Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances

Wang, Lianhua; Zhao, Yanpu

doi:10.1016/j.ijsolstr.2006.04.006

Cited by 39 publications

(17 citation statements)

References 37 publications

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“…The approximate dynamic strain exhibits two contributions due to the relative acceleration of the moving mass, which arise within the variational formulation of the equations of motion and ensue from retaining the inertia term of the moving mass and the friction in the condensation procedure. Both effects are neglected in the classical condensation, where the dynamic strain of the suspended cable turns out to be uniform along the cable span and is only a function of time t (Wang and Zhao, 2006;Srinil and Rega, 2007;Sofi and Muscolino, 2007). In contrast, in the present improved condensation, the strain (Eq.…”

Section: Condensed Planar Modelmentioning

confidence: 86%

Modelling and transient planar dynamics of suspended cables with moving mass

Wang

Rega

2010

International Journal of Solids and Structures

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In this study, the 3D nonlinear equations of motion of the suspended cable with moving mass are obtained via the Hamilton principle, and its transient linear planar dynamics is investigated. Considering the quasi-static assumption, the condensed planar model accounting for the effect of the moving mass is derived, and it is then discretized by choosing the static deflection and sine series as shape functions. It is shown that this expansion shows good convergence features. The Newmark method is used to investigate the transient response. The effects of the inertia force, mass, sag and velocity of the moving mass on the transient dynamics of the suspended cable are systematically investigated. Finally, the horizontal tension of the suspended cable and the case of sequentially moving masses are examined. (C) 2010 Elsevier Ltd. All rights reserved

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Section: Condensed Planar Modelmentioning

confidence: 86%

Modelling and transient planar dynamics of suspended cables with moving mass

Wang

Rega

2010

International Journal of Solids and Structures

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“…Although the nonlinear dynamic response of a single cable has been investigated in many works and many nonlinear phenomena have been highlighted [9,10], very few publications deal with the nonlinear dynamic phenomena of cable net structures. In Leonard [11], considering lumped or consistent mass, provided a formula for the frequencies of a cable net with initial sag.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic analysis of space cable net structures with one to one internal resonances

Wang

Shen

2014

Nonlinear Dyn

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The nonlinear dynamic analysis of cable net structures becomes more and more significant for their space applications required high surface accuracy, especially mesh reflector antennas. In this work, the resonant multi-modal dynamics due to 1:1 internal resonances in the finite-amplitude vibrations of cable net structures subjected to harmonic loads are investigated. The nonlinear dynamic equation of space cable net structures is first developed using the extended Hamilton principle, which belongs to the self-excited vibration with quadratic and cubic nonlinearities. Linear modal analysis is then performed to decouple the nonlinear differential equations, and yields a complete set of system quadratic/cubic coefficients. With the aim of parametrically revealing nonlinear behaviors of space cable net structures, the second-order asymptotic analysis under 1:1 internal resonance is accomplished by the method of multiple scales. The nonlinear phenomena of a planar cable net and cable net reflector, such as the bending of response curve, jump phenomena, instability regions, saddle-node bifurcation, are verified by means of numerical analysis.

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“…Wang and Zhao [10,11] studied the nonlinear planar oscillations of suspended cables subjected to external excitations with three-to-one internal resonances. The modulation equations with quadratic and cubic geometric nonlinearities govern the nonlinear dynamics of suspended cables.…”

Section: Introductionmentioning

confidence: 99%

Multiple Resonances and Nonlinear Behaviors of a Spindle Ball Bearings System with 3/2 Nonlinear Term

Gao¹,

Long²,

Meng³

2009

International Journal of Nonlinear Sciences and Numerical Simulation

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Considering the symmetry, the spindle ball bearings system can be simplified into a two-degree-of-freedom system and the three-term harmonic balance (Tl IB) method is used to examine the complex, nonlinear dynamic behavior of the spindle-bearing system. The analytical results obtained by the THB method indicate the resonances are found at the one-third of the first natural frequency, one-half of the first nature frequency, two-third of the first natural frequency, and the first natural frequency in the spindle-bearing system with 3/2 stiffness nonlinearity. These results agree well with the results obtained by the time domain simulations. With the variation of the natural frequency of the system, the phenomena of the jump in frequency-response curves are observed. The bending of the frequency-response curves significantly increase with the increase of the contact stiffness of the bearing and the eccentricity of the spindle.

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Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances

Cited by 39 publications

References 37 publications

Modelling and transient planar dynamics of suspended cables with moving mass

Modelling and transient planar dynamics of suspended cables with moving mass

Nonlinear dynamic analysis of space cable net structures with one to one internal resonances

Multiple Resonances and Nonlinear Behaviors of a Spindle Ball Bearings System with 3/2 Nonlinear Term

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