Nonlinear vibration analysis of initially stressed thin laminated rectangular plates on elastic foundations

Studies are made on the elastic behaviour of laminated rectangular thin plates on elastic foundations with combined lateral and compressive in-plane forces. The von Kلrmلnʹs large deflection equations for generally laminated elastic plates are derived in terms of stress function and deflection function. A deflection function satisfying the geometric boundary conditions is assumed and a stress function is then obtained after solving the compatibility equation. The modified Galerkinʹs method is applied to the governing nonlinear partial differential equation to obtain the nonlinear ordinary differential equation of motion (modal equation). Procedure for exact integration of the modal equation is described. Numerical results of simply supported as well as clamped square plates are presented. It is found that the nonlinear frequency increases with the amplitude for the applied lateral and compressive inplane forces. Analytical expressions for the constants in the modal equation are provided to use for any lay-up sequence.