Nonlinear Parametric Vibration Characteristics of Stay Cable Due to Strong Bridge Deck Vibration

2016 ◽  
Vol 106 (12) ◽  
pp. 196-203
Author(s):  
Qin LU ◽  
Zhi SUN
Keyword(s):  
Bridge Deck ◽  
Vibration Characteristics ◽  
Parametric Vibration ◽  
Stay Cable ◽  
Nonlinear Parametric Vibration

Optimal Design of Damper with Stiffness for Damping of Stay Cable under Bridge Deck Motion

2013 ◽  
Vol 438-439 ◽  
pp. 769-774
Author(s):  
Shuai Luo ◽  
Quan Sheng Yan ◽  
Hong Jun Liu
Keyword(s):  
Optimal Design ◽  
Bridge Deck ◽  
Damping Coefficient ◽  
Viscous Damper ◽  
Stay Cable ◽  
Rule Of Thumb ◽  
Modal Damping ◽  
Inclined Angle

This paper studies cable-damper mitigation model due to indirect excitation caused by bridge deck vibration. In the new mitigation model, as a rule of thumb, we considered a parallel association of idealize damper with a spring to simulate the inherent stiffness of the damper. The result shows that the interaction between the stiffness of the viscous damper could deeply impact the damper effectiveness, and the external damping should be increased deeply to provide the same non-dimensional modal damping when the inclined angle of cable decreases. The optimum damping coefficient of the non-idealized damper decreases when the stiffness of the damper increases.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Guangyun Min ◽  
Xiaohui Liu ◽  
Chuan Wu ◽  
Shuguang Yang ◽  
Mengqi Cai
Keyword(s):  
Bridge Deck ◽  
Multiple Scales ◽  
Nonlinear Coefficient ◽  
Coupling Model ◽  
Vibration Characteristics ◽  
Parameter Analysis ◽  
Calculation Methods ◽  
Dynamic Tension ◽  
Linear Coefficient ◽  
Vibration Equation

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.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Qi-Chang Zhang ◽  
Su-Yu Cui ◽  
Zhi Fu ◽  
Jian-Xin Han
Keyword(s):  
Natural Frequency ◽  
Parametric Resonance ◽  
Bridge Deck ◽  
Primary Resonance ◽  
Second Order ◽  
Stay Cable ◽  
Modal Interaction ◽  
External Excitation ◽  
First Order ◽  
Principal Parametric Resonance

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.

scholarly journals Experimental Research on 2 : 1 Parametric Vibration of Stay Cable Model under Support Excitation

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Li-Na Zhang ◽  
Feng-Chen Li ◽  
Xiang Yu ◽  
Peng-Fei Cui ◽  
Xiao-Yong Wang
Keyword(s):  
Numerical Simulation ◽  
Experimental Research ◽  
Excitation Frequency ◽  
Parametric Vibration ◽  
Vibration Test ◽  
Test Model ◽  
Stay Cable ◽  
Test Analysis ◽  
Support Excitation ◽  
Bridge Bearing

For 2 : 1 parametric vibration problem of stay cable under support excitation, a sliding support only in the vertical moving is designed to simulate the bridge stay cable’s vibration test model. Meanwhile, using numerical simulation of cable free vibration and dynamic characteristic test analysis, the experimental research under various conditions is implemented in the actual cable-stayed bridge as the research object, which is compared with the corresponding numerical simulation results. According to the analysis results, it shows that as the vibration test model has 2 : 1 parametric vibration under the support excitation the results of maximum cable displacement from experimental analysis and numerical simulation are basically consistent which revealed that the parametric vibration of stay cable exists and is easy to occur. Additionally, when the bridge bearing excitation frequency is similar to the 2 : 1 frequency ratio, small excitation can indeed lead to the sharp “beat” vibration of cable; therefore it is very necessary to limit the amplitude of support excitation to prevent the occurrence of a large main parametric resonance.

scholarly journals Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ying Li ◽  
Ye Tang
Keyword(s):  
Steady State ◽  
Viscoelastic Model ◽  
Material Model ◽  
Parametric Vibration ◽  
Axially Moving String ◽  
Stiffness Constant ◽  
Nonlinear Parametric Vibration ◽  
Steady State Responses ◽  
Axially Moving ◽  
State Responses

The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton’s second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff’s fractional material model are much larger than those predicted by Mote’s fractional material model.

Dynamic Response of the Stay Cable under Bridge Deck Excitation

2012 ◽  
Vol 193-194 ◽  
pp. 702-707 ◽  
Author(s):  
Shuai Luo ◽  
Hong Jun Liu ◽  
Quan Sheng Yan
Keyword(s):  
Dynamic Response ◽  
Bridge Deck ◽  
Harmonic Oscillation ◽  
Design Procedure ◽  
Maximum Amplitude ◽  
Stay Cable ◽  
Cable Vibration ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Mitigation Design

Modeling the dynamic response of the stay cable under bridge deck excitation represents a complex task for cable design procedure and forms an important step in the cable mitigation design. This paper analyses the characteristics of cable response under bridge deck excitation. The problem of cable vibration under the harmonic oscillation of the supports is considered as the external excitation. The formulae for the estimation of maximum amplitude of cable vibration are presented to determine the main cause of large amplitude vibration of the cable under indirect excitation.

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