Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs

  6. Systematic Equation Formulation

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2007-01-01

    A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

  7. Partial differential equations

    CERN Document Server

    Agranovich, M S

    2002-01-01

    Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener

  8. Generalized estimating equations

    CERN Document Server

    Hardin, James W

    2002-01-01

    Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th

  9. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  10. Vortex Dynamics around Pitching Plates

    Science.gov (United States)

    2014-04-29

    electrical signals are A/D converted in an ATI NetBox interface and recorded using a Java application, and are filtered in three steps. The first is a low...the plate while staying attached to the corners of the leading edge. During this process, a second vortex loop, created by the quick angular ...is a spike in CL centered around t = 0 due to non-circulatory6 effects from the angular acceleration of the wing. The amplitude of the peak is

  11. Micro plate fission chamber development

    International Nuclear Information System (INIS)

    Wang Mei; Wen Zhongwei; Lin Jufang; Jiang Li; Liu Rong; Wang Dalun

    2014-01-01

    To conduct the measurement of neutron flux and the fission rate distribution at several position in assemblies, the micro plate fission chamber was designed and fabricated. Since the requirement of smaller volume and less structure material was taken into consideration, it is convinient, commercial and practical to use fission chamber to measure neutron flux in specific condition. In this paper, the structure of fission chamber and process of fabrication were introduced and performance test result was presented. The detection efficiency is 91.7%. (authors)

  12. Non-cyanide silver plating

    International Nuclear Information System (INIS)

    Dini, J.W.

    1995-01-01

    Lawrence Livermore National Laboratory (LLNL) and Technic, Inc. have entered into a CRADA (Cooperative Research and Development Agreement) with the goal of providing industry with an environmentally benign alternative to the presently used silver cyanide plating process. This project has been in place for about six months and results are quite promising. The main objective, that of deposition of deposits as thick as 125 um (5 mils), has been met. Property data such as stress and hardness have been obtained and the structure of the deposit has been analyzed via metallography and x-ray diffraction. These results will be presented in this paper, along with plans for future work

  13. Three dimensional mathematical modeling of violin plate surfaces: An approach based on an ensemble of contour lines.

    Science.gov (United States)

    Piantadosi, Steven

    2017-01-01

    This paper presents an approach to describing the three dimensional shape of a violin plate in mathematical form. The shape description begins with standard contour lines and ends with an equation for a surface in three dimensional space. The traditional specification of cross sectional arching is unnecessary. Advantages of this approach are that it employs simple and universal description of plate geometry and yields a complete, smoothed, precise mathematical equation of the plate that is suitable for modern three dimensional production. It is quite general and suitable for both exterior and interior plate surfaces, yielding the ability to control thicknesses along with shape. This method can produce mathematical descriptions with tolerances easily less than 0.001 millimeters suitable for modern computerized numerical control carving and hand finishing.

  14. Numerical study on the effects of absorptivity on performance of flat plate solar collector of a water heater

    Science.gov (United States)

    Tambunan, D. R. S.; Sibagariang, Y. P.; Ambarita, H.; Napitupulu, F. H.; Kawai, H.

    2018-03-01

    The characteristics of absorber plate of a flat plate solar collector play an important role in the improvement of the performance. In this work, a numerical analysis is carried out to explore the effect of absorptivity and emissivity of absorber plate to the performance of the solar collector of a solar water heater. For a results comparison, a simple a simple solar box cooker with absorber area of 0.835 m × 0.835 m is designed and fabricated. It is employed to heat water in a container by exposing to the solar radiation in Medan city of Indonesia. The transient governing equations are developed. The governing equations are discretized and solved using the forward time step marching technique. The results reveal that the experimental and numerical results show good agreement. The absorptivity of the plate absorber and emissivity of the glass cover strongly affect the performance of the solar collector.

  15. Dynamics of a Circular Mindlin Plate under Mechanical Loading and Elevated Temperature

    Directory of Open Access Journals (Sweden)

    Warminska Anna

    2016-01-01

    Full Text Available Dynamics of a nonlinear circular Midlin plate is studied in the paper. The mathematical model represented by partial differential equations includes nonlinear geometrical terms resulted from large displacements. The plate is subjected to mechanical and thermal loadings. The dynamics of a coupled thermo-mechanical problem is reduced from partial to ordinary differential equations. Considering the first mode reduction and uniformly distributed temperature just a single nonlinear differential equation is obtained. The bifurcation analysis shows that elevated temperature shifts the rezonanse curve and new solutions arise. Depending on initial conditions this may lead to buckling phenomenon and then relatively small oscillations around this state, symmetric periodic oscillations of large amplitude, or irregular oscillations.

  16. Effect of magnetic field on Blasius and Sakiadis flow of nanofluids past an inclined plate

    Directory of Open Access Journals (Sweden)

    S.P. Anjali Devi

    2017-11-01

    Full Text Available A theoretical study on the effect of magnetic field on the classical Blasius and Sakiadis flow of nanofluids over an inclined plate is presented in this paper. The governing partial differential equations are converted into ordinary differential equations using suitable similarity transformations. The transformed boundary layer equations are solved numerically using MATLAB (bvp4c. Two types of nanoparticles are chosen namely copper and alumina in the base fluid of water with the Prandtl number (Pr = 6.2. The effects of the governing physical parameters over the velocity, temperature, skin friction coefficient and reduced Nusselt number for both the Blasius and Sakiadis flows are displayed graphically. The characteristics of physical and engineering interest are discussed in detail. Keywords: Nanofluid, Blasius flow, Sakiadis flow, MHD, Inclined plate, Mixed convection

  17. Analysis of wave equation in electromagnetic field by Proca equation

    International Nuclear Information System (INIS)

    Pamungkas, Oky Rio; Soeparmi; Cari

    2017-01-01

    This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

  18. Comparison of Kernel Equating and Item Response Theory Equating Methods

    Science.gov (United States)

    Meng, Yu

    2012-01-01

    The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

  19. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  20. Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

    OpenAIRE

    Wu, Lei

    2014-01-01

    We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

  1. Nonlinear streak computation using boundary region equations

    Energy Technology Data Exchange (ETDEWEB)

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

    2012-08-01

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

  2. Group-invariant solutions of nonlinear elastodynamic problems of plates and shells

    International Nuclear Information System (INIS)

    Dzhupanov, V.A.; Vassilev, V.M.; Dzhondzhorov, P.A.

    1993-01-01

    Plates and shells are basic structural components in nuclear reactors and their equipment. The prediction of the dynamic response of these components to fast transient loadings (e.g., loadings caused by earthquakes, missile impacts, etc.) is a quite important problem in the general context of the design, reliability and safety of nuclear power stations. Due to the extreme loading conditions a more adequate treatment of the foregoing problem should rest on a suitable nonlinear shell model, which would allow large deflections of the structures regarded to be taken into account. Such a model is provided in the nonlinear Donnell-Mushtari-Vlasov (DMV) theory. The governing system of equations of the DMV theory consists of two coupled nonlinear fourth order partial differential equations in three independent and two dependent variables. It is clear, as the case stands, that the obtaining solutions to this system directly, by using any of the general analytical or numerical techniques, would involve considerable difficulties. In the present paper, the invariance of the governing equations of DMV theory for plates and cylindrical shells relative to local Lie groups of local point transformations will be employed to get some advantages in connection with the aforementioned problem. First, the symmetry of a functional, corresponding to the governing equations of DMV theory for plates and cylindrical shells is studied. Next, the densities in the corresponding conservation laws are determined on the basis of Noether theorem. Finally, we study a class of invariant solutions of the governing equations. As is well known, group-invariant solutions are often intermediate asymptotics for a wider class of solutions of the corresponding equations. When such solutions are considered, the number of the independent variables can be reduced. For the class of invariant solutions studied here, the system of governing equations converts into a system of ordinary differential equations

  3. Comparative thermal buckling analysis of functionally graded plate

    Directory of Open Access Journals (Sweden)

    Čukanović Dragan V.

    2017-01-01

    Full Text Available A thermal buckling analysis of functionally graded thick rectangular plates accord¬ing to von Karman non-linear theory is presented. The material properties of the functionally graded plate, except for the Poisson’s ratio, were assumed to be graded in the thickness direction, according to a power-law distribution, in terms of the volume fractions of the metal and ceramic constituents. Formulations of equilibrium and stability equations are derived using the high order shear deformation theory based on different types of shape functions. Analytical method for determination of the critical buckling temperature for uniform increase of temperature, linear and non-linear change of temperature across thickness of a plate is developed. Numeri¬cal results were obtained in МATLAB software using combinations of symbolic and numeric values. The paper presents comparative results of critical buckling tempera¬ture for different types of shape functions. The accuracy of the formulation presented is verified by comparing to results available from the literature.

