Abstract
In this paper, the theoretical shell model of the bistable unsymmetric composite laminates is elucidated, elaborating the intra-well and inter-well dynamics. Deploying initial displacements delivered by the bistable plate model and utilizing the Reddy′s third-order shear deformation theory, the bistable shell model is introduced. Applying multiple sets of base excitation accelerations, sweeping frequency and sweeping amplitude, the intra-well and inter-well dynamics are detected. The intra-well dynamics are activated by the inadequate energy, while the inter-well dynamics are activated by the sufficient energy. The intra-well dynamics are characterized by the 1-cycle single-well vibration, the 2-cycle single-well vibration, the 3-cycle single-well vibration and the 4-cycle single-well vibration. The cycle-doubling bifurcation and the secondary Hopf bifurcation can be identified. The evolution process from the 1-cycle single-well vibration to dynamic snapthrough motions is judged to follow the cycle-doubling bifurcation which tends to generate all-around dynamic regimes. The frequency-amplitude response curve exhibits the softening nonlinear stiffness effect owing to the negative stiffness. The 1/2 subharmonic resonance actually represents superimposed responses which are constituted by the forced response activated by the high-level excitation frequency and the induced harmonic response equivalent to the primary resonance of the low-level mode frequency. The 1/2 subharmonic resonance is caused by quadratic nonlinear terms. The inter-well dynamics are characterized by limit-cycle oscillations, multiple-cycle snapthrough motions and chaotic snapthrough motions, which are attributed to loading conditions. The appearance of limit-cycle oscillations is decided by the level of initial displacements. The increasing level of initial displacements leads to the disappearance of limit-cycle oscillations. The first few mode frequencies tend to be the optimal excitation frequencies activating dynamic snapthrough motions. Limit-cycle oscillations are related to the first mode frequency while multiple-cycle and chaotic snapthrough motions are related to the third mode frequency. The discrepancies for different initial conditions are actually caused by the phase difference between the displacement response and the frequency sweeping, which denotes the hysteresis. With the increase of the number of layers, the actuation amplitude for dynamic snapthrough motions increases while the bandwidth of the actuation frequency range for dynamic snapthrough motions broadens correspondingly. The development of bistable energy harvesters and morphing aircrafts can be supported by the theoretical research.