Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables

N. Srinil, G. Rega

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Recent research literature mostly deals with nonlinear resonant dynamics of low-extensible cables involving transversal modes. Herein, we aim to investigate geometrically nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables, whose material properties are assumed to be linearly elastic. Depending on cable elasto-geometric properties, the spectrum of low-order planar frequencies manifests primary and secondary frequency crossover phenomena of transversal/transversal and longitudinal/transversal modes, respectively. By focusing on 1:1 internal resonances, nonlinear equations of finite-amplitude, harmonically forced and damped, cable motion are considered, fully accounting for overall inertia and displacement coupling effects. Meaningful quadratic nonlinear contributions of non-resonant, higher-order, longitudinal modes are highlighted via a multimode-based, second-order multiple scales solution. Overall coupled/uncoupled dynamic responses, bifurcations, stability and space-time-varying displacements due to longitudinal/transversal (vs. transversal/transversal) modal interactions at secondary (vs. primary) crossovers are analytically and numerically evaluated, along with the resonant longitudinal mode-induced dynamic forces.
LanguageEnglish
Pages230-242
Number of pages13
JournalJournal of Sound and Vibration
Volume310
Issue number1-2
DOIs
Publication statusPublished - 5 Feb 2008

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cables
Cables
crossovers
interactions
Bifurcation (mathematics)
dynamic response
Nonlinear equations
inertia
nonlinear equations
Dynamic response
Materials properties

Keywords

  • highly-extensible cable
  • longitudinal mode
  • modal interaction
  • internal resonance
  • non-linear forced vibration

Cite this

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title = "Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables",
abstract = "Recent research literature mostly deals with nonlinear resonant dynamics of low-extensible cables involving transversal modes. Herein, we aim to investigate geometrically nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables, whose material properties are assumed to be linearly elastic. Depending on cable elasto-geometric properties, the spectrum of low-order planar frequencies manifests primary and secondary frequency crossover phenomena of transversal/transversal and longitudinal/transversal modes, respectively. By focusing on 1:1 internal resonances, nonlinear equations of finite-amplitude, harmonically forced and damped, cable motion are considered, fully accounting for overall inertia and displacement coupling effects. Meaningful quadratic nonlinear contributions of non-resonant, higher-order, longitudinal modes are highlighted via a multimode-based, second-order multiple scales solution. Overall coupled/uncoupled dynamic responses, bifurcations, stability and space-time-varying displacements due to longitudinal/transversal (vs. transversal/transversal) modal interactions at secondary (vs. primary) crossovers are analytically and numerically evaluated, along with the resonant longitudinal mode-induced dynamic forces.",
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Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables. / Srinil, N.; Rega, G.

In: Journal of Sound and Vibration, Vol. 310, No. 1-2, 05.02.2008, p. 230-242.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables

AU - Srinil, N.

AU - Rega, G.

PY - 2008/2/5

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AB - Recent research literature mostly deals with nonlinear resonant dynamics of low-extensible cables involving transversal modes. Herein, we aim to investigate geometrically nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables, whose material properties are assumed to be linearly elastic. Depending on cable elasto-geometric properties, the spectrum of low-order planar frequencies manifests primary and secondary frequency crossover phenomena of transversal/transversal and longitudinal/transversal modes, respectively. By focusing on 1:1 internal resonances, nonlinear equations of finite-amplitude, harmonically forced and damped, cable motion are considered, fully accounting for overall inertia and displacement coupling effects. Meaningful quadratic nonlinear contributions of non-resonant, higher-order, longitudinal modes are highlighted via a multimode-based, second-order multiple scales solution. Overall coupled/uncoupled dynamic responses, bifurcations, stability and space-time-varying displacements due to longitudinal/transversal (vs. transversal/transversal) modal interactions at secondary (vs. primary) crossovers are analytically and numerically evaluated, along with the resonant longitudinal mode-induced dynamic forces.

KW - highly-extensible cable

KW - longitudinal mode

KW - modal interaction

KW - internal resonance

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