  4. Exact result in strong wave turbulence of thin elastic plates

    Science.gov (United States)

    Düring, Gustavo; Krstulovic, Giorgio

    2018-02-01

    An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

  5. Fire resistance of a steel plate reinforced concrete bearing wall

    International Nuclear Information System (INIS)

    Kodaira, Akio; Kanchi, Masaki; Fujinaka, Hideo; Akita, Shodo; Ozaki, Masahiko

    2003-01-01

    Samples from a steel plate reinforced concrete bearing wall composed of concrete slab sandwiched between studded steel plates, were subjected to loaded fire resistance tests. There were two types of specimens: some were 1800 mm high while the rest were 3000 mm high ; thickness and width were the same for all specimens, at 200 mm and 800 mm, respectively. Under constant load conditions, one side of each specimen was heated along the standard fire-temperature curve. The results enabled us to approximate the relationship between the ratio of working load to concrete strength N/(Ac x c σ b) and the fire resistance time (t: minutes), as equation (1) for the 1800 mm - high specimen, and equation (2) for the 3000 mm - high specimen. N/(Ac x c σ b) = 2.21 x (1/t) 0.323 (1), .N/(Ac x c σ b) 2.30 x (1/t) 0.378 (2) In addition, the temperature of the unheated side of the specimens was 100degC at 240 minutes of continuous heating, clearly indicating that there was sufficient heat insulation. (author)

  6. Thin-plate spline quadrature of geodetic integrals

    Science.gov (United States)

    Vangysen, Herman

    1989-01-01

    Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

  7. Parametric Studies of Flat Plate Trajectories Using VIC and Penalization

    Directory of Open Access Journals (Sweden)

    François Morency

    2018-01-01

    Full Text Available Flying debris is generated in several situations: when a roof is exposed to a storm, when ice accretes on rotating wind turbines, or during inflight aircraft deicing. Four dimensionless parameters play a role in the motion of flying debris. The goal of the present paper is to investigate the relative importance of four dimensionless parameters: the Reynolds number, the Froude number, the Tachikawa number, and the mass moment of inertia parameters. Flying debris trajectories are computed with a fluid-solid interaction model formulated for an incompressible 2D laminar flow. The rigid moving solid effects are modelled in the Navier-Stokes equations using penalization. A VIC scheme is used to solve the flow equations. The aerodynamic forces and moments are used to compute the acceleration and the velocity of the solid. A database of 64 trajectories is built using a two-level full factorial design for the four factors. The dispersion of the plate position at a given horizontal position decreases with the Froude number. Moreover, the Tachikawa number has a significant effect on the median plate position.

  8. Silicon-micromachined microchannel plates

    International Nuclear Information System (INIS)

    Beetz, Charles P.; Boerstler, Robert; Steinbeck, John; Lemieux, Bryan; Winn, David 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 ∼0.5 to ∼25 μm, 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 deposited or nucleated in the channels or the first strike surface. Results on resistivity, secondary emission and gain are presented

  9. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    The Raychaudhuri equation is central to the understanding of gravitational attraction in ... of K Gödel on the ideas of shear and vorticity in cosmology (he defines the shear. (eq. (8) in [1]) .... which follows from the definition of the scale factor l.

  10. Generalized reduced magnetohydrodynamic equations

    International Nuclear Information System (INIS)

    Kruger, S.E.

    1999-01-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics

  11. Calculus & ordinary differential equations

    CERN Document Server

    Pearson, David

    1995-01-01

    Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

  12. The Freudenstein Equation

    Indian Academy of Sciences (India)

    research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.

  13. Differential Equation of Equilibrium

    African Journals Online (AJOL)

    user

    ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...

  14. Equational binary decision diagrams

    NARCIS (Netherlands)

    J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)

    2000-01-01

    textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and

  15. Dunkl Hyperbolic Equations

    Directory of Open Access Journals (Sweden)

    Hatem Mejjaoli

    2008-12-01

    Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.

  16. Structural Equation Model Trees

    Science.gov (United States)

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2013-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

  17. ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...

    African Journals Online (AJOL)

    Keywords: Anthropometry, Predictive Equations, Percentage Body Fat, Nigerian Women, Bioelectric Impedance ... such as Asians and Indians (Pranav et al., 2009), ... size (n) of at least 3o is adjudged as sufficient for the ..... of people, gender and age (Vogel eta/., 1984). .... Fish Sold at Ile-Ife Main Market, South West Nigeria.

  18. dimensional Fokas equation

    Indian Academy of Sciences (India)

    However, one can associate the term with any solution of nonlinear partial differential equations (PDEs) which (i) represents a wave of permanent form, (ii) is localized ... In the past several decades, many methods have been proposed for solving nonlinear PDEs, such as ... space–time fractional derivative form of eq. (1) and ...

  19. A Quadratic Spring Equation

    Science.gov (United States)

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  20. Guiding center drift equations

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1979-03-01

    The quations for particle guiding center drift orbits are given in a new magnetic coordinate system. This form of the equations not only separates the fast motion along the lines from the slow motion across, but also requires less information about the magnetic field than many other formulations of the problem

  1. dimensional nonlinear evolution equations

    Indian Academy of Sciences (India)

    in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.

  2. Stochastic nonlinear beam equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan

    2005-01-01

    Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005

  3. Balancing Chemical Equations.

    Science.gov (United States)

    Savoy, L. G.

    1988-01-01

    Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)

  4. Buckling analysis for axially compressed flat plates, structural sections, and stiffened plates reinforced with laminated composites

    Science.gov (United States)

    Viswanathan, A. V.; Soong, T.; Miller, R. E., Jr.

    1971-01-01

    A classical buckling analysis is developed for stiffened, flat plates composed of a series of linked plate and beam elements. Plates are idealized as multilayered orthotropic elements. Structural beads and lips are idealized as beams. The loaded edges of the stiffened plate are simply-supported and the conditions at the unloaded edges can be prescribed arbitrarily. The plate and beam elements are matched along their common junctions for displacement continuity and force equilibrium in an exact manner. Offsets between elements are considered in the analysis. Buckling under uniaxial compressive load for plates, sections, and stiffened plates is investigated. Buckling loads are the lowest of all possible general and local failure modes, and the mode shape is used to determine whether buckling is a local or general instability. Numerical correlations with existing analysis and test data for plates, sections, and stiffened plates including boron-reinforced structures are discussed. In general correlations are reasonably good.

  5. Effect of partial heating at mid of vertical plate adjacent to porous medium

    Science.gov (United States)

    Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

    2018-05-01

    Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

  6. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  7. Quantum equations from Brownian motions

    International Nuclear Information System (INIS)

    Rajput, B.S.

    2011-01-01

    Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

  8. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  9. Aligned Magnetic Field, Radiation, and Rotation Effects on Unsteady Hydromagnetic Free Convection Flow Past an Impulsively Moving Vertical Plate in a Porous Medium

    Directory of Open Access Journals (Sweden)

    Sandeep Naramgari

    2014-01-01

    Full Text Available We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases.

  10. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  11. A theoretical response of the electrostatic parallel plate to constant and low-frequency accelerations

    International Nuclear Information System (INIS)

    Lee, Ki Bang

    2009-01-01

    A theoretical response of an electrostatic gap-closing actuator based on parallel plates to constant and low-frequency accelerations has been derived as a function of the applied acceleration and voltage. The nonlinear equation of motion is obtained in a dimensionless form from the fact that the inertial and damping forces are neglected at a frequency much less than the resonant frequency of the parallel plate, and thereafter the nonlinear equation is solved for the stable inter-plate gap at the acceleration and voltage. From the derived solution, the pull-in acceleration is obtained as a function of the applied voltage, and the pull-in voltage is also expressed as a function of the acceleration. The closed-form solution is validated by comparison with a numerical solution. The theoretical solution is in excellent agreement with the numerical results when the actuator is exposed to a constant acceleration as well as a low-frequency acceleration. The theoretical solution and pull-in acceleration and voltage thus provide guidance to prescribe operational constraints for devices that use the parallel plate actuator and to predict the response of the electrostatic gap-closing parallel plates to constant and low-frequency acceleration

  12. Vibration analysis of a trimorph plate as a precursor model for smart automotive bodywork

    International Nuclear Information System (INIS)

    Big-Alabo, A; Cartmell, M P

    2012-01-01

    This study investigates the vibration characteristics of a proposed candidate structure for smarter car bodies. The material is conceived as a three-layer laminated structure in the form of a trimorph plate. The vibration response of the plate is investigated for large deflections by considering the effects of geometric nonlinearity. First, the governing equation for the mid-point deflection of the plate is developed based on classical laminate plate theory (CLPT). The governing equation is solved, and a simulation is run for different possible layer-stacking sequences. Comparisons are made between the nonlinear vibration response of this trimorph plate both with and without the effects of the von Kármán geometric nonlinearity. The results show that for the same material properties the different layer-stacking sequences produce different vibration responses, and from there it is concluded that layer-stacking sequencing is a basis for the definition of a suitable material configuration for high performance automotive applications.

