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

doi:10.1007/s10483-019-2472-6

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (5): 649-678.doi: https://doi.org/10.1007/s10483-019-2472-6

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

Houjun KANG^1,2, Tieding GUO^1,3, Weidong ZHU², Junyi SU³, Bingyu ZHAO³

1. Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan University, Changsha 410082, China;
2. Department of Mechanical Engineering, University of Maryland, Baltimore County, Maryland 21250, U. S. A;
3. College of Civil Engineering, Hunan University, Changsha 410082, China

收稿日期:2018-06-19 修回日期:2018-10-03 出版日期:2019-05-01 发布日期:2019-05-01
通讯作者: Houjun KANG E-mail:khjun@hnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11572117 and 11502076)

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

Houjun KANG^1,2, Tieding GUO^1,3, Weidong ZHU², Junyi SU³, Bingyu ZHAO³

1. Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan University, Changsha 410082, China;
2. Department of Mechanical Engineering, University of Maryland, Baltimore County, Maryland 21250, U. S. A;
3. College of Civil Engineering, Hunan University, Changsha 410082, China

Received:2018-06-19 Revised:2018-10-03 Online:2019-05-01 Published:2019-05-01
Contact: Houjun KANG E-mail:khjun@hnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11572117 and 11502076)

摘要/Abstract

摘要： A dynamic model for an inclined carbon fiber 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 treatments. The 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.

关键词: moving boundary, elastic wave problem, excitation of wave, exploding wave, internal resonance, external resonance, inclined carbon fiber reinforced polymer (CFRP) cable, nonlinear dynamics, bifurcation

Abstract: A dynamic model for an inclined carbon fiber 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 treatments. The 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.

Key words: moving boundary, elastic wave problem, excitation of wave, exploding wave, inclined carbon fiber reinforced polymer (CFRP) cable, external resonance, bifurcation, nonlinear dynamics, internal resonance

中图分类号:

701K30

Houjun KANG, Tieding GUO, Weidong ZHU, Junyi SU, Bingyu ZHAO. Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(5): 649-678.

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

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

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