Nonlinear vibration analysis for a generic coupled-laminated plate with surface bonded or embedded induced strain actuators

Studies are made on the nonlinear vibrations of Piezo-laminated rectangular thin plates with induced strain actuation by following Kirchoff's hypothesis and using strain-displacement relations of von Kármán type. The von Kármán's large deflection equations for generally laminated elastic plates are derived in terms of stress function and transverse 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 Galerkin's method is applied to the governing nonlinear partial differential equation to obtain the nonlinear ordinary differential equation of motion (modal equation). This is of Duffing's type. Analytical expressions for the constants in the modal equation are provided to use for any lay-up sequence. Procedure for exact integration of the modal equation is described. Numerical results of simply supported rectangular plates with immovable edges are presented.