Free Transverse Vibration Analysis of thin rectangular plates having arbitrarily varying non-homogeneity along two concurrent edge

TL;DR

This study analyzes the free transverse vibration of thin rectangular plates with arbitrarily varying non-homogeneity along two edges, using Kirchhoff's theory and finite difference method to determine natural frequencies and mode shapes.

Contribution

It introduces a numerical approach to analyze vibration of non-homogeneous plates with linear property variation along edges, considering different boundary conditions.

Findings

Lowest three natural frequencies calculated for different boundary conditions.

Effect of non-homogeneity on vibration characteristics analyzed.

Mode shapes visualized in three dimensions.

Abstract

In this paper, I presented the analysis and numerical results for free transverse vibration of thin rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges. For finding the general governing differential equation first used the Kirchhoff's plate theory by considering their assumptions. After finding the governing equation for the plate. For the non- homogeneity a linear variation for Young's modulus and density of the plate has been assumed. Finite difference method (FDM) has been used to obtain the eigen value problem for such model plate for two different boundary condition at the edge namely (i) CCCC fully clamped (ii) CSCS two opposites are clamped and other two are simply supported. By solving these eigen value problem using MATLAB, the lowest three eigen value have been reported as the first three natural frequencies for the three mode of vibration. The effect of various plate parameters such on the vibration characteristics has been analysed. Three dimensional mode shape has been plotted.