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

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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.

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Acknowledgements

Interesting comments by the reviewers are gratefully acknowledged.

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Authors and Affiliations

  1. Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan University, Changsha, 410082, China

    Houjun Kang & Tieding Guo

  2. Department of Mechanical Engineering, University of Maryland, Maryland, 21250, USA

    Houjun Kang & Weidong Zhu

  3. College of Civil Engineering, Hunan University, Changsha, 410082, China

    Tieding Guo, Junyi Su & Bingyu Zhao

Authors
  1. Houjun Kang
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  2. Tieding Guo
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  3. Weidong Zhu
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  4. Junyi Su
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  5. Bingyu Zhao
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Corresponding author

Correspondence to Houjun Kang.

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Citation: KANG, H. J., GUO, T. D., ZHU, W. D., SU, J. Y., and ZHAO, B. Y. Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances. Applied Mathematics and Mechanics (English Edition) (2019) https://doi.org/10.1007/s10483-019-2472-6

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

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Kang, H., Guo, T., Zhu, W. et al. Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances. Appl. Math. Mech.-Engl. Ed. 40, 649–678 (2019). https://doi.org/10.1007/s10483-019-2472-6

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  • DOI: https://doi.org/10.1007/s10483-019-2472-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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