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

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Abstract

This paper is first of the two papers dealing with analytical investigation of resonant multi-modal 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 multi-dimensional Galerkin expansion of the solution of nonplanar/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 effects of 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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Authors and Affiliations

  1. Department of Structural and Geotechnical Engineering, University of Rome ‘La Sapienza’, via A. Gramsci 53, Rome, 00197, Italy

    Narakorn Srinil & Giuseppe Rega

  2. Department of Civil Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok, 10140, Thailand

    Somchai Chucheepsakul

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  1. Narakorn Srinil
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  2. Giuseppe Rega
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  3. Somchai Chucheepsakul
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Correspondence to Giuseppe Rega.

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Srinil, N., Rega, G. & Chucheepsakul, S. Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation. Nonlinear Dyn 48, 231–252 (2007). https://doi.org/10.1007/s11071-006-9086-0

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  • DOI: https://doi.org/10.1007/s11071-006-9086-0

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