Super-harmonic and internal resonances of a suspended cable with nearly commensurable natural frequencies

G. Zheng, J. M. Ko, Yiqing Ni

Research output: Journal article publicationJournal articleAcademic researchpeer-review

23 Citations (Scopus)


In this paper, super-harmonic and internal resonance characteristics of a viscously damped cable with nearly commensurable natural frequencies are investigated by use of a novel method. The proposed frequency-domain solution method is based on the combined use of a three-dimensional nonlinear finite element approach and the incremental harmonic balance technique. It is an accurate algorithm in the sense that it accommodates multi-harmonic components and no mode-based model reduction is utilized in the solution process. The alternating frequency/amplitude-controlled algorithm enables complete solution to the frequency-response curves including unstable branches, sub- and super-harmonic resonance and internal resonance. A suspended cable paradigm under internal resonance condition is studied using the proposed method. Nonlinear response and modal interaction characteristics of the cable at different frequency regions are identified from analysis of response profiles and harmonic component features. The super-harmonic and internal resonance responses are respectively characterized based on the harmonic distribution. Under an in-plane harmonic excitation, the two-to-one internal resonance between the in-plane and out-of-plane modes and the super-harmonic resonance around the second symmetric in-plane mode are revealed. Strong nonlinear interaction among different modes in the parameter space ranging from primary resonance to super-harmonic resonance is observed.
Original languageEnglish
Pages (from-to)55-70
Number of pages16
JournalNonlinear Dynamics
Issue number1
Publication statusPublished - 1 Oct 2002


  • Finite element formulation
  • Incremental harmonic balance technique
  • Internal resonance
  • Nonlinear periodic oscillation
  • Super-harmonic resonance
  • Suspended cable

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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