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

  • Houjun KangEmail author
  • Tieding Guo
  • Weidong Zhu
  • Junyi Su
  • Bingyu Zhao
Article
  • 9 Downloads

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.

KeyWords

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

Chinese Library Classification

O175.14 

2010 Mathematics Subject Classification

701K30 

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Notes

Acknowledgements

Interesting comments by the reviewers are gratefully acknowledged.

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Houjun Kang
    • 1
    • 2
    Email author
  • Tieding Guo
    • 1
    • 3
  • Weidong Zhu
    • 2
  • Junyi Su
    • 3
  • Bingyu Zhao
    • 3
  1. 1.Hunan Provincial Key Lab on Damage Diagnosis for Engineering StructuresHunan UniversityChangshaChina
  2. 2.Department of Mechanical EngineeringUniversity of MarylandMarylandUSA
  3. 3.College of Civil EngineeringHunan UniversityChangshaChina

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