The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Lalit Kumar - One of the best experts on this subject based on the ideXlab platform.
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vibration of non homogeneous visco elastic circular plate of linearly varying thickness in steady state temperature field
Journal of Theoretical and Applied Mechanics, 2010Co-Authors: A K Gupta, Lalit KumarAbstract:An analysis is presented for free vibration of a non-homogeneous visco-elastic circular plate with linearly varying thickness in the radial direction subjected to a linear temperature distribution in that direction. The Governing Differential Equation of motion for free vibration is obtained by the method of separation of variables. Rayleigh-Ritz's method has been applied. Deflection, time period and logarithmic decrement corresponding to the first two modes of vibrations of a clamped non-homogeneous visco-elastic circular plate for various values of non-homogeneity parameter, taper constant and thermal gradients are obtained and shown graphically for the Voigt-Kelvin model.
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effect of thermal gradient on vibration of non homogeneous visco elastic elliptic plate of variable thickness
Meccanica, 2009Co-Authors: Ankit Gupta, Lalit KumarAbstract:An analysis and numerical results are presented for free transverse vibrations of non-homogeneous visco-elastic elliptic plate whose temperature and thickness spatial variations both are parabolic along a line through plate centre. The variation in density is assumed as parabolic along a line through plate centre, which raise non-homogeneity of the plate materials and make problem interesting as introducing variation in non-homogeneity of the material mass density reduce the problem practical importance in comparison to homogenous plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The Governing Differential Equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement corresponding to the first two modes of vibrations of a clamped non-homogeneous visco-elastic elliptic plate for various values of taper constant, thermal constants, non-homogeneity constant and aspect ratio are obtained and shown graphically.
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effect of thermal gradient on free vibration of non homogeneous visco elastic rectangular plate of parabolically varying thickness
Acta technica ČSAV, 2009Co-Authors: A K Gupta, Lalit KumarAbstract:An analysis on free vibration of non-homogeneous visco-elastic rectangular plate with parabolically varying thickness subjected to linear temperature gradient is discussed. Vibrational behavior of non-homogeneous rectangular plates of variable thickness having two opposite edges simply supported is analyzed on the basis of classical plate theory. The other two edges are clamped. For non-homogeneity of the plate material, density are assumed to vary linearly in one direction. Using the method of separation of variables, the Governing Differential Equation is solved. The use of trigonometric sine function for the mode shapes between the simply supported edges reduces the Governing partial Differential Equation of motion for such plates to an ordinary Differential Equation with variable coefficients. Galerkin technique is applied. Deflection, time period and logarithmic decrement at different points for the first two modes of vibration are calculated for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio for non-homogenous rectangular plate which is clamped on two parallel edges and simply supported on remaining two edges. A comparison of the results is presented.
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thermal effect on vibration of non homogenous visco elastic rectangular plate of linearly varying thickness
Meccanica, 2008Co-Authors: Arun Gupta, Lalit KumarAbstract:An analysis for vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness subjected to thermal gradient has been discussed in the present investigation. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The Governing Differential Equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement at different points for the first two modes of vibration are calculated for various values of thermal gradients, non homogeneity constant, taper constant and aspect ratio for non-homogenous visco-elastic rectangular plate which is clamped on two parallel edges and simply supported on remaining two edges. Comparison studies have been carried out with homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.
Ankit Gupta - One of the best experts on this subject based on the ideXlab platform.
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effect of thermal gradient on vibration of non homogeneous visco elastic elliptic plate of variable thickness
Meccanica, 2009Co-Authors: Ankit Gupta, Lalit KumarAbstract:An analysis and numerical results are presented for free transverse vibrations of non-homogeneous visco-elastic elliptic plate whose temperature and thickness spatial variations both are parabolic along a line through plate centre. The variation in density is assumed as parabolic along a line through plate centre, which raise non-homogeneity of the plate materials and make problem interesting as introducing variation in non-homogeneity of the material mass density reduce the problem practical importance in comparison to homogenous plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The Governing Differential Equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement corresponding to the first two modes of vibrations of a clamped non-homogeneous visco-elastic elliptic plate for various values of taper constant, thermal constants, non-homogeneity constant and aspect ratio are obtained and shown graphically.
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study of the effect of thermal gradient on free vibration of clamped visco elastic rectangular plates with linearly thickness variation in both directions
Meccanica, 2008Co-Authors: Ankit Gupta, Harvinder KaurAbstract:The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations in both the directions has been studied here. The Governing Differential Equation has been solved using Rayleigh-Ritz technique. The frequency Equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped plate have been computed for various values of aspect ratio, thermal constants, and taper constants.
J.r. Banerjee - One of the best experts on this subject based on the ideXlab platform.
