Nonlinear Vibration Analysis of Bistable Morphing Composite Laminated Shell Based on High-Dimensional Dynamical Model

Abstract

The bistable morphing composite laminated shell presents promising potential for aerospace morphing structures design, as it is capable of shape-changing under small energy inputs and maintaining two stable states without external loading. The bistable nonlinearity is distinct from the typical geometrical nonlinearity, as it arises from thermal residual stresses that cannot be equalized. During the derivation of a three-degree-of-freedom nonlinear dynamic model, Sanders’ nonlinear strain is incorporated into the strain–displacement relationship, while thermal residual stresses are taken into account in the constitutive relationship. The nonlinear dynamic model effectively captures the snap-through phenomena with orthogonal asymmetry in bistable morphing composite laminated shells. In order to reveal the resonance response and chaotic characteristics due to the interaction of vibrations between degrees of freedom, high-dimensional nonlinear dynamical model is derived by multiple scales method based on the 1:1:1 internal resonance relationship. The resonance response curves reflect the parametric influence law of the dynamical system stability. The nonlinear dynamic behaviors are described by the bifurcation diagrams and the maximum Lyapunov exponent. The significant motions under particular excitation conditions are visualized by phase portraits, time histories and Poincaré maps.