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

Narakorn Srinil, Giuseppe Rega

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51 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)180-195
Number of pages16
JournalInternational Journal of Non-Linear Mechanics
Issue number1
Publication statusPublished - 31 Jan 2007


  • horizontal cable
  • kinematic condensation
  • modal interaction
  • non-linear forced vibration
  • primary resonance
  • internal resonance


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