NON-LINEAR VIBRATION OF ORTHOTROPIC THIN RECTANGULAR-PLATES ON ELASTIC FOUNDATIONS

This study deals with the large amplitude free vibrations of rectilinearly orthotropic thin rectangular plates resting on elastic foundations. The von Karman-type of governing equations are employed. The displacements are assumed to be harmonic in time and are expanded space-wise in terms of polynomial basis functions which satisfy the boundary conditions exactly. The time co-ordinate is eliminated by the Kantorovich averaging method. The orthogonal point collocation method is used to obtain the discretized equations. The nonlinear eigenvalue problem is solved by an iterative method. Numerical results are presented for the linear frequency of the fundamental mode and for the ratio of the nonlinear frequency to the linear frequency. Plates with opposite edges clamped or simply supported with immovable in-plane conditions and resting on Winkler, Pasternak and nonlinear Winkler foundations are considered. The effects of foundation parameters, material parameters, edge conditions and the aspect ratio on the nonlinear vibration behavior have been investigated.