Nonlinear dynamics of composite laminated thin plate with 1∶2∶3 inner resonance

The nonlinear oscillations and chaotic dynamics are studied for a simply-supported symmetric cross-ply composite laminated rectangular thin plate with parametric and forcing excitations. Based on the Reddy´s third-order shear deformation plate theory and the von Karman type equation, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton´s principle. The governing equations get reduced to ordinary differential equations in thickness direction with variable coefficients and these are solved by the Galerkin method. The case of 1:2:3 internal resonance is considered. The method of multiple scales is employed to obtain the six-dimensional averaged equation. The stability analysis is given for the steady state solutions of the averaged equation. The Numerical method is used to investigate the periodic and chaotic motions of the composite laminated rectangular thin plate. The results of numerical simulation demonstrate that there exist different kinds of periodic and chaotic motions of the composite laminated rectangular thin plate under certain conditions.