Dynamic snap-through and nonlinear vibrations of bistable composite laminated shells

This paper investigates the dynamic snap-through and nonlinear vibrations of asymmetric bistable composite laminated shells under base excitation. A dynamic model is established considering geometric nonlinearity based on classic plate-shell theory and Hamilton's principle. The effects of temperature difference and base excitation on the shells are discussed. Through modal analysis and numerical calculations using the Runge-Kutta method, the motion patterns (periodic, quasi-periodic, chaotic) and resonance phenomena (main resonance, 1/2 and 1/3 subharmonic resonances, 2nd superharmonic resonance) are revealed. It is found that excitation amplitude and frequency significantly influence dynamic snap-through, with quadratic nonlinear terms causing 1/2 subharmonic resonance and cubic terms leading to 1/3 subharmonic resonance.