Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode  

作　　者：Meiqi WU Pengyu LV Hongyuan LI Jiale YAN Huiling DUAN Wei ZHANG 

机构地区：[1]State Key Laboratory for Turbulence and Complex Systems,Department of Mechanics and Engineering Science,BIC-ESAT,College of Engineering,Peking University,Beijing 100871,China [2]Nanchang Innovation Institute of Peking University,Nanchang 330096,China [3]Department of Mechanics,Guangxi University,Nanning 530004,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第4期581-602,共22页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12293000,12293001,11988102,12172006,and 12202011)。

摘　　要：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.

关 键 词：bistable laminated composite shell dynamic snap-through mode Hopf bifurcation chaotic dynamics vibration experiment 

分 类 号：O347[理学—固体力学]