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.

Instability-Induced Origami Design by Topology Optimization

Instability-induced wrinkle patterns of thin sheets are ubiquitous in nature,which often result in origami-like patterns that provide inspiration for the engineering of origami designs.Inspired by instability-induced origami patterns,we propose a computational origami design method based on the nonlinear analysis of loaded thin sheets and topology optimization.The bar-and-hinge model is employed for the nonlinear structural analysis,added with a displacement perturbation strategy to initiate out-of-plane buckling.Borrowing ideas from topology optimization,a continuous crease indicator is introduced as the design variable to indicate the state of a crease,which is penalized by power functions to establish the mapping relationships between the crease indicator and hinge properties.Minimizing the structural strain energy with a crease length constraint,we are able to evolve a thin sheet into an origami structure with an optimized crease pattern.Two examples with different initial setups are illustrated,demonstrating the effectiveness and feasibility of the method.