Inter-well internal resonance analysis of rectangular asymmetric cross-ply bistable composite laminated cantilever shell under transverse foundation excitation

The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell, in cases of 1 : 2 inter-well internal resonance and primary resonance. The transverse foundation excitation is applied to the fixed end of the structure, and the other end is in a free state. The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation. The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms. Deriving from the obtained frequency-amplitude and force-amplitude response curves, a detailed analysis is conducted to examine the impacts of excitation amplitude, damping coefficient, and tuning parameter on the nonlinear internal resonance characteristics of the system. The nonlinear softening characteristic is exhibited in the upper stable-state, while the lower stable-state demonstrates the softening and linearity characteristics. Numerical simulation is carried out using the fourth-order Runge-Kutta method, and a series of nonlinear response curves are plotted. Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.