  13. Transient convective heat transfer to laminar flow from a flat plate with constant heat capacity

    International Nuclear Information System (INIS)

    Hanawa, Juichi

    1980-01-01

    Most basic transient heat transfer problem is the transient response characteristics of forced convection heat transfer in the flow along a flat plate or in a tube. In case of the laminar flow along a flat plate, the profile method using steady temperature distribution has been mostly adopted, but its propriety has not been clarified yet. About the unsteady heat transfer in the laminar flow along a flat plate, the analysis or experiment evaluating the heat capacity of the flat plate exactly was never carried out. The purpose of this study is to determine by numerical calculation the unsteady characteristics of the boundary layer in laminar flow and to confirm them by experiment concerning the unsteady heat transfer when a flat plate with a certain heat capacity is placed in parallel in uniform flow and given a certain quantity of heat generation suddenly. The basic equation and the solution are given, and the method of numerical calculation and the result are explained. The experimental setup and method, and the experimental results are shown. Both results were in good agreement, and the response of wall temperature, the response of Nusselt number and the change of temperature distribution in course of time were able to be determined by applying Laplace transformation and numerical Laplace inverse transformation to the equation. (Kako, I.)

  14. Three-Dimensional Elasticity Solutions for Sound Radiation of Functionally Graded Materials Plates considering State Space Method

    Directory of Open Access Journals (Sweden)

    Tieliang Yang

    2016-01-01

    Full Text Available This paper presents an analytical study for sound radiation of functionally graded materials (FGM plate based on the three-dimensional theory of elasticity. The FGM plate is a mixture of metal and ceramic, and its material properties are assumed to have smooth and continuous variation in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. Based on the three-dimensional theory of elasticity and state space method, the governing equations with variable coefficients of the FGM plate are derived. The sound radiation of the vibration plate is calculated with Rayleigh integral. Comparisons of the present results with those of solutions in the available literature are made and good agreements are achieved. Finally, some parametric studies are carried out to investigate the sound radiation properties of FGM plates.

  15. A solution for the Graetz problem in parallel plates, with axial heat conduction in the fluid and in the wall

    International Nuclear Information System (INIS)

    Biage, M.

    1983-04-01

    A heat transfer problem in parallel plates with infinite with has been solved, with axial heat conduction in the fluid and in the wall, considering steady-state laminar flow for a Newtonian fluid and a fully developed velocity profile. The duct consists of an infinite inicial part, insulated on both plates, an intermediale part of finite length, with a prescribed heat flux in the upper plate and insulated on the botton plate, and by another infinite part also insulated on both plates. The problem has been solved by a numerical combination of the integral equation method and the variational method. Both, the performance of the numerical technique employed and results obtained are analyzed in this work. It is demostrated that the heat conduction in the wall significantly modifies the heat transfer parameters. (Author) [pt

  16. Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories

    Science.gov (United States)

    Ghodrati, Behnam; Yaghootian, Amin; Ghanbar Zadeh, Afshin; Mohammad-Sedighi, Hamid

    2018-01-01

    In this paper, Lamb wave propagation in a homogeneous and isotropic non-classical micro/nano-plates is investigated. To consider the effect of material microstructure on the wave propagation, three size-dependent models namely indeterminate-, modified- and consistent couple stress theories are used to extract the dispersion equations. In the mentioned theories, a parameter called 'characteristic length' is used to consider the size of material microstructure in the governing equations. To generalize the parametric studies and examine the effect of thickness, propagation wavelength, and characteristic length on the behavior of miniature plate structures, the governing equations are nondimensionalized by defining appropriate dimensionless parameters. Then the dispersion curves for phase and group velocities are plotted in terms of a wide frequency-thickness range to study the lamb waves propagation considering microstructure effects in very high frequencies. According to the illustrated results, it was observed that the couple stress theories in the Cosserat type material predict more rigidity than the classical theory; so that in a plate with constant thickness, by increasing the thickness to characteristic length ratio, the results approach to the classical theory, and by reducing this ratio, wave propagation speed in the plate is significantly increased. In addition, it is demonstrated that for high-frequency Lamb waves, it converges to dispersive Rayleigh wave velocity.

  17. Rapidly Moving Divertor Plates In A Tokamak

    International Nuclear Information System (INIS)

    Zweben, S.

    2011-01-01

    It may be possible to replace conventional actively cooled tokamak divertor plates with a set of rapidly moving, passively cooled divertor plates on rails. These plates would absorb the plasma heat flux with their thermal inertia for ∼10-30 sec, and would then be removed from the vessel for processing. When outside the tokamak, these plates could be cooled, cleaned, recoated, inspected, and then returned to the vessel in an automated loop. This scheme could provide nearoptimal divertor surfaces at all times, and avoid the need to stop machine operation for repair of damaged or eroded plates. We describe various possible divertor plate designs and access geometries, and discuss an initial design for a movable and removable divertor module for NSTX-U.

  18. Methods for Equating Mental Tests.

    Science.gov (United States)

    1984-11-01

    1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

  19. Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA Approach

    Directory of Open Access Journals (Sweden)

    Zheng Ling

    2011-01-01

    Full Text Available Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an

  20. equateIRT: An R Package for IRT Test Equating

    Directory of Open Access Journals (Sweden)

    Michela Battauz

    2015-12-01

    Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

  1. Diffraction of a plane electromagnetic wave on a dielectric plate of variable density. [Field equatios, diffracted-wave angular distributions

    Energy Technology Data Exchange (ETDEWEB)

    Aivazyan, Yu M; Mergelyan, O S; Poulatov, M P

    1974-01-01

    Aproblem for the diffraction of a plane electromagnetic wave on a dielectric plate between two other dielectrics is solved. The dielectric constant of the plate depends periodically on three coordinates. From this solution it is possible to obtain the equations for fields and the angular distribution of diffracted waves for the particular cases of a crystal plate and a dielectric surface fluted in all directions. If the expansion is made in the variable of the electron density in crystals, the results will correspond to the problem for the X-ray diffraction on a crystal lattice, the values of the coefficient ..cap alpha -->..sub(tau) being determined by the lattice parameters.

  2. Hall effects on unsteady MHD reactive flow of second grade fluid through porous medium in a rotating parallel plate channel

    Science.gov (United States)

    Krishna, M. Veera; Swarnalathamma, B. V.

    2017-07-01

    We considered the transient MHD flow of a reactive second grade fluid through porous medium between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The governing equations are solved by Laplace transform technique. The effects of the pertinent parameters on the velocity, temperature are discussed in detail. The shear stress and Nusselt number at the plates are also obtained analytically and computationally discussed with reference to governing parameters.

  3. On the contact interaction of two identical stringers with an elastic semi-infinite continuous or vertically cracked plate

    Science.gov (United States)

    Grigoryan, M. S.

    2018-04-01

    This paper considers two connected contact problems on the interaction of stringers with an elastic semi-infinite plate. In the first problem, an elastic half-infinite continuous plate is reinforced on its boundary by two identical stringers exposed to a tensile external force. In the second problem, in the presence of the same stringers, the plate contains a collinear system of cracks on its vertical axis. The solution of both problems is reduced to the solution of singular integral equations (SIE) that are solved by a known numerical-analytical method.

  4. Sigmoid plate dehiscence: Congenital or acquired condition?

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Zhaohui, E-mail: lzhtrhos@163.com [Capital Medical University, Beijing Tongren Hospital, No 1 Dong Jiao Min Street, Dongcheng District, Beijing 100730 (China); Li, Jing, E-mail: lijingxbh@yahoo.com.cn [Capital Medical University, Beijing Tongren Hospital, No 1 Dong Jiao Min Street, Dongcheng District, Beijing 100730 (China); Zhao, Pengfei, E-mail: zhaopengf05@163.com [Capital Medical University, Beijing Friendship Hospital, No 95 Yongan Road, Xicheng District, Beijing 100050 (China); Lv, Han, E-mail: chrislvhan@126.com [Capital Medical University, Beijing Friendship Hospital, No 95 Yongan Road, Xicheng District, Beijing 100050 (China); Dong, Cheng, E-mail: derc007@sina.com [Capital Medical University, Beijing Friendship Hospital, No 95 Yongan Road, Xicheng District, Beijing 100050 (China); Liu, Wenjuan, E-mail: wenjuanliu@163.com [Jining No. 1 People' s Hospital, No. 6 Health Street, Jining 272100 (China); Wang, Zhenchang, E-mail: cjr.wzhch@vip.163.com [Capital Medical University, Beijing Friendship Hospital, No 95 Yongan Road, Xicheng District, Beijing 100050 (China)

    2015-05-15

    Highlights: • CT with multiplanar reformations can accurately display the sigmoid platet dehiscence. • The prevalence of sigmoid plate dehiscence was no significant difference among different age groups. • The size of sigmoid plate bony defects were not statistically different among different age groups. • The sigmoid plate dehiscence is more commonly a congenital than an acquired condition. - Abstract: Background and purpose: The imaging features of sigmoid plate dehiscence-induced pulsatile tinnitus have been presented. The origin of the sigmoid plate dehiscence, however, remains unclear. Our aim was to assess the prevalence and extent of sigmoid plate dehiscence on computed tomography (CT) images in multiple age groups to determine whether this condition is more likely to be congenital or acquired. Materials and methods: We retrospectively reviewed contrast-enhanced CT images of sigmoid plates of temporal bones in 504 patients. Each temporal bone was characterized as normal or dehiscent. Patients were then subcategorized into four age groups, and the prevalence and extent of dehiscent sigmoid plates in each group were calculated and compared. Results: Overall, 80 patients had sigmoid plate dehiscence, nine of whom had it bilaterally. In successively older age groups, the prevalences of sigmoid plate dehiscence were 18.9%, 20.1%, 14.5%, and 12.7%, respectively. Respective average anteroposterior bony defect diameters were 3.7 ± 1.7, 3.0 ± 1.3, 3.1 ± 1.5, and 3.0 ± 1.1 mm. Respective average vertical bony defect diameters were 3.6 ± 2.3, 2.6 ± 1.2, 3.2 ± 1.5, and 3.0 ± 1.7 mm. The prevalence and extent of sigmoid plate dehiscence were not statistically different among the four age groups. Conclusions: The similar radiologic prevalence and extent of dehiscent sigmoid plates among the age groups suggest that the dehiscence is more commonly a congenital than an acquired condition.

