Abstract
This study deals with the large amplitude free vibrations of rectilinearly orthotropic thin rectangular plates resting on elastic foundations. The von Kármán-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 discretised equations. The non-linear 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 non-linear frequency to the linear frequency. Plates with opposite edges clamped or simply supported with immovable in-plane conditions and resting on Winkler, Pasternak and non-linear Winkler foundations are considered. The effects of foundation parameters, material parameters, edge conditions and the aspect ratio on the non-linear vibration behaviour have been investigated.
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