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

Narakorn Srinil, Giuseppe Rega

Research output: Contribution to journalArticle

71 Citations (Scopus)
148 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)253-274
Number of pages21
JournalNonlinear Dynamics
Volume48
Issue number3
DOIs
Publication statusPublished - May 2007

Keywords

  • Horizontal/inclined sagged cable
  • Internal resonance
  • Higher-order effects
  • Reduced-order models
  • Non-linear normal modes
  • Asymmetry effects

Fingerprint Dive into the research topics of 'Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II: internal resonance activation, reduced-order models and nonlinear normal modes'. Together they form a unique fingerprint.

Cite this