  5. Empirical Study of Car License Plates Recognition

    OpenAIRE

    Dina, Nasa Zata; Dailey, Matthew

    2015-01-01

    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 ...

  6. 431K/CD vehicle number plates

    CERN Multimedia

    GS Department

    2009-01-01

    The Green Plates Service, which is responsible for issuing the 431K/CD vehicle number plates , wishes to apologise for the delay in processing applications over the past weeks. The delay is outside the Service’s control, as it is due to the recent introduction of new rules governing the vehicle registration process in France. Normal service will be resumed as soon as possible. Thank you for your understanding. GS-SEM-LS – Green Plates Service

  7. Replacement divider plate performance under LOCA loading

    International Nuclear Information System (INIS)

    Huynk, H.M.; MClellan, G.H.; Schneider, W.G.

    1997-01-01

    A primary divider plate in a nuclear steam generator is required to perform its partitioning function with a minimum of cross leakage, without degradation in operating performance and without loss of structural integrity resulting from normal and accident loading. The design of the replacement divider plate for normal operating conditions is discussed in some detail in reference 1 and 2. This paper describes the structural response of the replacement divider plate to the severe loading resulting from a burst primary pipe. The loads for which the divider plate structural performance must be evaluated are mild to severe differential pressure transients resulting from several postulated sizes and types of pipe break scenarios. In the unlikely event of a severe Loss of Coolant Accident (LOCA) the divider plate or parts thereof must not exit the steam generator nor completely block the outlet nozzle. For the milder LOCA loads, the integrity of the divider plate and seat bars must be maintained. Analysis for the milder LOCA loads was carried out employing a conservative approach which ignores the actual interaction between the structure and the primary fluid. For these load cases it was shown that the divider plate does not become disengaged from the seat bars. For the more severe pipe breaks, the thermal-hydraulic analysis was coupled iteratively with the structural analysis, thereby taking into account divider plate deformation, in order to obtain a better prediction of the behaviour of the divider plate. In this manner substantial reduction in divider plate response to the more severe LOCA loading was achieved. It has been shown that, for the case of a postulated large LOCA (100% reactor inlet header), the disengagement of the divider plate from the seat bars resulted in an opening smaller than 1% of the divider plate area. (author)

  8. Sigmoid plate dehiscence: Congenital or acquired condition?

    International Nuclear Information System (INIS)

    Liu, Zhaohui; Li, Jing; Zhao, Pengfei; Lv, Han; Dong, Cheng; Liu, Wenjuan; Wang, Zhenchang

    2015-01-01

    Highlights: • CT with multiplanar reformations can accurately display the sigmoid platet dehiscence. • The prevalence of sigmoid plate dehiscence was no significant difference among different age groups. • The size of sigmoid plate bony defects were not statistically different among different age groups. • The sigmoid plate dehiscence is more commonly a congenital than an acquired condition. - Abstract: Background and purpose: The imaging features of sigmoid plate dehiscence-induced pulsatile tinnitus have been presented. The origin of the sigmoid plate dehiscence, however, remains unclear. Our aim was to assess the prevalence and extent of sigmoid plate dehiscence on computed tomography (CT) images in multiple age groups to determine whether this condition is more likely to be congenital or acquired. Materials and methods: We retrospectively reviewed contrast-enhanced CT images of sigmoid plates of temporal bones in 504 patients. Each temporal bone was characterized as normal or dehiscent. Patients were then subcategorized into four age groups, and the prevalence and extent of dehiscent sigmoid plates in each group were calculated and compared. Results: Overall, 80 patients had sigmoid plate dehiscence, nine of whom had it bilaterally. In successively older age groups, the prevalences of sigmoid plate dehiscence were 18.9%, 20.1%, 14.5%, and 12.7%, respectively. Respective average anteroposterior bony defect diameters were 3.7 ± 1.7, 3.0 ± 1.3, 3.1 ± 1.5, and 3.0 ± 1.1 mm. Respective average vertical bony defect diameters were 3.6 ± 2.3, 2.6 ± 1.2, 3.2 ± 1.5, and 3.0 ± 1.7 mm. The prevalence and extent of sigmoid plate dehiscence were not statistically different among the four age groups. Conclusions: The similar radiologic prevalence and extent of dehiscent sigmoid plates among the age groups suggest that the dehiscence is more commonly a congenital than an acquired condition

  9. Evaluation of korzincalloy prepared by Hohman Plating

    Energy Technology Data Exchange (ETDEWEB)

    Korinko, P. S. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Hollingshad, A. N. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

    2017-07-17

    A commercial vendor, Hohman Plating performed contract engineering work to determine the feasibility of producing pin hole free KorZincAlloy bronze material used for zinc gettering. Samples were tested for Sn plating thickness, heat treatability, and chemistry prior to being subjected to a standardized zinc exposure. The samples absorbed zinc and were examined using visual and scanning electron microscopy. Hohman Plating successfully produced KZA that met the target composition, was pin hole free, and was an effective zinc getter.

  10. Flow induced deformation and collapse of a thin rectangular plate with application to the Engineering Test Reactor nuclear fuel elements

    International Nuclear Information System (INIS)

    Davis, C.D.

    1981-01-01

    This work examines a single flat fuel plate bounded by two channels and determines static plate deflections, resultant forces and bending stresses due to pressure differential and hydrodynamic loadings. The classical then reactangular plate equations are used to model the fuel plate. These equations contain as an input the hydrodynamic loading function for modeling the fluid-structural interaction. Two models of the channel flow are developed. One assumes the accelerating potential core flow is laminar with developing two-dimensional laminar boundary layers being formed on the channel walls. The Schlichting entry length solution for developing laminar flow is found to be valid the entire length of the channel. The second model assumes the core flow is fully-developed turbulent the entire length of the channel. Hydrodynamic loading functions are developed for both flow models containing parameters for fluid density, fluid velocity, Reynolds number and channel and plate dimensions. Hence the effects of each parameter can be examined independently. A criterion is developed for predicting ETR fuel plate collapse at high channel flow velocities, 1067 cm/s (420 in/sec) (R/sub e/ = 60,000). The criterion predicts that in order to prevent ETR plate collapse the inlet velocities between channels must not differ by more than 2%

  11. Calculation of the heat flow peak in case of local defect of the fuel plate of a nuclear reactor

    International Nuclear Information System (INIS)

    Fabrega, Serge

    1965-11-01

    The author reports the calculation of the local thermal flow which exits a fuel plate in a nuclear reactor, where a fabrication defect creates a much localized peak of the power density released in the plate. He first reports the development of the problem equations: hypotheses and data, equation elaboration, simplification and resolution. He presents the results of a numeric application to actual cases, and describes how the conduction in the sheath is taken into account (study of the influence of peak width and shape), and gives a synthetic presentation of the formula for the approximate calculation of the heat flow in case of local defect [fr

  12. Locking screw-plate interface stability in carbon-fibre reinforced polyetheretherketone proximal humerus plates.

    Science.gov (United States)

    Hak, David J; Fader, Ryan; Baldini, Todd; Chadayammuri, Vivek B S

    2017-09-01

    Carbon-fibre reinforced polyetheretherketone (CFR-PEEK) plates have recently been introduced for proximal humerus fracture treatment. The purpose of this study was to compare the locking screw-plate interface stability in CFR-PEEK versus stainless steel (SS) proximal humerus plates. Locking screw mechanical stability was evaluated independently in proximal and shaft plate holes. Stiffness and load to failure were tested for three conditions: (1) on-axis locking screw insertion in CFR-PEEK versus SS plates, (2) on-axis locking screw insertion, removal, and reinsertion in CFR-PEEK plates, and (3) 10-degree off-axis locking screw insertion in CFR-PEEK plates. Cantilever bending at a rate of 1 mm/minute was produced by an Instron machine and load-displacement data recorded. Shaft locking screw load to failure was significantly greater in CFR-PEEK plates compared to SS plates (746.4 ± 89.7 N versus 596.5 ± 32.6 N, p PEEK plates (p PEEK plates. The mechanical stability of locking screws in CFR-PEEK plates is comparable or superior to locking screws in SS plates.

