Double excitation multi-stability and multi-pulse chaotic vibrations of a bistable asymmetric laminated composite square panels under foundation force.

Abstract

The double excitation multi-stability and Shilnikov-type multi-pulse jumping chaotic vibrations are analyzed for the bistable asymmetric laminated composite square panel under foundation force for the first time. Based on the extended new high-dimensional Melnikov function, the explicit sufficient conditions are obtained for the existence of the Shilnikov-type multi-pulse jumping homoclinic orbits and chaotic vibrations in the bistable asymmetric laminated composite square panel, which implies that multi-pulse jumping chaotic vibrations may occur in the sense of Smale horseshoes. The extended new high-dimensional Melnikov function gives the parameters domain of the intersection for the homoclinic orbits, which illustrates the relationship among the coefficients of damping, parametric, and external excitations. Numerical simulations including the bifurcation diagrams, largest Lyapunov exponents, phase portraits, waveforms, and Poincaré sections are utilized to study the double excitation multi-pulse jumping and metastable chaotic vibrations and dynamic snap-through phenomena. The numerical results demonstrate that double excitation Shilinikov multi-pulse jumping chaotic and small metastable chaotic vibrations coexist in the bistable asymmetric laminated composite square panel. It is found that the external excitation changes the complexity of the chaos, while the parameter excitation changes the type of chaos. It is verified that the bistable asymmetric laminated composite square panel with small damping is easier to produce double excitation Shilinikov multi-pulse jumping chaotic vibrations.