Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/18935
Title: Super-harmonic and internal resonances of a suspended cable with nearly commensurable natural frequencies
Authors: Zheng, G
Ko, JM
Ni, YQ 
Keywords: Finite element formulation
Incremental harmonic balance technique
Internal resonance
Nonlinear periodic oscillation
Super-harmonic resonance
Suspended cable
Issue Date: 2002
Publisher: Kluwer Academic Publ
Source: Nonlinear dynamics, 2002, v. 30, no. 1, p. 55-70 How to cite?
Journal: Nonlinear Dynamics 
Abstract: 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.
URI: http://hdl.handle.net/10397/18935
ISSN: 0924-090X
DOI: 10.1023/A:1020395922392
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