Coexistence of double-parameter nonlinear dynamics and metastable chaos for bistable asymmetric composite laminated square panel under combined external and parametric excitations

Abstract

This paper studies the double-parameter multi-pulse jumping chaotic vibrations and metastable chaos of the bistable asymmetric composite laminated square panel under combined external and parametric excitations for the first time. The double-parameter multi-pulse jumping chaotic motions are studied by using the extended Melnikov method for the bistable asymmetric composite laminated square panel. It is indicated that there exist the Shilnikov type multi-pulse jumping orbits. The occurred mechanism of the metastable chaos is first analyzed. A theoretical explanation is given for coexisting in the double-parameter multi-pulse jumping chaotic vibrations and metastable chaotic behaviors. Using the double-parameter Lyapunov exponents, the double-parameter nonlinear dynamics of the bistable asymmetric composite laminated square panel are analyzed. According to the numerical simulation results, the in-depth investigation of the topological changes is obtained for the double-parameter multi-pulse jumping chaotic vibrations. It is found that the dynamic snap-through phenomena and the coupled effects of the external and parametric excitations on the double-parameter nonlinear dynamic behaviors are obtained for the bistable asymmetric composite laminated square panel. It is also observed that the change of the external excitation can only affect the complexity of the chaotic vibrations. However, the parametric excitations determine the types of the chaotic vibrations. There exists a direct connection between the occurrence of the metastable state chaos and the increase of parametric excitations for the bistable asymmetric composite laminated square panel.