Multi-Pulse Chaotic Dynamics of a Cantilever Plate by Using Extended Melnikov Method

Abstract

The nonlinear dynamic behavior of a laminated composite cantilever plate is investigated in this paper. The extended Melnikov method is employed to predict the multi-pulse chaotic motions of the cantilever plate. The model is based on the wing flutter of the airplane. The cantilever plate is considered to be subjected to the in-plane and transversal excitations. The Reddy’s high-order shear deformation theory as well as von Ka´rma´n type equations are used to establish the equation of motion for the cantilever plate. Applying the Galerkin procedure to the partial differential governing equations of motion for the system, we obtain equations of transverse displacement. Then the method of multiple scales is used to obtain the averaged equations. Finally, the extended Melnikov method is used to analyze the nonlinear behavior in the cantilever plate system. The theoretical result shows that there exists multi-pulse jumping movement. The numerical results also reveal such chaotic phenomenon.