Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution

Arun Kumar Gupta,Shanu Sharma

doi:10.1155/2014/392325

Abstract

The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness inx-direction subjected to linear temperature distribution inx-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant, and aspect ratio for the first two modes of vibrations.

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
Analysis of orthotropic trapezoidal plate under different conditions has always been an area of immense interest to researchers

Summary

Introduction

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. Tomar et al [2] attempted a problem of axisymmetric vibrations of an isotropic elastic nonhomogeneous circular plate of linearly varying thickness. Tomar et al [3] studied features of the free vibration of an isotropic nonhomogeneous infinite plate of parabolically varying thickness.

Results

Conclusion