Abstract
The forced, nonlinear, 3D dynamics of an elastic cable is analyzed by means of a reduced 4 d.o.f. model, already obtained several years ago by some of the Authors of this paper. The system is analyzed in the case of multiple internal resonance conditions and a 1:1 external primary resonance condition. The reduced model, because of a strong intrinsic symmetry due to the fact that anti-symmetric in-plane and out-of-plane modes have the same natural frequency (Irvine’s theory), is in principle not able to catch some interesting classes of motion, such as ballooning, which on the other hand have been observed in experimental tests. In the present paper, an imperfection between the equations ruling the in-plane and out-of-plane components is introduced through an internal detuning, which simulates the slight difference between the frequencies of the two involved modes, which is plausible as a consequence of the initial curvature of the cable as well as obtainable through more refined analytical models. A discussion on the similarity and differences with the solutions previously obtained is presented. Regions of non-regular response in the excitation control parameter plane are located and ballooning trajectories are analyzed.
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References
Benedettini F, Rega G, Alaggio R (1995) Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions. J Sound Vib 182(5):775–798
Rega G, Lacarbonara W, Nayfeh AH, Chin CM (1999) Multiple resonances in suspended cables: direct versus reduced-order models. Int J Nonlinear Mech 34(5):901–924
Rega G (2004) Nonlinear vibrations of suspended cables—Part I: modeling and analysis. Appl Mech Rev 57:443–478
Rega G (2004) Nonlinear vibrations of suspended cables—Part II: deterministic phenomena. Appl Mech Rev 57:479–514
Berlioz A, Lamarque CH (2005) A non-linear model for the dynamics of an inclined cable. J Sound Vib 279(3–5):619–639
Srinil N, Rega G, Chucheepsakul S (2007) Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part i: theoretical formulation and model validation. Nonlinear Dynam 48(3):231–252
Srinil N, Rega G (2007) Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part ii: internal resonance activation, reduced-order models and nonlinear normal modes. Nonlinear Dynam 48(3):253–274
Rega G, Srinil N, Alaggio R (2008) Experimental and numerical studies of inclined cables: free and parametrically-forced vibrations. J Theor Appl Mech 46(3):621–640
Rega G, Alaggio R, Benedettini F (1997) Experimental investigation of the nonlinear response of a hanging cable. Part I: local analysis. Nonlinear Dynam 14:89–117
Alaggio R, Rega G (2000) Characterizing bifurcations and classes of motion in the transition to chaos through 3D-tori of a continuous experimental system in solid mechanics. Phys D 137:70–93
Rega G, Alaggio R (2001) Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system. Int J Solid Struct 38:2049–2068
Rega G, Alaggio R (2009) Experimental unfolding of the nonlinear dynamics of a cable-mass suspended system around a divergence-Hopf bifurcation. J Sound Vib 322:581–611
Golubitsky M, Schaeffer DG (1985) Singularities and groups in bifurcation theory, vol 1. Springer, Berlin
Alaggio R, Rega G (2009) Unfolding complex dynamics of sagged cables around a divergence-Hopf bifurcation: experimental results and phenomenological model. XIX AIMETA Conference—Italian Theoretical and Applied Mechanics Association, Ancona, Italy, 14–17 September 2009
Irvine M (1992) Cable structures. Dover Publications, New York
LaCarbonara W, Paolone A, Vestroni F (2007) Elastodynamics of nonshallow suspended cables: linear modal properties. J Vib Acoust 129: 425–433
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Alaggio, R., Benedettini, F., Rega, G., Zulli, D. (2013). Forced 3D Nonlinear Dynamics of a Hanging Cable Under Multiple Resonance Conditions. In: Catbas, F., Pakzad, S., Racic, V., Pavic, A., Reynolds, P. (eds) Topics in Dynamics of Civil Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6555-3_22
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DOI: https://doi.org/10.1007/978-1-4614-6555-3_22
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