Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 26081, 17 pages
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.
This paper deals with effects of large amplitude on the free and
forced flexural vibrations of elastic orthotropic plates of
arbitrary shape. -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.