Dynamic stability of a rectangular plate on non-homogeneous winkler foundation

Abstract

The dynamic stability of a rectangular plate on non-homogeneous foundation, subjected to uniform compressive in-plane bi-axial dynamic loads and supported on completely elastically restrained boundaries is studied. The non-homogeneous foundation consists of two regions having different stiffnesses but symmetric about the centre lines of the plate. The equation governing the small amplitude motion of the system is derived by a variational method. The use of Galerkin method with reduced beam eigenfunctions transforms the system equations in matrix form. The system of coupled Mathieu-Hill equations thus obtained, are analysed by the method of multiple scales which yields the stability boundaries for different combinations of the excitation amplitude and frequency. The effects of stiffness and geometry of the foundation, boundary conditions, static load factor, in-plane load ratio and aspect ratio on the stability boundaries of the plate for first- and second-order simple and combination resonances are studied.