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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 26081, 17 pages
http://dx.doi.org/10.1155/MPE/2006/26081

Research of nonlinear vibrations of orthotropic plates with a complex form

1Department of Applied Mathematics, National Polytechnic University KhPI, 21 Frunze Street, Kharkov 61002, Ukraine
2Department of Higher Mathematics, National Polytechnic University KhPI, 21 Frunze Street, Kharkov 61002, Ukraine

Received 30 November 2004; Revised 27 May 2005; Accepted 7 July 2005

Copyright © 2006 L. V. Kurpa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with effects of large amplitude on the free and forced flexural vibrations of elastic orthotropic plates of arbitrary shape. R-function method (RFM) is applied to obtain the basis functions need for expansion of sought solution into Fourier series. The initial nonlinear system of differential equations with partial derivatives is reduced to system of ordinary nonlinear differential equations by Galerkin procedure. The solving-obtained system is carried out by Runge-Kutta or Galerkin methods. The numerical results for the plate of complex form and also rectangular form and different boundary conditions have been presented and compared with other known results.