Periodic and chaotic dynamics of composite laminated piezoelectric rectangular plate with one-to-two internal resonance

The bifurcations and chaotic dynamics of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate are studied for the first time, which are simultaneously forced by the transverse, in-plane excitations and the excitation loaded by piezoelectric layers. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by using the Hamilton’s principle. The Galerkin’s approach is used to discretize partial differential governing equations to a two-degreeof-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation. Numerical method is utilized to find the periodic and chaotic responses of the composite laminated piezoelectric rectangular plate. The numerical results indicate the existence of the periodic and chaotic responses in the averaged equation. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcations and chaotic behaviors of the composite laminated piezoelectric rectangular plate is investigated numerically. Supported by the National Natural Science Foundation of China (Grant Nos. 10732020, 10872010), and the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10425209)