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Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II: internal resonance activation, reduced-order models and nonlinear normal modes

Srinil, N. and Rega, G. (2007) Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II: internal resonance activation, reduced-order models and nonlinear normal modes. Nonlinear Dynamics, 48 (3). pp. 253-274. ISSN 0924-090X

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    Abstract

    Resonant multi-modal dynamics due to planar 2:1 internal resonances in the nonlinear, finite-amplitude, free vibrations of horizontal/inclined cables are parametrically investigated based on the second-order multiple scales solution in Part I [1]. The already validated kinematically non-condensed cable model accounts for the effects of both non-linear dynamic extensibility and system asymmetry due to inclined sagged configurations. Actual activation of 2:1 resonances is discussed, enlightening on a remarkable qualitative difference of horizontal/inclined cables as regards non-linear orthogonality properties of normal modes. Based on the analysis of modal contribution and solution convergence of various resonant cables, hints are obtained on proper reduced-order model selections from the asymptotic solution accounting for higher-order effects of quadratic nonlinearities. The dependence of resonant dynamics on coupled vibration amplitudes, and the significant effects of cable sag, inclination and extensibility on system non-linear behavior are highlighted, along with meaningful contributions of longitudinal dynamics. The spatio-temporal variation of non-linear dynamic configurations and dynamic tensions associated with 2:1 resonant non-linear normal modes is illustrated. Overall, the analytical predictions are validated by finite difference-based numerical investigations of the original partial-differential equations of motion.

    Item type: Article
    ID code: 18556
    Keywords: Horizontal/inclined sagged cable, Internal resonance, Higher-order effects, Reduced-order models, Non-linear normal modes, Asymmetry effects, Engineering (General). Civil engineering (General)
    Subjects: Technology > Engineering (General). Civil engineering (General)
    Department: Faculty of Engineering > Naval Architecture and Marine Engineering
    Related URLs:
    Depositing user: Dr Narakorn Srinil
    Date Deposited: 05 Apr 2010 11:24
    Last modified: 05 Oct 2012 23:32
    URI: http://strathprints.strath.ac.uk/id/eprint/18556

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