Inter-well internal resonance analysis of rectangular asymmetric cross-ply bistable composite laminated cantilever shell under transverse foundation excitation

作     者：Lele REN Wei ZHANG Yufei ZHANG 

作者机构：State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Department of Mechanics Guangxi University Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical StructuresCollege of Mechanical Engineering Beijing University of Technology 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学(英文))

年 卷 期：2024年第45卷第8期

页      面：1353-1373页

核心收录：

学科分类：08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0701[理学-数学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Natural Science Foundation of China (Nos. 11832002 and 12072201) 

主　　题：74K10 bistable composite laminated cantilever shell chaotic dynamic snap-through complex nonlinear vibration inter-well internal resonance O322 primary resonance 

摘      要：The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell, in cases of 1 : 2 inter-well internal resonance and primary resonance. The transverse foundation excitation is applied to the fixed end of the structure, and the other end is in a free state. The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation. The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms. Deriving from the obtained frequency-amplitude and force-amplitude response curves, a detailed analysis is conducted to examine the impacts of excitation amplitude, damping coefficient, and tuning parameter on the nonlinear internal resonance characteristics of the system. The nonlinear softening characteristic is exhibited in the upper stable-state, while the lower stable-state demonstrates the softening and linearity characteristics. Numerical simulation is carried out using the fourth-order Runge-Kutta method, and a series of nonlinear response curves are plotted. Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.