  13. Fuel cell cooler-humidifier plate

    Science.gov (United States)

    Vitale, Nicholas G.; Jones, Daniel O.

    2000-01-01

    A cooler-humidifier plate for use in a proton exchange membrane (PEM) fuel cell stack assembly is provided. The cooler-humidifier plate combines functions of cooling and humidification within the fuel cell stack assembly, thereby providing a more compact structure, simpler manifolding, and reduced reject heat from the fuel cell. Coolant on the cooler side of the plate removes heat generated within the fuel cell assembly. Heat is also removed by the humidifier side of the plate for use in evaporating the humidification water. On the humidifier side of the plate, evaporating water humidifies reactant gas flowing over a moistened wick. After exiting the humidifier side of the plate, humidified reactant gas provides needed moisture to the proton exchange membranes used in the fuel cell stack assembly. The invention also provides a fuel cell plate that maximizes structural support within the fuel cell by ensuring that the ribs that form the boundaries of channels on one side of the plate have ends at locations that substantially correspond to the locations of ribs on the opposite side of the plate.

  14. Maximizing band gaps in plate structures

    DEFF Research Database (Denmark)

    Halkjær, Søren; Sigmund, Ole; Jensen, Jakob Søndergaard

    2006-01-01

    periodic plate using Bloch theory, which conveniently reduces the maximization problem to that of a single base cell. Secondly, we construct a finite periodic plate using a number of the optimized base cells in a postprocessed version. The dynamic properties of the finite plate are investigated......Band gaps, i.e., frequency ranges in which waves cannot propagate, can be found in elastic structures for which there is a certain periodic modulation of the material properties or structure. In this paper, we maximize the band gap size for bending waves in a Mindlin plate. We analyze an infinite...... theoretically and experimentally and the issue of finite size effects is addressed....

  15. Metallized xerographic plates and their preparation

    International Nuclear Information System (INIS)

    1976-01-01

    Xerographic plates, particularly xeroradiographic plates, suitable for soft or hard x-ray exposure require margins or edges suitable for handling and mounting. In order to fabricate such plates, it is convenient to apply a peripheral mask over the substrate during application of at least the photoconductive layer. Use of masks, however, tend to promote peripheral plate irregularities usually because of scratches or other uneveness at or under the margin of the applied mask. Such imperfections spawn corresponding electrical field irregularities which can now be minimized or avoided altogether by grounding the margins with metal overcoats

  16. Bipolar plates for PEM fuel cells

    Science.gov (United States)

    Middelman, E.; Kout, W.; Vogelaar, B.; Lenssen, J.; de Waal, E.

    The bipolar plates are in weight and volume the major part of the PEM fuel cell stack, and are also a significant contributor to the stack costs. The bipolar plate is therefore a key component if power density has to increase and costs must come down. Three cell plate technologies are expected to reach targeted cost price levels, all having specific advantages and drawbacks. NedStack has developed a conductive composite materials and a production process for fuel cell plates (bipolar and mono-polar). The material has a high electric and thermal conductivity, and can be processed into bipolar plates by a proprietary molding process. Process cycle time has been reduced to less than 10 s, making the material and process suitable for economical mass production. Other development work to increase material efficiency resulted in thin bipolar plates with integrated cooling channels, and integrated seals, and in two-component bipolar plates. Total thickness of the bipolar plates is now less than 3 mm, and will be reduced to 2 mm in the near future. With these thin integrated plates it is possible to increase power density up to 2 kW/l and 2 kW/kg, while at the same time reducing cost by integrating other functions and less material use.

  17. Line Heat-Source Guarded Hot Plate

    Data.gov (United States)

    Federal Laboratory Consortium — Description:The 1-meter guarded hot-plate apparatus measures thermal conductivity of building insulation. This facility provides for absolute measurement of thermal...

  18. No quantum friction between uniformly moving plates

    Energy Technology Data Exchange (ETDEWEB)

    Philbin, T G; Leonhardt, U [School of Physics and Astronomy, University of St Andrews, North Haugh St Andrews, Fife KY16 9SS, Scotland (United Kingdom)], E-mail: tgp3@st-andrews.ac.uk

    2009-03-15

    The Casimir forces between two plates moving parallel to each other at arbitrary constant speed are found by calculating the vacuum electromagnetic stress tensor. The perpendicular force between the plates is modified by the motion but there is no lateral force on the plates. Electromagnetic vacuum fluctuations do not therefore give rise to 'quantum friction' in this case, contrary to previous assertions. The result shows that the Casimir-Polder force on a particle moving at constant speed parallel to a plate also has no lateral component.

  19. No quantum friction between uniformly moving plates

    International Nuclear Information System (INIS)

    Philbin, T G; Leonhardt, U

    2009-01-01

    The Casimir forces between two plates moving parallel to each other at arbitrary constant speed are found by calculating the vacuum electromagnetic stress tensor. The perpendicular force between the plates is modified by the motion but there is no lateral force on the plates. Electromagnetic vacuum fluctuations do not therefore give rise to 'quantum friction' in this case, contrary to previous assertions. The result shows that the Casimir-Polder force on a particle moving at constant speed parallel to a plate also has no lateral component.

  20. Lattice Wigner equation

    Science.gov (United States)

    Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

    2018-01-01

    We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

  1. Energy master equation

    DEFF Research Database (Denmark)

    Dyre, Jeppe

    1995-01-01

    energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk model—the energy master equation...... (EME)—is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...

  2. Classical Diophantine equations

    CERN Document Server

    1993-01-01

    The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...

  3. Flavored quantum Boltzmann equations

    International Nuclear Information System (INIS)

    Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean

    2010-01-01

    We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.

  4. Causal electromagnetic interaction equations

    International Nuclear Information System (INIS)

    Zinoviev, Yury M.

    2011-01-01

    For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.

  5. Imaging plates for nuclear radiations

    International Nuclear Information System (INIS)

    Abe, Ken; Takebe, Masahiro

    1997-01-01

    Full text. The imaging plate (IP, hereafter) is a new opto-electronic X-ray film developed by Fuji Photo Film Co. Ltd., formed with a large area of thin flexible plastic plate coated with photo-estimulable storage phosphor (e.g. Ba F Br: Eu 2+ ). Recently, it has been found highly sensitive to soft X-ray (SR), soft electrons, and also usual alpha, beta, gamma rays and others, e.g. cosmic rays, energy heavy ions, and moreover neutrons through suitable converters inside or outside of the IP. Many types of IP are now used in various fields, such as medical examinations, auto-radiography in vivo/ in situ/ in vitro, X-ray/neutron diffraction/ radiography, electron microscopy. RI contamination, assay of ore. The IP has other striking performances, e.e. extremely low intrinsic noises, a high position resolution, high detection efficiency (100-1000 times) as high as an X-ray film), extremely wide dynamic range of dose (more than 10 5 ). Besides the thermal fading yet left unresolved materially, the only feature lacking and that one has ben longing for is the radiation identification by itself. We found out that the IP has a full potential ability of radiation identification in itself. One evidence found is that the ratio of the twin peaks of the PSL (photo-stimulated luminescence) excitation spectra indicates simply the particle energies, studied and now established. Another is that the photo-beaching provides the fluorescent responses different enough to discriminate the radiations, yet in progress with cyclotron experiments, into the usage of double labeled bio tracers

  6. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  7. Equations of multiparticle dynamics

    International Nuclear Information System (INIS)

    Chao, A.W.

    1987-01-01

    The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions

  8. Electroweak evolution equations

    International Nuclear Information System (INIS)

    Ciafaloni, Paolo; Comelli, Denis

    2005-01-01

    Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings

  9. Differential equations with Mathematica

    CERN Document Server

    Abell, Martha L

    2004-01-01

    The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica

  10. Damped nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

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

    1976-01-01

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

  11. Fun with Differential Equations

    Indian Academy of Sciences (India)

    IAS Admin

    tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...

