Natural Frequencies of Thin Rectangular Plates using Homotopy-Perturbation Method

Meng Koon Lee, Mohammad Hosseini Fouladi, Satesh Namasivayam

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The homotopy perturbation method (HPM) was developed to search for asymptotic solutions of nonlinear problems involving parabolic partial differential equations with variable coefficients. This paper illustrates that HPM be easily adapted to solve parabolic partial differential equations with constant coefficients. Natural frequencies of a rectangular plate of uniform thickness, simply-supported on all sides, are obtained with minimum amount of computation. The solution is shown to converge rapidly to a combination of sine and cosine functions. Truncating the series solution by using only the first three terms of the sine and cosine functions as compared to the exact solution results in an absolute error not exceeding 2 × 10−4 and 9×10−4 for the trigonometric functions respectively. HPM is then applied to solve the nonlinear problem of a rectangular plate of variable thickness. A direct expression for the eigenvalues (natural frequencies) of the rectangular plate is obtained as compared to determining its eigenvalues by solving the characteristic equation using the conventional method. Comparison of results for the frequency parameter with existing literature show that HPM is highly efficient and accurate. Natural frequencies of a simply-supported guitar soundboard were obtained using an equivalent rectangular plate with the same boundary condition.
Original languageEnglish
Pages (from-to)524-543
Number of pages20
JournalApplied Mathematical Modelling
Volume50
Early online date12 Jun 2017
DOIs
Publication statusPublished - Oct 2017

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