Archive of Applied Mechanics

, Volume 87, Issue 6, pp 989–1006 | Cite as

An investigation into cables’ in-plane dynamics under multiple support motions using a boundary modulation approach

  • Tieding Guo
  • Houjun Kang
  • Lianhua Wang
  • Yueyu Zhao


Cables’ in-plane nonlinear vibrations under multiple support motions with a phase lag are investigated in this paper, which is a continuation of our previous work (Guo et al. in Arch Appl Mech 1647–1663, 2016). The main results are twofold. Firstly, asymptotically reduced models for the cable’s in-plane nonlinear vibrations, with or without internal resonance, excited by multiple support motions, are established using a boundary modulation approach. Two in-plane boundary dynamic coefficients are derived for characterizing moving supports’ effects, which depend closely on the cable’s initial sag, distinct from the out-of-plane ones Guo et al. (2016), and are also found to be equal for symmetric in-plane dynamics while opposite for antisymmetric dynamics. Secondly, cable’s in-plane nonlinear responses due to multiple support motions are calculated and phase lag’s dynamic effects are fully investigated. Two important factors associated with phase lags, i.e., the excitation-reduced and excitation-amplified factors, are both derived analytically, indicating theoretically that the phase lags would weaken the cable’s single-mode symmetric dynamics but amplify the antisymmetric dynamics. Furthermore, through constructing frequency response diagrams, the phase lag is found to change the characteristics of cables’ two-to-one modal resonant dynamics, both qualitatively and quantitatively. All these semi-analytical results obtained from the reduced models are also verified by applying the finite difference method to the cable’s full model, i.e., the continuous partial differential equation.


Cables Multiple support motions Phase lags Boundary modulation Finite difference method 



This study is funded by National Science Foundation of China under Grant No. 11502076 and No.11572117, and also by Program for Supporting Young Investigators, Hunan University.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Tieding Guo
    • 1
  • Houjun Kang
    • 1
  • Lianhua Wang
    • 1
  • Yueyu Zhao
    • 1
  1. 1.College of Civil EngineeringHunan UniversityChangshaPeople’s Republic of China

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