The extended Melnikov method for non-autonomous nonlinear dynamical systems and application to multi-pulse chaotic dynamics of a buckled thin plate

The extended Melnikov method, which was used to solve autonomous perturbed Hamiltonian systems, is improved to deal with high-dimensional non-autonomous nonlinear dynamical systems. The multi-pulse Shilnikov type chaotic dynamics of a parametrically and externally excited, simply supported rectangular thin plate is studied by using the extended Melnikov method. A two-degree-of-freedom non-autonomous nonlinear system of the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. The case of buckling is considered for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of motion to investigate multi-pulse Shilnikov type chaotic motions of the buckled rectangular thin plate for the first time. The results obtained here indicate that multi-pulse chaotic motions can occur in the parametrically and externally excited, simply supported buckled rectangular thin plate.