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free vibration analysis for plates with arbitrary boundary conditions using a novel spectral dynamic stiffness method
Computers & Structures, 2016Co-Authors: Xiang Liu, J.r. BanerjeeAbstract:Exact method for modal analysis of plates with arbitrary boundary conditions.Enhancement of the Wittrick-Williams algorithm by resolving the J0 count elegantly.Securing exact solutions for free vibration of plates for benchmark purposes.The method has two orders of magnitude higher computational efficiency than the FEM.Discussion and conclusions on a wide range of existing analytical and exact methods. An exact method for free vibration analysis of plates with arbitrary boundary conditions is presented. This is achieved by integrating the spectral method into the classical dynamic stiffness method. The formulation satisfies the Governing Differential Equation exactly and any arbitrary boundary conditions are satisfied in a series sense. The Wittrick-Williams algorithm is enhanced with several elegant techniques to obtain solutions. The exactness and computational efficiency of the method are demonstrated by comparing results obtained from other methods. Finally, mathematical and physical insights are gained and significant conclusions are drawn for various analytical methods for free vibration analysis of plates.
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Dynamic stiffness matrix development and free vibration analysis of a moving beam
Journal of Sound and Vibration, 2007Co-Authors: J.r. Banerjee, W.d. GunawardanaAbstract:Abstract The dynamic stiffness matrix of a moving Bernoulli–Euler beam is developed and used to investigate its free flexural vibration characteristics. In order to develop the dynamic stiffness matrix, it is necessary to derive and solve the Governing Differential Equation of motion of the moving beam in closed analytical form. The solution is then used to obtain the general expressions for both responses and loads. Boundary conditions are applied to determine the constants in the general solution, leading to the formation of the frequency dependent dynamic stiffness matrix of the moving beam, relating the amplitudes of the harmonically varying loads to those of the corresponding responses. The application of the resulting dynamic stiffness matrix using the Wittrick–Williams algorithm is demonstrated by some illustrative examples. Numerical results for both simply supported and fixed–fixed end conditions of the beam are discussed, and wherever possible, some are compared with those available in the literature.
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an exact dynamic stiffness matrix for coupled extensional torsional vibration of structural members
Computers & Structures, 1994Co-Authors: J.r. Banerjee, F W WilliamsAbstract:Abstract Exact analytical expressions for coupled extensional-torsional dynamic stiffness matrix elements of a uniform structural member are derived from the basic Governing Differential Equation of the member in free vibration. Application of the derived dynamic stiffness matrix is discussed with particular reference to an established algorithm. The theory developed is demonstrated by numerical results.
Sritawat Kitipornchai - One of the best experts on this subject based on the ideXlab platform.
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size effect on the free vibration of geometrically nonlinear functionally graded micro beams under electrical actuation and temperature change
Composite Structures, 2015Co-Authors: X.l. Jia, Sritawat Kitipornchai, Jie Yang, C B FengAbstract:This paper investigated the size effect on the free vibration of functionally graded micro-beams under the combined electrostatic force, temperature change and Casimir force based on Euler-Bernoulli beam theory and von Karman geometric nonlinearity. Taking into consideration the temperature-dependency of the effective material properties, material properties of the functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to the Voigt model and exponential distribution model. The principle of minimum total potential energy is used to derive the nonlinear Governing Differential Equation which is then solved using the Differential quadrature method (DQM). A parametric study is conducted to show the significant combined effects of the size effect, material gradient, temperature change, geometric parameters and Casimir force.
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thermal effect on the pull in instability of functionally graded micro beams subjected to electrical actuation
Composite Structures, 2014Co-Authors: X.l. Jia, Jie Yang, S M Zhang, Sritawat KitipornchaiAbstract:The thermal effect on the pull-in instability of functionally graded micro-beams under the combined electrostatic force, temperature change and Casimir force is studied based on Euler-Bernoulli beam theory and von Karman geometric nonlinearity. Take into consideration the temperature-dependency of the effective material properties, the Voigt model and exponential distribution model is used to simulate the material properties of the functionally graded materials (FGMs). Principle of virtual work is used to derive the nonlinear Governing Differential Equation which is then solved using the Differential quadrature method (DQM). A parametric study is conducted to show the significant effects of material composition, temperature change, geometric nonlinearity and Casimir force.
Harvinder Kaur - One of the best experts on this subject based on the ideXlab platform.
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study of the effect of thermal gradient on free vibration of clamped visco elastic rectangular plates with linearly thickness variation in both directions
Meccanica, 2008Co-Authors: Ankit Gupta, Harvinder KaurAbstract:The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations in both the directions has been studied here. The Governing Differential Equation has been solved using Rayleigh-Ritz technique. The frequency Equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped plate have been computed for various values of aspect ratio, thermal constants, and taper constants.
