Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors. The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified. The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated, and the four-dimensional (4D) nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method. The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed. The discussion focuses on investigating the effects of key parameters, e.g., excitation amplitude, damping coefficient, and detuning parameters, on the resonance responses. The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system. Furthermore, the significant motions under particular excitation conditions are visualized by bifurcation diagrams, time histories, phase portraits, three-dimensional (3D) phase portraits, and Poincare maps. Finally, the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell, yielding results that are qualitatively consistent with the theoretical results.