Nonlinear interactions in the planar dynamics of cable-stayed beam

Gattulli, Vincenzo; Lepidi, Marco

doi:10.1016/s0020-7683(03)00266-x

Cited by 120 publications

(55 citation statements)

References 23 publications

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“…The work given by Royer-Carfagni [15] established simple formulas to analyze the global vibration of a cable-stayed bridge. Gattulli [16,17] studied the nonlinear interaction between beam and cable in a cable-stayed bridge system and also verified the results by both experimental and finite element models. Cao and Zhang [18] investigated the nonlinear oscillations and chaotic dynamics of a string-beam coupled system with four-degrees-of-freedom nonlinear system.…”

Section: Introductionmentioning

confidence: 77%

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

Zhang

Cao

2006

Nonlinear Dyn

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In this paper, research on nonlinear dynamic behavior of a string-beam coupled system subjected to parametric and external excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin's method is employed to simplify the governing equations to a set of ordinary differential equations with two degrees-of-freedom. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric resonance for the beam, and primary resonance for the string is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system. Based on the averaged equation obtained here, the techniques of phase portrait, waveform, and Poincare map are applied to analyze the periodic and chaotic motions. It is found from numerical simulations that there are obvious jumping phenomena in the resonant response-frequency curves. It is indicated from the phase portrait and Poincare map that period-4, period-2, and periodic solutions and chaotic motions occur in the transverse nonlinear vibrations of the string-beam coupled system under certain conditions.

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Section: Introductionmentioning

confidence: 77%

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

Zhang

Cao

2006

Nonlinear Dyn

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“…He proved that the considered system had at least three period oscillations. Gattulli et al [3,4] studied the nonlinear interaction between beam and cable dynamics in a cable-stayed bridge system and verified the results by both experimental and finite element models. Hamilton's principle was utilized to derive the equations of motion of a cablestayed beam structure, and finite element techniques were used to analyze the effect of the tension and the length of the cable [5].…”

Section: Introductionmentioning

confidence: 91%

Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

et al. 2011

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In this paper, the nonlinear dynamic behavior of a string-beam coupled system subjected to external, parametric and tuned excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system which are described by a set of ordinary differential equations with two degrees of freedom. The case of 1:1 internal resonance between the modes of the beam and string, and the primary and combined resonance for the beam is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system and obtain approximate solutions up to and including the second-order approximations. All resonance cases are extracted and investigated. Stability of the system is studied using frequency response equations and the phase-plane method. Numerical solutions are carried out and the results are presented graphically and discussed. The effects of the different parameters on both response and stability of the system are investigated. The reported results are compared to the available published work.

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“…Subharmonic (r≈0.5) and superharmonic (r≈2) resonance conditions bound two nonlinear interaction regions, where global modes may provide parametric and angle variation excitation of local modes respectively [8,9]. The excitation from angle variation between cable tension and bridge girder is a phenomenon detailed by Gattulli and Lepidi and Gattulli et al [9,10]. Fig.…”

Section: External Excitationmentioning

confidence: 96%

Control of dynamic stability of stays using passive viscous dampers

Landi¹,

Formichi²,

Croce³

et al. 2017

Fifth International Conference on Advances in Civil, Structural and Mechanical Engineering - CSM 2017

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Abstract-Since cable vibrations cause cable-stayed bridge users discomfort and may also lead to bridge collapse, assessment and control of dynamic behavior of stays are key aspects in designing such a bridge type. Mounting viscous dampers close to deck anchorages is an efficient way to control all kind of cable vibrations. In the paper, relevant issues as parametric excitation, external excitation and cable-structure interaction are investigated in order to define the required damping ratio to control the dynamic stability of stays. The study ends with a damper design example, referring to a relevant case study.Keywords-cable-stayed bridge, cable vibrations, cablestructure interaction, viscous damper.

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Nonlinear interactions in the planar dynamics of cable-stayed beam

Cited by 120 publications

References 23 publications

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

Control of dynamic stability of stays using passive viscous dampers

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