Periodic and chaotic oscillations of a composite laminated plate using the third-order shear deformation plate theory

摘要

An analysis on nonlinear oscillations and chaotic dynamics is presented for a simply-supported symmetric cross-ply composite laminated rectangular thin plate with parametric and forcing excitations in the case of 1:3:3 internal resonance. Based on Reddy's third-order shear deformation plate theory and the von Karman-type equations, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate can be established via the Hamilton's principle. Such partial differential equations are further discretized by the Galerkin method to form a three-degree-of-freedom coupled nonlinear system including the cubic nonlinear terms. The method of multiple scales is then employed to derive a set of averaged equations. Through the stability analysis, the steady-state solutions of the averaged equations are provided. An illustrative case of 1:3:3 internal resonance and fundamental parametric resonance, 1/3 subharmonic resonance is considered. Numerical simulation is applied to investigate the intrinsically nonlinear behavior of the composite laminated rectangular thin plate. With certain external load excitations, the simulation results demonstrate that the nonlinear dynamical system of the composite laminated plate exhibits different kinds of periodic and chaotic motions.