Vibration study of non-homogeneous trapezoidal plates of variable thickness under thermal gradient

Abstract

The aim of the present work is to study the free transverse vibrations of non-homogeneous trapezoidal plates of linear thickness variation in the x-direction under thermal gradient effect. The non-homogeneity of the plate is assumed to arise due to parabolic density variation in the y-direction. A two term deflection function has been taken for clamped-simply supported–clamped-simply supported boundary conditions. The Rayleigh-Ritz method is used to obtain a frequency equation for the first two modes of vibration. The effect of non-homogeneity constant, aspect ratios, taper constant and thermal gradient on the frequencies of non-homogeneous trapezoidal plate has been illustrated for the first two modes of vibration. Results are presented in graphical form. Confirmation of results in special cases with authors published one has also been presented.

Effect of density and Poisson’s ratio on thermal induced vibration of parallelogram plate

“…[3][4][5][6][7][8]. With the help of this model, author drags the attentions of the readers on two important aspects.…”

“…Gupta and Mamta [3] studied non linear thickness variation of non homogeneous rectangle plate using spline technique. Free vibration has been discussed by Gupta and Sharma [4] on trapezoidal plate with thickness variation under temperature effect. Rotary inertial effect in isotropic plates (uniform and tapered thickness) has been carried out in two companion papers by Kalita et al [5,6].…”

Vibration of rectangle plate with variable density and Poisson’s ratio

“…The mean square bending moment of a rectangular plate has been discussed in [9]. Rayleigh Ritz technique is used to calculate vibrational frequency of non-homogeneous trapezoidal plate [10] on clamped and simply supported edge condition. The effect of rotary inertia [11] on vibration of rectangular plate with central cutout is studied, using first order shear deformation theory.…”

Vibration of Skew Plate with Circular Variation in Thickness and Poisson’s Ratio

“…The effect of structural parameter on vibration of non homogeneous visco elastic rectangular plate has been studied by Khanna and Kaur [15]. Gupta and Sharma [16] studied free vibration of non-homogeneous trapezoidal plates with variable thickness under thermal gradient.…”