Abstract
The present of goal investigation is to study the effect of 2D linearly varying temperature on the vibrations of non-homogeneous trapezoidal plate whose thickness also varies linearly in both directions and density varies linearly in one direction. Boundary condition which is C-S-C-S with two term deflection is taken into consideration. Rayleigh-Ritz method is used to find the solution of the problem. The effect of other plate parameters such as non-homogeneity constant, taper constant and aspect ratios have also been studied. Results are calculated with accuracy and presented in tabular graphical form.
Highlights
Plate theory has been applied to reduce vibration and noise in structures since the end of the 19th century where it began with the work of German physicist Chladni, who discovered various modes of free vibrations experimentally
In marine and aerospace engineering fields, where lightweight structural elements with orthotropic materials are of primary importance, orthotropic trapezoidal plate has extensive application
Gupta and Sharma [9] studied the thermal effect on free vibration of orthotropic thin trapezoidal plate of linearly varying thickness
Summary
Plate theory has been applied to reduce vibration and noise in structures since the end of the 19th century where it began with the work of German physicist Chladni, who discovered various modes of free vibrations experimentally Since it has developed into an escalating and expansive field with a wide variety of theoretical and empirical techniques, dealing with increasingly complicated problems. In marine and aerospace engineering fields, where lightweight structural elements with orthotropic materials are of primary importance, orthotropic trapezoidal plate has extensive application. ANALYSIS OF FREE VIBRATION OF NON-HOMOGENOUS TRAPEZOIDAL PLATE WITH 2D VARYING THICKNESS AND THERMAL EFFECT. Gupta and Sharma [9] studied the thermal effect on free vibration of orthotropic thin trapezoidal plate of linearly varying thickness. The frequencies for the first two modes of vibration are obtained for C-S-C-S non-homogeneous trapezoidal plate by Rayleigh-Ritz method and display in the form of graphs
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