Research of nonlinear vibrations of orthotropic plates with a complex form

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.

Investigation of the stress‐strain state of the laminated shallow shells by R‐functions method combined with spline‐approximation

“…R-functions method (RFM) is one of them. The efficiency of this method had been demonstrated on a wide class of mechanics problems including static and dynamic problems of plates and shallow shells [4][5][6][7][8][9][10][11][12]. The main idea of the RFM is the construction of the complete solution structures including indefinite components at any choice of which the boundary conditions will be satisfied exactly.…”