Nonlinear dynamics of a cable-stayed beam driven by sub-harmonic and principal parametric resonance

Wei, Minghai; Lin, Kun; Jin, Lu; Zou, Dujian

doi:10.1016/j.ijmecsci.2016.03.007

Cited by 43 publications

(7 citation statements)

References 26 publications

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“…In 2012, the continuous nonlinear refined vibration model of tower-cable-bridge deck was established in [12], and the influences of frequency ratio of the bridge deck to cables, amplitude of excitation, force of cables, and damping on the vibration characteristics of the model were studied. In 2016, considering the synergistic effects of cable-tower-beam, the authors in [13] analyzed the parameter vibration mechanism of cables and calculated the dynamic characteristics of the bridge deck and cables. e research results can provide a theoretical value for the installation of vibration suppression devices for cables.…”

Section: Introductionmentioning

confidence: 99%

Influences of Two Calculation Methods about Dynamic Tension on Vibration Characteristics of Cable-Bridge Coupling Model

Min

Liu

Wu³

et al. 2021

Discrete Dynamics in Nature and Society

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For the cable-bridge coupling model, the dynamic tension of cables is an important parameter to study the vibration characteristics of the model. Based on this concept, two calculation methods about dynamic tension of cables were introduced in great detail, and the influences of these two calculation methods on the vibration characteristics of cable-bridge coupling model were systematically investigated. Firstly, the vibration equation of the cable was derived based on the variational principle for Hamiltonian, and the vibration equation of the bridge deck was obtained by Newton’s law. Then, the vibration equation of the cable and bridge deck was transformed into ordinary differential vibration equation by the Galerkin method. In addition, the differences of the coefficients in the ordinary differential vibration equation obtained by these two calculation methods about dynamic tension were compared, and a parameter analysis was listed. Finally, the resonance mode of the cable-bridge coupling model was analyzed by a multiple scales method, and an example analysis was listed. The results of parameter analysis show that there are obvious differences in the linear coefficient and nonlinear coefficient of the ordinary differential vibration equation obtained by these two calculation methods. The results of example analysis show that, for the cable-bridge coupling model with 1 : 1 resonance, the amplitude of the model would not be different because of the two calculation methods about dynamic tension, but the amplitude of the cable would be affected by the calculation method significantly. It can be found that the research conclusions here can be helpful to the perfection of theoretical modeling and has certain guiding value for practical engineering.

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Section: Introductionmentioning

confidence: 99%

Influences of Two Calculation Methods about Dynamic Tension on Vibration Characteristics of Cable-Bridge Coupling Model

Min

Liu

Wu³

et al. 2021

Discrete Dynamics in Nature and Society

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“…Results show that the flexible cable parametrically resonated by excitations may result in instability or even damage of the bridge [2][3][4][5], which show greater destructiveness than that caused by the primary resonance [6,7]. Dynamic analysis and design of parametrically excited cables are significant in the construction and application of the bridge [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Modal Interaction-Induced Parametric Resonance of Stayed Cable: A Combined Theoretical and Experimental Investigation

Zhang

Cui

Zhi

et al. 2021

Mathematical Problems in Engineering

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The cable-stayed bridge is widely used due to its strong spanning capacity and navigability. However, flexible cables parametrically resonated by external excitation may result in instability or even damage to the bridge. To prevent such undesirable resonance, this paper discusses an in-plane modal interaction-induced parametric resonance of the stayed cable excited by the bridge deck vibration via nonlinear dynamic analysis. Based on the nonlinear distributed model, two modal governing equations of the cable are established via the Galerkin method. A certain working condition, when the external excitation frequency is close to the second-order natural frequency of the stay cable while nearly twice the first-order natural frequency, is theoretically and experimentally investigated. Specifically, the frequency response equations are obtained by the multiscale method, and the stability of solutions is examined through the Routh Hurwitz criterion. Theoretical and experimental results show that bridge deck vibration can induce not only the primary and superharmonic resonance of the cable but also the principal parametric resonance. Parametric resonance-induced bifurcations are also observed in the system. Particularly, the energy exchange from second-order primary resonance to first-order principal parametric resonance is found, which can induce the parametric resonance with the response amplitude one to three times higher than that of the primary resonance. This paper also validates the superiority of the present modal interaction model over the traditional single-mode model in practical engineering applications.

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“…Based on the fact that the cable cannot be modeled without the consideration of the rest components of the cable-stayed bridge, the cable-beam model (Wang et al, 2020, 2014, Wei et al, 2016) is introduced to investigate the mode localization/globalization (Gattulli and Lepidi, 2003) and the cable-deck interactions. From the global modeling view, a 4-DOF multi-body model (Lepidi and Gattulli, 2016) is used to describe the cable-deck interactions and the vibration mechanism of the cable-supported bridges; a fully analytical model (Cao et al, 2012) for the cable-stayed bridge with four cables and seven deck beams is founded to investigate the planar free vibration, and a double-cable-stayed shallow-arch model (Kang et al, 2017) is built to study the planar 1:1:1 internal resonance between the deck and cable of the cable-stayed bridge.…”

Section: Introductionmentioning

confidence: 99%

Analytically measure the vibratory characteristics of the cable-stayed bridge during dual-cantilever erection

Pan

Yan

et al. 2021

Journal of Vibration and Control

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To analytically measure the vibratory characteristics of the cable-stayed bridge with beam-tower constraint during the dual-cantilever erection, the isolating/assembling technique is used to derive the global equation. Eigen-equation governing the frequencies/modes is obtained by applying the coefficients vectors transferring between adjacent cable-beams and the boundary/matching conditions. An illustrative example of the dual-cantilever erection system is given to verify the effectiveness of the analytical method by comparing with the finite element method. The influences of the vertical/rotational beam-tower constraint stiffness and the beam/cable relative stiffness on the frequencies/modes are studied; the sensitive interval and unstable/veering regions in frequency spectrum are ascertained. The twin frequencies are analytically measured and it is found that the symmetry plays a fundamental role in its existence and distribution range. The measuring method supplies reference for similar cable-supported structures; the results provide suggestions to avoid unstable/veering zone depending on the designed parameters combination in cable-stayed bridge.

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Nonlinear dynamics of a cable-stayed beam driven by sub-harmonic and principal parametric resonance

Cited by 43 publications

References 26 publications

Influences of Two Calculation Methods about Dynamic Tension on Vibration Characteristics of Cable-Bridge Coupling Model

Influences of Two Calculation Methods about Dynamic Tension on Vibration Characteristics of Cable-Bridge Coupling Model

Modal Interaction-Induced Parametric Resonance of Stayed Cable: A Combined Theoretical and Experimental Investigation

Analytically measure the vibratory characteristics of the cable-stayed bridge during dual-cantilever erection

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