  12. Rotation and Radiation Effects on MHD Flow through Porous Medium Past a Vertical Plate with Heat and Mass Transfer

    Directory of Open Access Journals (Sweden)

    Uday Singh Rajput

    2017-11-01

    Full Text Available Effects of rotation and radiation on unsteady MHD flow past a vertical plate with variable wall temperature and mass diffusion in the presence of Hall current is studied here. Earlier we studied chemical reaction effect on unsteady MHD flow past an exponentially accelerated inclined plate with variable temperature and mass diffusion in the presence of Hall current. We had obtained the results which were in agreement with the desired flow phenomenon. To study further, we are changing the model by considering radiation effect on fluid, and changing the geometry of the model. Here in this paper we are taking the plate positioned vertically upward and rotating with velocity Ω . Further, medium of the flow is taken as porous. The plate temperature and the concentration level near the plate increase linearly with time. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations under consideration have been solved by Laplace transform technique. The model contains equations of motion, diffusion equation and equation of energy. To analyze the solution of the model, desirable sets of the values of the parameters have been considered. The governing equations involved in the flow model are solved by the Laplace-transform technique. The results obtained have been analyzed with the help of graphs drawn for different parameters. The numerical values obtained for the drag at boundary and Nusselt number have been tabulated. We found that the values obtained for velocity, concentration and temperature are in concurrence with the actual flow of the fluid

  13. Natural convective magneto-nanofluid flow and radiative heat transfer past a moving vertical plate

    Directory of Open Access Journals (Sweden)

    S. Das

    2015-03-01

    Full Text Available An investigation of the hydromagnetic boundary layer flow past a moving vertical plate in nanofluids in the presence of a uniform transverse magnetic field and thermal radiation has been carried out. Three different types of water-based nanofluids containing copper, aluminum oxide and titanium dioxide are taken into consideration. The governing equations are solved using Laplace transform technique and the solutions are presented in closed form. The numerical values of nanofluid temperature, velocity, the rate of heat transfer and the shear stress at the plate are presented graphically for several values of the pertinent parameters. The present study finds applications in engineering devices.

  14. Thermal resistance of a convectively cooled plate with applied heat flux and variable internal heat generation

    International Nuclear Information System (INIS)

    Venkataraman, N.S.; Cardoso, H.P.; Oliveira Filho, O.B. de

    1981-01-01

    The conductive heat transfer in a rectangular plate with nonuniform internal heat generation, with one end convectively cooled and a part of the opposite end subjected to external heat flux is considered. The remaining part of this end as well as the other two sides are thermally insulated. The governing differential equation is solved by a finite difference scheme. The variation of the thermal resistance with Biot modulus, the plate geometry, the internal heat generation parameter and the type of profile of internal heat generation is discussed. (author) [pt

  15. Heat transfer in porous medium embedded with vertical plate: Non-equilibrium approach - Part A

    Energy Technology Data Exchange (ETDEWEB)

    Badruddin, Irfan Anjum [Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 (Malaysia); Quadir, G. A. [School of Mechatronic Engineering, University Malaysia Perlis, Pauh Putra, 02600 Arau, Perlis (Malaysia)

    2016-06-08

    Heat transfer in a porous medium embedded with vertical flat plate is investigated by using thermal non-equilibrium model. Darcy model is employed to simulate the flow inside porous medium. It is assumed that the heat transfer takes place by natural convection and radiation. The vertical plate is maintained at isothermal temperature. The governing partial differential equations are converted into non-dimensional form and solved numerically using finite element method. Results are presented in terms of isotherms and streamlines for various parameters such as heat transfer coefficient parameter, thermal conductivity ratio, and radiation parameter.

  16. Heat transfer in porous medium embedded with vertical plate: Non-equilibrium approach - Part A

    International Nuclear Information System (INIS)

    Badruddin, Irfan Anjum; Quadir, G. A.

    2016-01-01

    Heat transfer in a porous medium embedded with vertical flat plate is investigated by using thermal non-equilibrium model. Darcy model is employed to simulate the flow inside porous medium. It is assumed that the heat transfer takes place by natural convection and radiation. The vertical plate is maintained at isothermal temperature. The governing partial differential equations are converted into non-dimensional form and solved numerically using finite element method. Results are presented in terms of isotherms and streamlines for various parameters such as heat transfer coefficient parameter, thermal conductivity ratio, and radiation parameter

  17. Simulation of Stress Concentration Problems in Laminated Plates by Quasi-Trefftz Finite Element Models

    Directory of Open Access Journals (Sweden)

    Flávio Luiz de Silva Bussamra

    Full Text Available Abstract Hybrid quasi-Trefftz finite elements have been applied with success to the analysis of laminated plates. Two independent fields are approximated by linearly independent, hierarchical polynomials: the stress basis in the domain, adapted from Papkovitch-Neuber solution of Navier equations, and the displacement basis, defined on element surface. The stress field that satisfies the Trefftz constraint a priori for isotropic material is adapted for orthotropic materials, which leads to the term "quasi". In this work, the hexahedral hybrid quasi-Trefftz stress element is applied to the modeling of nonsymmetric laminates and laminated composite plates with geometric discontinuities. The hierarchical p-refinement is exploited.

  18. Rigid-Plastic Post-Buckling Analysis of Columns and Quadratic Plates

    DEFF Research Database (Denmark)

    Jönsson, Jeppe

    2008-01-01

    the compressive load as a function of the transverse displacement. An estimate of the magnitude of the transverse displacement prior to the forming of the collapse mechanism is introduced into the compressive load function, determined by the virtual work equation, thereby revealing a qualified estimate...... yield lines accommodate differential rotations of rigid parts and the area “collapse” yield lines accommodate local area changes of the rigid parts thereby preserving compatibility of the rigid parts of a plate. The approach will be illustrated for rigid plastic column analysis and for a quadratic plate...

  19. Mathematics and Maxwell's equations

    International Nuclear Information System (INIS)

    Boozer, Allen H

    2010-01-01

    The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.

  20. Information Equation of State

    Directory of Open Access Journals (Sweden)

    M. Paul Gough

    2008-07-01

    Full Text Available Landauer’s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the ‘Why now?’ question we wonder ‘What next?’ as we expect the information equation of state to tend towards w = 0 in the future.c

  1. Generalized reduced MHD equations

    International Nuclear Information System (INIS)

    Kruger, S.E.; Hegna, C.C.; Callen, J.D.

    1998-07-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

  2. Application of a Brittle Damage Model to Normal Plate-on-Plate Impact

    National Research Council Canada - National Science Library

    Raftenberg, Martin N

    2005-01-01

    A brittle damage model presented by Grinfeld and Wright of the U.S. Army Research Laboratory was implemented in the LS-DYNA finite element code and applied to the simulation of normal plate-on-plate impact...

  3. Exact solution of nonsteady thermal boundary layer equation

    International Nuclear Information System (INIS)

    Dorfman, A.S.

    1995-01-01

    There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

  4. Analysis of Heat Transfer and Pressure Drop for a Gas Flowing Through a set of Multiple Parallel Flat Plates at High Temperatures

    Science.gov (United States)

    Einstein, Thomas H.

    1961-01-01

    Equations were derived representing heat transfer and pressure drop for a gas flowing in the passages of a heater composed of a series of parallel flat plates. The plates generated heat which was transferred to the flowing gas by convection. The relatively high temperature level of this system necessitated the consideration of heat transfer between the plates by radiation. The equations were solved on an IBM 704 computer, and results were obtained for hydrogen as the working fluid for a series of cases with a gas inlet temperature of 200 R, an exit temperature of 5000 0 R, and exit Mach numbers ranging from 0.2 to O.8. The length of the heater composed of the plates ranged from 2 to 4 feet, and the spacing between the plates was varied from 0.003 to 0.01 foot. Most of the results were for a five- plate heater, but results are also given for nine plates to show the effect of increasing the number of plates. The heat generation was assumed to be identical for each plate but was varied along the length of the plates. The axial variation of power used to obtain the results presented is the so-called "2/3-cosine variation." The boundaries surrounding the set of plates, and parallel to it, were assumed adiabatic, so that all the power generated in the plates went into heating the gas. The results are presented in plots of maximum plate and maximum adiabatic wall temperatures as functions of parameters proportional to f(L/D), for the case of both laminar and turbulent flow. Here f is the Fanning friction factor and (L/D) is the length to equivalent diameter ratio of the passages in the heater. The pressure drop through the heater is presented as a function of these same parameters, the exit Mach number, and the pressure at the exit of the heater.

  5. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  6. Dynamic Response of a Rigid Pavement Plate Based on an Inertial Soil.

    Science.gov (United States)

    Gibigaye, Mohamed; Yabi, Crespin Prudence; Alloba, I Ezéchiel

    2016-01-01

    This work presents the dynamic response of a pavement plate resting on a soil whose inertia is taken into account in the design of pavements by rational methods. Thus, the pavement is modeled as a thin plate with finite dimensions, supported longitudinally by dowels and laterally by tie bars. The subgrade is modeled via Pasternak-Vlasov type (three-parameter type) foundation models and the moving traffic load is expressed as a concentrated dynamic load of harmonically varying magnitude, moving straight along the plate with a constant acceleration. The governing equation of the problem is solved using the modified Bolotin method for determining the natural frequencies and the wavenumbers of the system. The orthogonal properties of eigenfunctions are used to find the general solution of the problem. Considering the load over the center of the plate, the results showed that the deflections of the plate are maximum about the middle of the plate but are not null at its edges. It is therefore observed that the deflection decreased 18.33 percent when the inertia of the soil is taken into account. This result shows the possible economic gain when taking into account the inertia of soil in pavement dynamic design.

