Effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of rectangular plate

Anup Kumar,Amit Sharma,Neeraj Lather,Reeta Bhardwaj,Naveen Mani

doi:10.21595/vp.2018.20367

Abstract

In this paper, a theoretical analysis is carried out to investigate the effect of linear variation in density and circular variation in Poisson’s ratio on time period of frequency modes of rectangular plate with variable thickness under temperature field. The thickness variation is considered to be circular and temperature variation on the plate is assumed to be bi-linear. Rayleigh Ritz method is used to solve the differential equation. All the results (time period for first two modes of vibration) are presented with the help of tables.

Highlights

The study of vibration of non-homogeneous plate is essential in these days because non-homogeneous plate with variable thickness are used in almost all engineering structures such as power plants, wings of an aircrafts, machines, bridges etc
Vibration analysis of rectangular plates with rectangular cutouts is investigated by using extended Hencky bar-net method (HBM) [4]
The present study reveals the effect of plate parameters especially density and Poisson’s ratio on time period of vibration of clamped rectangular plate with variable thickness under temperature field

Summary

Introduction

The study of vibration of non-homogeneous plate is essential in these days because non-homogeneous plate with variable thickness are used in almost all engineering structures such as power plants, wings of an aircrafts, machines, bridges etc. Natural vibration of thick rectangular plate [7] without two parallel supported edges is studied and new analytic solutions are obtained. The effect of circular variation in density and exponential variation in Poisson’s ratio on vibrational frequency of parallelogram plate under temperature field is examined in [9]. The effect of two-dimensional thickness and temperature effect on natural vibration of parallelogram plate on clamped edges is studied using Rayleigh Ritz method [10]. EFFECT OF LINEAR VARIATION IN DENSITY AND CIRCULAR VARIATION IN POISSON’S RATIO ON TIME PERIOD OF VIBRATION OF RECTANGULAR PLATE. Authors show the effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of non homogeneous rectangular plate on clamped edges.

Analysis and assumptions

Solution for frequency equation and time period

Results and discussion

Conclusions