Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: theoretical formulation and model validation

Narakorn Srinil, Giuseppe Rega, Somchai Chucheepsakul

Research output: Contribution to journalArticle

93 Citations (Scopus)

Abstract

This paper is first of the two papers dealingwith analytical investigation of resonant multimodal dynamics due to 2:1 internal resonances in the finite-amplitude free vibrations of horizontal/inclined cables. Part I deals with theoretical formulation and validation of the general cable model. Approximate nonlinear partial differential equations of 3-D coupled motion of small sagged cables - which account for both spatio-temporal variation of nonlinear dynamic tension and system asymmetry due to inclined sagged configurations - are presented. A multidimensional Galerkin expansion of the solution ofnonplanar/planar motion is performed, yielding a complete set of system quadratic/cubic coefficients. With the aim of parametrically studying the behavior of horizontal/inclined cables in Part II [25], a second-order asymptotic analysis under planar 2:1 resonance is accomplished by the method of multiple scales. On accounting for higher-order effectsof quadratic/cubic nonlinearities, approximate closed form solutions of nonlinear amplitudes, frequencies and dynamic configurations of resonant nonlinear normal modes reveal the dependence of cable response on resonant/nonresonant modal contributions. Depending on simplifying kinematic modeling and assigned system parameters, approximate horizontal/inclined cable models are thoroughly validated by numerically evaluating statics and non-planar/planar linear/non-linear dynamics against those of the exact model. Moreover, the modal coupling role and contribution of system longitudinal dynamics are discussed for horizontal cables, showing some meaningful effects due to kinematic condensation.
LanguageEnglish
Pages231-252
Number of pages21
JournalNonlinear Dynamics
Volume48
Issue number3
DOIs
Publication statusPublished - May 2007

Fingerprint

Model Validation
Inclined
Cable
Cables
Horizontal
Formulation
Nonlinear Dynamics
Kinematics
Second-order Asymptotics
Internal Resonance
Method of multiple Scales
Quadratic Systems
Configuration
Asymptotic analysis
Motion
Normal Modes
Free Vibration
Condensation
Closed-form Solution
Nonlinear Partial Differential Equations

Keywords

  • Exact/approximate model
  • Horizontal/inclined sagged cable
  • Higher-order effects
  • Internal resonance
  • Longitudinal dynamicsNonlinear free vibration

Cite this

Srinil, Narakorn ; Rega, Giuseppe ; Chucheepsakul, Somchai. / Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I : theoretical formulation and model validation. In: Nonlinear Dynamics. 2007 ; Vol. 48, No. 3. pp. 231-252.
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Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I : theoretical formulation and model validation. / Srinil, Narakorn; Rega, Giuseppe; Chucheepsakul, Somchai.

In: Nonlinear Dynamics, Vol. 48, No. 3, 05.2007, p. 231-252.

Research output: Contribution to journalArticle

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AB - This paper is first of the two papers dealingwith analytical investigation of resonant multimodal dynamics due to 2:1 internal resonances in the finite-amplitude free vibrations of horizontal/inclined cables. Part I deals with theoretical formulation and validation of the general cable model. Approximate nonlinear partial differential equations of 3-D coupled motion of small sagged cables - which account for both spatio-temporal variation of nonlinear dynamic tension and system asymmetry due to inclined sagged configurations - are presented. A multidimensional Galerkin expansion of the solution ofnonplanar/planar motion is performed, yielding a complete set of system quadratic/cubic coefficients. With the aim of parametrically studying the behavior of horizontal/inclined cables in Part II [25], a second-order asymptotic analysis under planar 2:1 resonance is accomplished by the method of multiple scales. On accounting for higher-order effectsof quadratic/cubic nonlinearities, approximate closed form solutions of nonlinear amplitudes, frequencies and dynamic configurations of resonant nonlinear normal modes reveal the dependence of cable response on resonant/nonresonant modal contributions. Depending on simplifying kinematic modeling and assigned system parameters, approximate horizontal/inclined cable models are thoroughly validated by numerically evaluating statics and non-planar/planar linear/non-linear dynamics against those of the exact model. Moreover, the modal coupling role and contribution of system longitudinal dynamics are discussed for horizontal cables, showing some meaningful effects due to kinematic condensation.

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