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FREE VIBRATION ANALYSIS OF THIN RECTANGULAR ISOTROPIC CCCC PLATE USING TAYLOR SERIES FORMULATED SHAPE FUNCTION IN GALERKIN’S METHOD

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Author(s): K. O. Njoku | J. C. Ezeh | O. M. Ibearugbulem | L. O. Ettu | L. Anyaogu

Journal: Academic Research International
ISSN 2223-9944

Volume: 4;
Issue: 4;
Start page: 126;
Date: 2013;
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Keywords: Boundary Conditions | Free Vibration | Fundamental Natural Frequency | Galerkin’s Functional | Peculiar Shape Function | Taylor Series

ABSTRACT
In this study, Taylor series peculiar shape functions for CCCC isotropic thin rectangular plates were used on Galerkin’s functional to determine the fundamental frequency of the plate under vibration. The study involved a theoretical derivation of peculiar shape function by applying the boundary conditions of the plate on Taylorseries form of the plate equation. This initial result of the formulation was substituted on Galerkin’s functional to obtain equation for the fundamental frequency of the free vibrating plate. Non – dimensional frequency parameter “k” was determined fordifferent aspect ratios from 0.1 to 2.0 at an incremental rate of 0.1 respectively. The effectiveness of this method was demonstrated by comparing the solution obtained in the present study with existing approximate solution obtained from previous studies. The result as contained in table 2 show differences ranging from -0.0475% to6.0557% which are acceptable in statistics. Thus, we can conclude that the present method is a good approximate method for analyzing plates in vibration.
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