  7. Flow over a traveling wavy foil with a passively flapping flat plate

    Science.gov (United States)

    Liu, Nansheng; Peng, Yan; Liang, Youwen; Lu, Xiyun

    2012-05-01

    Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The study reveals that the passively oscillating flat plate contributes half of the propulsive force. The flexibility, represented by the nondimensional natural frequency F, plays a very important role in the movement and propulsive force generation of the whole body. When the plate is too flexible, the drag force is observed. As the flat plate becomes more rigid, the propulsive force that is generated when the undulation is confined to last part of the wavy foil becomes larger. The steady movement occurs at F=5. These results are consistent with the observations of some swimming animals in nature.

  8. Reduction operators of Burgers equation.

    Science.gov (United States)

    Pocheketa, Oleksandr A; Popovych, Roman O

    2013-02-01

    The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

  9. A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets

    Science.gov (United States)

    Sahmani, Saeid; Aghdam, Mohammad Mohammadi; Rabczuk, Timon

    2018-04-01

    By gradually changing of the porosity across a specific direction, functionally graded porous materials (FGPMs) are produced which can impart desirable mechanical properties. To enhance these properties, it is common to reinforce FGPMs with nanofillers. The main aim of the current study is to investigate the size-dependent nonlinear axial postbuckling characteristics of FGPM micro/nano-plates reinforced with graphene platelets. For this purpose, the theory of nonlocal strain gradient elasticity incorporating the both stiffness reduction and stiffness enhancement mechanisms of size effects is applied to the refined exponential shear deformation plate theory. Three different patterns of porosity dispersion across the plate thickness in conjunction with the uniform one are assumed for FGPM as an open-cell metal foam is utilized associated with the coefficients of the relative density and porosity. With the aid of the virtual work’s principle, the non-classical governing differential equations are constructed. Thereafter, an improved perturbation technique is employed to capture the size dependencies in the nonlinear load-deflection and load-shortening responses of the reinforced FGPM micro/nano-plates with and without initial geometric imperfection. It is indicated that by increasing the value of porosity coefficient, the size-dependent critical buckling loads of reinforced FGPM micro/nano-plates with all types of porosity dispersion pattern reduce, but the associated shortening may increase or decrease which depends on the type of dispersion pattern.

  10. Heat transfer and flow analysis of nanofluid flow between parallel plates in presence of variable magnetic field using HPM

    Energy Technology Data Exchange (ETDEWEB)

    Hatami, M., E-mail: m.hatami@tue.nl [Esfarayen University of Technology, Mechanical Engineering Department, Esfarayen, North Khorasan (Iran, Islamic Republic of); Jing, Dengwei; Song, Dongxing [International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi' an 710049 (China); Sheikholeslami, M.; Ganji, D.D. [Department of Mechanical Engineering, Babol University of Technology, Babol (Iran, Islamic Republic of)

    2015-12-15

    In this study, effect of variable magnetic field on nanofluid flow and heat transfer analysis between two parallel disks is investigated. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy perturbation method. The analytical investigation is carried out for different governing parameters namely: squeeze number, suction parameter, Hartmann number, Brownian motion parameter, thermophrotic parameter and Lewis number. Results show that Nusselt number has direct relationship with Brownian motion parameter and thermophrotic parameter but it is a decreasing function of squeeze number, suction parameter, Hartmann number and Lewis number. - Highlights: • Heat and mass transfer of nanofluids between parallel plates investigated. • A variable magnetic field is applied on the plates. • Governing equations are solved analytically. • Effects of physical parameters are discussed on the Nusselt number.

  11. Heat transfer and flow analysis of nanofluid flow between parallel plates in presence of variable magnetic field using HPM

    International Nuclear Information System (INIS)

    Hatami, M.; Jing, Dengwei; Song, Dongxing; Sheikholeslami, M.; Ganji, D.D.

    2015-01-01

    In this study, effect of variable magnetic field on nanofluid flow and heat transfer analysis between two parallel disks is investigated. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy perturbation method. The analytical investigation is carried out for different governing parameters namely: squeeze number, suction parameter, Hartmann number, Brownian motion parameter, thermophrotic parameter and Lewis number. Results show that Nusselt number has direct relationship with Brownian motion parameter and thermophrotic parameter but it is a decreasing function of squeeze number, suction parameter, Hartmann number and Lewis number. - Highlights: • Heat and mass transfer of nanofluids between parallel plates investigated. • A variable magnetic field is applied on the plates. • Governing equations are solved analytically. • Effects of physical parameters are discussed on the Nusselt number

  12. Auxiliary equation method for solving nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Sirendaoreji,; Jiong, Sun

    2003-01-01

    By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

  13. Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

    Science.gov (United States)

    Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

    2012-01-01

    This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

  14. Steel plate reinforcement of orthotropic bridge decks

    NARCIS (Netherlands)

    Teixeira de Freitas, S.

    2012-01-01

    The PhD research is focused on the reinforcement of fatigue cracked orthotropic steel bridge decks (OBD) by adding a second steel plate to the existing deck. The main idea is to stiffen the existing deck plate, which will reduce the stresses at the fatigue sensitive details and extend the fatigue

  15. Plastic collapse load of corroded steel plates

    Indian Academy of Sciences (India)

    Keywords. Corroded steel plate; plastic collapse; FEM; rough surface. ... The main aim of present work is to study plastic collapse load of corroded steel plates with irregular surfaces under tension. Non-linear finite element method ... Department of Ocean Engineering, AmirKabir University of Technology, 15914 Tehran, Iran ...

  16. DOES TUBULARIZED INCISED PLATE URETHROPLASTY FIT

    African Journals Online (AJOL)

    posterior or proximal hypospadias. Patient age ranged from 22 months to 9 years (mean 5.4 years). Twenty-two cases were primary, while. 10 cases were repeat cases after failed onlay procedures with preserved urethral plate. Cases with severe chordee necessitating ex- cision of the urethral plate or with a very thin.

  17. Method of nickel-plating large components

    International Nuclear Information System (INIS)

    Wilbuer, K.

    1997-01-01

    The invention concerns a method of nickel-plating components, according to which even large components can be provided with an adequate layer of nickel which is pore- and stress-free and such that water is not lost. According to the invention, the component is heated and, after heating, is pickled, rinsed, scoured, plated in an electrolysis process, and rinsed again. (author)

  18. Improved nickel plating of Inconel X-750

    Science.gov (United States)

    Farmer, M. E.; Feeney, J. E.; Kuster, C. A.

    1969-01-01

    Electroplating technique with acid pickling provides a method of applying nickel plating on Inconel X-750 tubing to serve as a wetting agent during brazing. Low-stress nickel-plating bath contains no organic wetting agents that cause the nickel to blister at high temperatures.

  19. Application of viscoplastic constitutive equations in finite element programs

    International Nuclear Information System (INIS)

    Hornberger, K.; Stamm, H.

    1987-04-01

    The general mathematical formulation of frequently used viscoplastic constitutive equations is explained and Robinson's model is discussed in more detail. The implementation of viscoplastic constitutive equations into Finite Element programs (such as ABAQUS) is described using Robinson's model as an example. For the numerical integration both an explicit (explicit Euler) and an implicit (generalized midpoint rule) integration scheme is utilized in combination with a time step control strategy. In the implicit integration scheme, convergence in solving a system of nonlinear algebraic equation is improved introducing a projection method. The efficiency of the implemented procedures is demonstrated for different homogeneous load cases as well as for creep loading and strain controlled cyclic loading of a perforated plate. (orig./HP) [de

  20. Is There Really A North American Plate?

    Science.gov (United States)

    Krill, A.

    2011-12-01

    Lithospheric plates are typically identified from earthquake epicenters and evidence such as GPS movements. But no evidence indicates a plate boundary between the North American and South American Plates. Some plate maps show them separated by a transform boundary, but it is only a fracture zone. Other maps show an "undefined plate boundary" or put no boundary between these two plates (check Google images). Early plate maps showed a single large American Plate, quite narrow east of the Caribbean Plate (Le Pichon 1968, Morgan 1968). The North and South American Plates became established by the leading textbook Earth (Press & Siever 1974). On their map, from a Scientific American article by John Dewey (1972), these new plates were separated by an "uncertain plate boundary." The reasons for postulating a North American Plate were probably more psychological than geological. Each of the other continents of the world had its own plate, and North American geologists naturally wanted theirs. Similarly, European geographers used to view Europe as its own continent. A single large plate should again be hypothesized. But the term American Plate would now be ambiguous ("Which plate, North or South?") Perhaps future textbook authors could call it the "Two-American Plate." Textbook authors ultimately decide such global-tectonic matters. I became aware of textbook authors' opinions and influence from my research into the history of Alfred Wegener's continental drift (see Fixists vs. Mobilists by Krill 2011). Leading textbook author Charles Schuchert realized that continental drift would abolish his cherished paleogeographic models of large east-west continents (Eria, Gondwana) and small oceans (Poseiden, Nereis). He and his junior coauthors conspired to keep drift evidence out of their textbooks, from the 1934-editions until the 1969-editions (Physical Geology by Longwell et al. 1969, Historical Geology by Dunbar & Waage 1969). Their textbooks ruled in America. Textbooks

  1. Blast response of corroded steel plates

    Energy Technology Data Exchange (ETDEWEB)

    Eslamimajd, Alireza; RahbarRanji, Ahmad [AmirKabir University of Technology, Tehran (Korea, Republic of)

    2014-05-15

    Numerical results for one- and both-sided corroded steel plates subjected to blast loading are presented. Finite element analysis, with ABAQUS software, is employed to determine the deformation and stress distributions. The results for the case of triangular pulse pressure on un-corroded plates are validated against literature-based data and then, detailed parametric studies are carried-out. The effects of influential parameters including, plate aspect ratio, degree of pit and different ratio of pit depth at each sides of the plate are investigated. The results show that position of pitted surface in respect to applied pressure is the most influential parameter on reduction of dynamic load carrying capacity of pitted plates. By increasing degree of pitting, reduction of dynamic load carrying capacity decrease more.

