Thermal Effect on Vibration of Tapered Rectangular Plate

Anupam Khanna,Ashish Singhal

doi:10.1155/2014/642926

Anupam Khanna, Ashish Singhal

Open Access

https://doi.org/10.1155/2014/642926

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Abstract

A mathematical model is constructed to help the engineers in designing various mechanical structures mostly used in satellite and aeronautical engineering. In the present model, vibration of rectangular plate with nonuniform thickness is discussed. Temperature variations are considered biparabolic, that is, parabolic in x-direction and parabolic in y-direction. The fourth-order differential equation of the motion is solved by Rayleigh Ritz method for three different boundary conditions around the boundary of plate. Numerical values of frequencies for the first two modes of vibration are presented in tabular form for different values of thermal gradient, taper constants, and aspect ratio.

Highlights

The structures are designed to support the high speed engines and turbines subjected to the vibration
Lal et al [12] analyzed the transverse vibrations of nonhomogeneous rectangular plates of uniform thickness using boundary characteristic orthogonal polynomials
Computations have been made for calculating frequencies for different values of thermal gradient (α), taper constants (β1 and β2), and aspect ratio (a/b) for the first two modes of vibration

Summary

Introduction

The structures are designed to support the high speed engines and turbines subjected to the vibration. Leissa [2] discussed different models on free vibration of rectangular plates. Tomar and Gupta [4] studied the effect of thermal gradient on the vibration of a rectangular plate with bidirectional variation in thickness. Leissa [5] investigated the effect of thermal gradient on the vibration of parallelogram plate with bidirectional thickness variation in both directions. Gupta and Khanna [10] analyzed time period and deflection for the first two modes of vibrations of viscoelastic rectangular plate with linear thickness variations in both directions. Gupta and Khanna [11] had evaluated time period and deflection for the first two modes of vibration of viscoelastic rectangular plate for biparabolic thickness variation.

Materials and Methods

Results and Discussion

Comparison

Conclusions