Multi-pulse orbits and chaotic dynamics of a symmetric cross-ply composite laminated cantilever rectangular plate

The multi-pulse homoclinic orbits and chaotic dynamics of a symmetric cross-ply composite laminated cantilever rectangular plate under in-plane and moment excitations are investigated with 1:2 internal resonance. Based on the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues, the energy-phase method proposed by Haller and Wiggins is employed to analyze the multi-pulse homoclinic bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The analysis of the global dynamics indicates that there exist the Shilnikov-type multi-pulse jumping orbits homoclinic to certain invariant sets for the resonance case which may lead to chaos in the sense of Smale horseshoes for the system. Homoclinic trees that describe the repeated bifurcations of multi-pulse solutions are presented. It can be found a gradual breakup of the homoclinic tree and the reducing of pulse numbers for the jumping homoclinic orbits if the dissipation factor is increased. The chaotic motions of the symmetric cross-ply composite laminated cantilever plate are also found by using the numerical simulation.