Effect of Non-Homogeneity on Thermally Induced Vibration of Orthotropic Visco-Elastic Rectangular Plate of Linearly Varying Thickness

Arun Kumar Gupta,Pooja Singhal

doi:10.4236/am.2010.14043

Abstract

The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection 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. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.

Highlights

Thermal effect on vibration of non-homogenous viscoelastic plates are of great interest in the field of engineering such as for better designing of gas turbines, jet engine, space craft and nuclear power projects, where metals and their alloys exhibits visco-elastic behavior
The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness
Johri and Vats [10] solved the problem of thermal effect on vibration of non-homogeneous orthotropic rectangular plate having bi-directional parabolically varying thickness

Summary

Introduction

Thermal effect on vibration of non-homogenous viscoelastic plates are of great interest in the field of engineering such as for better designing of gas turbines, jet engine, space craft and nuclear power projects, where metals and their alloys exhibits visco-elastic behavior. Tomar and Gupta [6,7,8] solved the vibration problem of orthotropic rectangular plate of varying thickness subjected to a thermal gradient. Johri and Vats [10] solved the problem of thermal effect on vibration of non-homogeneous orthotropic rectangular plate having bi-directional parabolically varying thickness. Gupta and Kumar [12] solved the vibration problem of non-homogeneous visco-elastic rectangular plate of linearly varying thickness subjected to linearly thermal effect. An analysis is presented in this paper is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. It is clamped supported on all the four edges. Time period and deflection for the first two modes of vibration are calculated for the various values of thermal gradients, non-homogeneity constant, aspect ratio and taper constant

Analysis

Solution and Frequency Equation

Time Functions of Vibration of Viscoelastic Plates

Results and Discussions