  2. Heat receiving plates in thermonuclear device

    International Nuclear Information System (INIS)

    Kitamura, Kazunori.

    1988-01-01

    Purpose: To obtain a heat receiving plate structure capable of withstanding sputtering wear and retaining the thermal deformation and residual stress low upon junction and available at a reduced cost. Constitution: Junction structures between heat sinks and armours are the same as usual, whereas high melting armour (for example, made of tungsten) are used at the portion on a heat receiving plate where the thermal load and particle load are higher while materials having a heat expansion coefficient similar to that of the heat sink (stainless steel) are used at the portion where the thermal load and particle load are lower on a heat receiving plate depending on the thermal load and particle load distribution. This can reduce the thermal deformation for the entire divertor heat receiving plate to obtain a heat receiving plate of a good surface dimensional accuracy. (Takahashi, M.)

  3. High thermal load receiving heat plate

    International Nuclear Information System (INIS)

    Shibutani, Jun-ichi; Shibayama, Kazuhito; Yamamoto, Keiichi; Uchida, Takaho.

    1993-01-01

    The present invention concerns a high thermal load heat receiving plate such as a divertor plate of a thermonuclear device. The high thermal load heat receiving plate of the present invention has a cooling performance capable of suppressing the temperature of an armour tile to less than a threshold value of the material against high thermal loads applied from plasmas. Spiral polygonal pipes are inserted in cooling pipes at a portion receiving high thermal loads in the high temperature load heat receiving plate of the present invention. Both ends of the polygonal pipes are sealed by lids. An area of the flow channel in the cooling pipes is thus reduced. Heat conductivity on the cooling surface of the cooling pipes is increased in the high thermal load heat receiving plate having such a structure. Accordingly, temperature elevation of the armour tile can be suppressed. (I.S.)

  4. 2017 Bipolar Plate Workshop Summary Report

    Energy Technology Data Exchange (ETDEWEB)

    Kopasz, John P. [Argonne National Lab. (ANL), Argonne, IL (United States); Benjamin, Thomas G. [Argonne National Lab. (ANL), Argonne, IL (United States); Schenck, Deanna [Argonne National Lab. (ANL), Argonne, IL (United States)

    2017-08-17

    The Bipolar Plate (BP) Workshop was held at USCAR1 in Southfield, Michigan on February 14, 2017 and included 63 participants from industry, government agencies, universities, and national laboratories with expertise in the relevant fields. The objective of the workshop was to identify research and development (R&D) needs, in particular early-stage R&D, for bipolar plates for polymer electrolyte membrane (PEM) fuel cells for transportation applications. The focus of the workshop was on materials, manufacturing, and design aspects of bipolar plates with the goal of meeting DOE’s 2020 bipolar plate targets. Of special interest was the cost target of ≤$3/kW for the bipolar plate.

  5. Pyramidal approach to license plate segmentation

    Science.gov (United States)

    Postolache, Alexandru; Trecat, Jacques C.

    1996-07-01

    Car identification is a goal in traffic control, transport planning, travel time measurement, managing parking lot traffic and so on. Most car identification algorithms contain a standalone plate segmentation process followed by a plate contents reading. A pyramidal algorithm for license plate segmentation, looking for textured regions, has been developed on a PC based system running Unix. It can be used directly in applications not requiring real time. When input images are relatively small, real-time performance is in fact accomplished by the algorithm. When using large images, porting the algorithm to special digital signal processors can easily lead to preserving real-time performance. Experimental results, for stationary and moving cars in outdoor scenes, showed high accuracy and high scores in detecting the plate. The algorithm also deals with cases where many character strings are present in the image, and not only the one corresponding to the plate. This is done by the means of a constrained texture regions classification.

  6. New technique for number-plate recognition

    Science.gov (United States)

    Guo, Jie; Shi, Peng-Fei

    2001-09-01

    This paper presents an alternative algorithm for number plate recognition. The algorithm consists of three modules. Respectively, they are number plate location module, character segmentation module and character recognition module. Number plate location module extracts the number plate from the detected car image by analyzing the color and the texture properties. Different from most license plate location methods, the algorithm has fewer limits to the car size, the car position in the image and the image background. Character segmentation module applies connected region algorithm both to eliminate noise points and to segment characters. Touching characters and broken characters can be processed correctly. Character recognition module recognizes characters with HHIC (Hierarchical Hybrid Integrated Classifier). The system has been tested with 100 images obtained from crossroad and parking lot, etc, where the cars have different size, position, background and illumination. Successful recognition rate is about 92%. The average processing time is 1.2 second.

  7. HEAT AND MASS TRANSFER FOR VISCO-ELASTIC MHD BOUNDARY LAYER FLOW PAST A VERTICAL FLAT PLATE

    OpenAIRE

    Rita Choudhury; Hridi Ranjan Deb

    2012-01-01

    The two-dimensional free convection flow of visco-elastic and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to ordinary differential equation by introducing appropriate co-ordinate transformation. The analytical expressions for the velocity, temperature and species concentration fields have been obtained. The corresponding expressions for the non-dimensional rates of he...

  8. Differential Equations as Actions

    DEFF Research Database (Denmark)

    Ronkko, Mauno; Ravn, Anders P.

    1997-01-01

    We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....

  9. Partial differential equations

    CERN Document Server

    Levine, Harold

    1997-01-01

    The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.

  10. Ordinary differential equations

    CERN Document Server

    Cox, William

    1995-01-01

    Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further

  11. Partial differential equations

    CERN Document Server

    Sloan, D; Süli, E

    2001-01-01

    /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in

  12. Elliptic partial differential equations

    CERN Document Server

    Han, Qing

    2011-01-01

    Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo

  13. dimensional Jaulent–Miodek equations

    Indian Academy of Sciences (India)

    (2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...

  14. Equationally Noetherian property of Ershov algebras

    OpenAIRE

    Dvorzhetskiy, Yuriy

    2014-01-01

    This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.

  15. Neutron radiography using neutron imaging plate

    International Nuclear Information System (INIS)

    Chankow, Nares; Wonglee, Sarinrat

    2008-01-01

    Full text: The aims of this research are to study properties of neutron imaging plate, to obtain a suitable condition for neutron radiography and to use the neutron imaging plate for testing of materials nondestructively. The experiments were carried out by using a neutron beam from the Thai Research Reactor TRR-1/M1 at a power of 1.2 MW. A BAS-ND 2040 FUJI neutron imaging plate and a MX125 Kodak X-ray film/Gadolinium neutron converter screen combination were tested for comparison. It was found that the photostimulated light (PSL) read out of the imaging plate was directly proportional to the exposure time. It was also found that radiography with neutron using the imaging plate was approximately 40 times faster than the conventional neutron radiography using x-ray film/Gd converter screen combination. The sensitivity of the imaging plate to gamma-rays was investigated by using gamma-rays from an 192 Ir and a 60 Co radiographic sources. The imaging plate was found to be 5-6 times less sensitive to gamma-rays than a FUJI BAS-MS 2040 gamma-ray imaging plate. Finally, some specimens were selected to be radiographed with neutrons using the imaging plate and the x-ray film/Gd converter screen combination in comparison to x-rays. Parts containing light elements could be clearly observed by the two neutron radiographic techniques. It could be concluded that the image quality from the neutron imaging plate was comparable to the conventional x-ray film/Gd converter screen combination but the exposure time could be approximately reduced by a factor of 40

  16. The Dirac equation

    International Nuclear Information System (INIS)

    Thaller, B.

    1992-01-01

    This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics

  17. Cryostatic stability equation

    International Nuclear Information System (INIS)

    Sydoriak, S.G.

    1976-01-01

    Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings

  18. Solving Nonlinear Coupled Differential Equations

    Science.gov (United States)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  19. Completely integrable operator evolutionary equations

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1979-01-01

    The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)

  20. On the F-equation

    International Nuclear Information System (INIS)

    Kalinowski, M.W.; Szymanowski, L.

    1982-03-01

    A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)