Nonlinear analysis of an elastic cable under harmonic excitation

Kamel, M.; Hamed, Y. S.

doi:10.1007/s00707-010-0293-x

Cited by 34 publications

(22 citation statements)

References 25 publications

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“…Thus, in this case, there is no coupled behavior between the beam and the cable. The nonlinear responses that are caused solely by the geometric nonlinearity have been studied extensively in a lot of literatures [6,18,19] and, as such, we do not examine this issue.…”

Section: Excitation Acting On the Cablementioning

confidence: 99%

Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances

2011

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The bifurcation and chaos of a cable-beam coupled system under simultaneous internal and external resonances are investigated. The combined effects of the nonlinear term due to the cable's geometric and coupled behavior between the modes of the beam and the cable are considered. The nonlinear partialdifferential equations are derived by the Hamiltonian principle. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. The bifurcation diagrams in three separate loading cases, namely, excitation acting on the cable, on the beam and simultaneously on the beam and cable, are analyzed with changing forcing amplitude. Based on careful numerical simulations, bifurcations and possible chaotic motions are represented to reveal the combined effects of nonlinearities on the dynamics of the beam and the cable when they act as an overall structure.

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Section: Excitation Acting On the Cablementioning

confidence: 99%

Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances

2011

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“…The dynamic behavior was investigated for the inclined cable resonance under harmonic excitation [10]. The passive control approach was performed to study system behavior under multiple types of excitation forces [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Structural Control Analysis of an Offshore Wind Turbine Tower System

et al. 2019

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This paper investigates the vibration control, stability, and energy transfer of the offshore wind turbine tower system with control force and nonlinearity terms. A nonlinear proportional derivative (NPD) controller was connected to the system to reduce a high oscillation amplitude and to transfer the energy in the wind turbine system. Furthermore, the averaging method and Poincaré maps were used with respect to the controlled system to study the stability and bifurcation analysis in the worst resonance cases. The curves of force response and frequency response were plotted before and after the control unit was added to the wind turbine system. In addition, we discuss the performances of the control parameters on the vibration magnitudes. Numerical simulations were carried out with Maple and Matlab algorithms to confirm the analytical results. The results show the effectiveness of the NPD controller in suppressing the nonlinear oscillations of the wind turbine system.

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“…Primary and subharmonic resonances as well as multiple internal resonances have been investigated by many researchers. Condition for stability of dynamic response near the simultaneous primary internal resonances is established (Kamel and Hamed 2010).…”

Section: Introductionmentioning

confidence: 99%

Theory of Weightless Sagging Elasto-Flexible Cables

Benipal¹,

Ganguli²,

Kumar³

2016

Lat. Am. j. solids struct.

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In this Paper, a theory of single sagging planer weightless elastoflexible cables is proposed. In reference to the instantaneous natural state, hypoelastic rate-type constitutive equations and third-order nonlinear differential equations of planer motion for massless cables with nodal masses are derived. New concepts like configurational complementary potential and contra-gradient principles are proposed. Typical dynamic response of these elastic cables with different sustained loads, axial rigidity and sag/span ratios is determined. Modal, subharmonic and internal resonances, jump and beat phenomena, etc., are predicted. A new mode of damping of 'free' vibration of the system perturbed from its equilibrium state is identified. Significance of the proposed theory of weightless sagging elasto-flexible cables is discussed.

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Nonlinear analysis of an elastic cable under harmonic excitation

Cited by 34 publications

References 25 publications

Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances

Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances

Nonlinear Structural Control Analysis of an Offshore Wind Turbine Tower System

Theory of Weightless Sagging Elasto-Flexible Cables

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