A theoretical mathematical model on vibration of rectangular plate is discussed. In this study, the vibration of the bi-parabolic tapered rectangular plate is analyzed under two different boundary conditions i.e. clamped (C-C-C-C) and simply supported (SS-SS-SS-SS). Also, the author considered bi-parabolic variation in the temperature field which occurs due to thermally induced vibration in rectangular plate. Results of frequency for the first two modes of vibration are obtained by using Rayleigh-Ritz method. Variations in frequency for first two modes of vibration at different values of structural parameters (thermal gradient, taper constants, and aspect ratio) and boundary conditions are well explained with the help of graphs.

The present study investigates the thermoelastic vibrational analysis of biexponential tapered triangular plates with substantial accuracy numerically using the classic Rayleigh-Ritz technique. Frequency for the first two modes of vibration is computed for different types of triangular plates viz. an isosceles right angle triangular plate, a right angle triangular plate, an acute angle scalene triangular plate, and an obtuse angle triangular plate under the exponential thermal condition at various values of structural parameter. A comprehensive and methodical presentation of the results of frequency for two boundary conditions viz. fully clamped (C−C−C) and fully simply-supported (SS−SS−SS) is provided in the section discussion of result.

This work deals with natural vibration of isotropic triangular plate under different geometrical and thermal conditions. In this paper, effects of bilinear tapering along with linear thermal condition are discussed for the vibration of triangular plates. Time period and deflection for both the modes of vibration for different types of clamped triangular plates, i.e., an isosceles triangular plate, right-angled triangular plate, and scalene triangular plate, are determined by using Rayleigh-Ritz method. Numerical results are calculated for different values of structural parameters, i.e., thermal gradient, taper parameters, and aspect ratios, and presented in tabular form.

In the present study, the effect of thermal gradient on the vibration of different types of triangular plates is discussed. Tapering in triangular plate is assumed bilinear. Variation in temperature of plate material is considered as linear in x -direction. The Rayleigh–Ritz technique is employed to evaluate the first two modes of frequency parameter for different values of thermal gradient, taper parameters and aspect ratios. The author reported frequency for both the modes of vibration for different types of clamped triangular plates, i.e., an isosceles triangular plate, right-angled isosceles triangular plate and scalene triangular plate. All numerical results are presented in tabular form.

A temperature-thickness coupling problem of non-homogeneous rectangular plate is analyzed. Here authors considered bi-parabolic variation in temperature i.e. parabolic in x-direction and parabolic in y-direction while variation in plate’s thickness is assumed bi-linear i.e. linear in x-direction and linear in y-direction. To characterize the non-homogeneity present in plate’s material, authors considered that poisson ratio and density of the plate’s material vary exponentially and linearly in one direction respectively. Along with, material of the plate is considered isotropic and visco-elastic. Rayleigh Ritz approach has been applied to find the time period and deflection for first two modes of vibration for diverse values of non-homogeneity constant, taper constant, density parameter, aspect ratio and thermal gradient. Results for both modes of vibration are shown in tabular form.

In this paper, authors studied the effect of varying structural parameters on vibration of non-homogeneous visco-elastic rectangular plate. Since a lot of factors affect the vibrational properties of plate, authors worked with some considerations. Here, authors assumed bi-linear thermal conductivity in the plate with non-uniform thickness. Non-uniformity in thickness is assumed parabolic in x-direction while non-homogeneity present in plate's material is assumed to vary exponentially in x-direction. Time period and deflection are calculated and tabulated for first two modes of vibration for different values of structural parameters i.e. non-homogeneity constant, taper constant, aspect ratio and thermal gradient.

Here, a theoretical model is presented to analyze the effect of bilinear temperature variations on vibration of non-homogeneous visco-elastic rectangular plate with non-uniform thickness. Non-uniformity in thickness of the plate is assumed linear in one direction. Since plate’s material is considered as non-homogeneous, authors characterized non-homogeneity in poisson ratio and density of the plate’s material exponentially in x-direction. Plate is supposed to be clamped at the ends. Deflection for first two modes of vibration is calculated by using Rayleigh–Ritz technique and tabulated for various values of plate’s parameters i.e. taper constant, aspect ratio, non-homogeneity constants and thermal gradient. Comparison of present findings with existing literature is also provided in tabular and graphical manner.

A mathematical model is developed for the use of design engineers to analyze temperature-thickness coupling problem of a non-homogeneous isotropic visco elastic rectangular plate. Here, authors considered that temperature varies bi-parabolic i.e. parabolic in x– and parabolic in y– direction while thickness of plate varies linearly in one direction. The non-homogeneity of the plate's material is characterized by assuming an exponential variation of poisson's ratio of the plate's material. The first two modes of time period and deflection are reported here for various combinations of frequency parameters i.e. non-homogeneity constant, thermal gradient, taper constant and aspect ratio of the plate. Numerical results for time period and deflection for both the modes of vibration are shown in tabular form.

In this paper, an analysis is presented about the effect of bi-parabolic temperature variations on mechanical vibrations of non-homogeneous rectangular plate which is clamped along the boundary. It is considered that thickness of plate varies linearly in x direction. Also, exponential variation in poisson ratio is taken due to non-homogeneity present in plate’s material. The governing differential equation is solved by the Rayleigh-Ritz method to calculate first two modes of frequencies for different values of taper constant, thermal gradient, aspect ratio and nonhomogeneity constant. All the numeric values of both the modes of frequency are given in tabular form. Mathematics Subject Classification 70J30