Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances

作     者：Houjun KANG Tieding GUO Weidong ZHU Junyi SU Bingyu ZHAO 

作者机构：Hunan Provincial Key Lab on Damage Diagnosis for Engineering StructuresHunan University Department of Mechanical EngineeringUniversity of Maryland College of Civil EngineeringHunan University 

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

年 卷 期：2019年第40卷第5期

页      面：649-678页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11572117 and 11502076) 

主　　题：inclined carbon fiber reinforced polymer(CFRP)cable bifurcation nonlinear dynamics internal resonance external resonance 

摘      要：A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton s principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless *** steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young s modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.