Research on periodic and chaotic oscillations of composite laminated plates with one-to-one internal resonance

This paper presents an analysis on the nonlinear vibrations of a simply supported composite laminated rectangular thin plate with parametric and forcing excitations. In accordance with the Reddy's high-order shear deformation theory and the model of von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion can be derived by the using the Hamiltonian principle. The Galerkin discretization approach and the method of multiple scales are then incorporated to formulate the four-dimensional averaged equation. The case of 1:1 internal resonance as well as fundamental parametric resonance for the simply supported composite laminated rectangular thin plate is studied by numerical simulation. The results of numerical simulation demonstrate that periodic and chaotic motions exist in the composite laminated rectangular thin plate under certain excitation conditions.