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The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables

Srinil, N. and Rega, G. (2007) The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables. International Journal of Non-Linear Mechanics, 42 (1). pp. 180-195. ISSN 0020-7462

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    Abstract

    This study aims at comparing non-linear modal interactions in shallow horizontal cables with kinematically non-condensed vs. condensed modeling, under simultaneous primary external and internal resonances. Planar 1:1 or 2:1 internal resonance is considered. The governing partial-differential equations of motion of non-condensed model account for spatio-temporal modification of dynamic tension, and explicitly capture non-linear coupling of longitudinal/vertical displacements. On the contrary, in the condensed model, a single integro-differential equation is obtained by eliminating the longitudinal inertia according to a quasi-static cable stretching assumption, which entails spatially uniform dynamic tension. This model is largely considered in the literature. Based on a multi-modal discretization and a second-order multiple scales solution accounting for higher-order quadratic effects of a infinite number of modes, coupled/uncoupled dynamic responses and the associated stability are evaluated by means of frequency- and force-response diagrams. Direct numerical integrations confirm the occurrence of amplitude-steady or -modulated responses. Non-linear dynamic configurations and tensions are also examined. Depending on internal resonance condition, system elasto-geometric and control parameters, the condensed model may lead to significant quantitative and/or qualitative discrepancies, against the non-condensed model, in the evaluation of resonant dynamic responses, bifurcations and maximal/minimal stresses. Results of even shallow cables reveal meaningful drawbacks of the kinematic condensation and allow us to detect cases where the more accurate non-condensed model has to be used.

    Item type: Article
    ID code: 18552
    Keywords: horizontal cable, kinematic condensation, modal interaction, non-linear forced vibration, primary resonance, internal resonance, Naval architecture. Shipbuilding. Marine engineering, Engineering (General). Civil engineering (General)
    Subjects: Naval Science > Naval architecture. Shipbuilding. Marine engineering
    Technology > Engineering (General). Civil engineering (General)
    Department: Faculty of Engineering > Naval Architecture and Marine Engineering
    Related URLs:
      Depositing user: Dr Narakorn Srinil
      Date Deposited: 08 Apr 2010 09:54
      Last modified: 12 Mar 2012 17:53
      URI: http://strathprints.strath.ac.uk/id/eprint/18552

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