Research on the Modal Damping Ratio for Stay Cable with Viscoselasticity Damper in Cable-Stayed Bridges

2013 ◽  
Vol 779-780 ◽  
pp. 671-674
Author(s):  
Shui Sheng Chen ◽  
De Shan Wang
Keyword(s):  
Damping Ratio ◽  
Bending Stiffness ◽  
Complex Eigenvalue ◽  
Stay Cable ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Out Of Plane ◽  
Damper Design ◽  
Inclined Angle ◽  
Separation Strategy

Taking the bending stiffness, cable static sag and cable inclined angle into consideration, equations of space free vibration of the cable-damper system are derived in this paper. Joining the variable separation strategy and center difference method, the partial differential equations are discretized in space and a set of complex eigenvalue equations, which are solved by state space method, are derived, and both the maximum modal damping ration and the optimal damper parameter are obtained. Several typical stay cables are investigated for both the in-plane and out-of-plane modes under different cable parameters and damper parameters. The results demonstrate that modal damping ratio for the first in-plane mode is significantly affected by the cable static sag only, but those for the other modes affected by cable sag are slight, and cable static sag do not affect the optimal damper parameter for all modes, however the bending stiffness will changes both the maximum modal damping ratios and the optimal damper parameters. Some valuable suggestions are proposed for the optimal damper design.

Damping of Stay Cable-Passive Damper System with Effects of Cable Bending Stiffness and Damper Stiffness

2012 ◽  
Vol 204-208 ◽  
pp. 4513-4517 ◽  
Author(s):  
Min Liu ◽  
Guang Qiao Zhang
Keyword(s):  
Numerical Analysis ◽  
Damping Ratio ◽  
Bending Stiffness ◽  
Damping Coefficient ◽  
Stay Cable ◽  
Modal Damping Ratio ◽  
Passive Damper ◽  
Modal Damping ◽  
Optimal Damping ◽  
Coefficient Increase

In the present paper, the asymptotic solution of modal damping ratio of stay cable-passive damper system with the influence of cable bending stiffness and damper stiffness was derived. Maximum modal damping ratio and corresponding optimal damping coefficient, which indicated the relationships of the characteristics of the damper and the cable bending stiffness was theoretically analyzed to obtain their close solutions. On the basis of these close solutions, numerical analysis of modal damping of stay cable-passive damper system with the effects of cable bending stiffness and damper stiffness was conducted. The numerical and analytical results show that the maximum modal damping ratio decrease and the corresponding damping coefficient increase, when considering the influence of the damper stiffness and the cable bending stiffness.

Calculation on Modal Damping Ratio of Stay Cable Using Nonlinear Friction Damper

2012 ◽  
Vol 538-541 ◽  
pp. 1800-1803
Author(s):  
Hui Ping Wang
Keyword(s):  
Damping Ratio ◽  
Free Vibrations ◽  
Nonlinear Friction ◽  
Friction Damper ◽  
Stay Cable ◽  
Lumped Mass ◽  
Mass Model ◽  
Modal Damping Ratio ◽  
Stay Cables ◽  
Modal Damping

Stay cables of long span cable-stayed bridges are easy to vibrate under wind or wind/rain loads owning to their very low inherent damping. To install cable dampers near to the anchorages of cable has become a common practice for cable vibration control of cable-stayed bridge structures. In this study, the behaviors of a nonlinear frictional type of damper were investigated. The equations of motion of a cable with a friction damper were derived by using a lumped mass model. Then by introducing modal transformation, the analytical solution for the motion equations was obtained. The results show that the friction damper evokes linearly decaying of free vibrations of the cable as long as the damper does not lock the cable. The modal damping ratio of cable with the friction damper is strongly amplitude dependent. Calculation of modal damping ratio can be simplified using control parameter and the maximum modal damping ratio can be obtained. A universal estimation curve is proposed that is similar to linear viscous damper. These studies could provide design basis for the vibration mitigation of stay cables using nonlinear friction.

Theoretical Study on Cable’s Vibration Control by Single TMD

2014 ◽  
Vol 935 ◽  
pp. 211-214 ◽  
Author(s):  
Dong Liang ◽  
Ji Xiang Song
Keyword(s):  
Damping Ratio ◽  
Tuned Mass Damper ◽  
Design Parameters ◽  
Stay Cable ◽  
Coupling Vibration ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Vibration Model ◽  
Mass Damper ◽  
Complex Models

The commonly used viscous dampers for cable’s vibration mitigation have some unfavorable factors, such as the damping effect is not obvious for super long stay cable, the limitation of installation position, coupling vibration, etc. The cable-tuned mass damper system vibration model is put forward to solve this problem. The optimal cable-tuned mass damper system modal damping ratio and optimum design parameters, including cable vibration order, TMD’s stiffness, TMD’s mass, and TMD’s damping, were obtained by the method of complex models. The results can provide important reference for the design of TMD for stay cable.

Non-Linear Free Vibration of Submerged Floating Tunnel Tether

2014 ◽  
Vol 580-583 ◽  
pp. 1388-1391 ◽  
Author(s):  
Zhi Bin Su ◽  
Sheng Nan Sun
Keyword(s):  
Free Vibration ◽  
Damping Ratio ◽  
Direct Proportion ◽  
Initial Tension ◽  
Modal Damping Ratio ◽  
Inverse Proportion ◽  
Modal Damping ◽  
Non Linear ◽  
Out Of Plane ◽  
Submerged Floating Tunnel

Taking the free vibration system of a submerged floating tunnel tether as research object, the non-linear free vibration equation was set up. By means of Galerkin method, the partial differential equation was transformed into a set of ordinary ones. The damping ratios of the first four modes were obtained after complex eigenvalue analysis. Subsequently, effects of inclination, sag, initial tension force and length of tether on its modal damping ratios were analyzed. The results show that inclination and sag of tether merely affect the damping ratio of first in-plane mode; they have no effect on the damping ratios of higher order in-plane modes and out of plane modes; the first in-plane modal damping ratio of tether is in direct proportion to its inclination, whereas in inverse proportion to its sag; the first modal damping ratio of tether (both in-plane and out of plane) is in direct proportion to its length, whereas in inverse proportion to its initial tension.

scholarly journals Refined Study on Free Vibration of a Cable with an Inertial Mass Damper

2019 ◽  
Vol 9 (11) ◽  
pp. 2271 ◽  
Author(s):  
Zhihao Wang ◽  
Fangfang Yue ◽  
Hao Wang ◽  
Hui Gao ◽  
Buqiao Fan
Keyword(s):  
Flexural Rigidity ◽  
Damping Ratio ◽  
Inertial Mass ◽  
Experimental Results ◽  
Complex Eigenvalue ◽  
Cable Model ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Mass Damper ◽  
Actual Design

To accurately predict the optimum supplemental modal damping ratio of the cable and the corresponding size of the inertial mass damper (IMD), combined effects of the cable sag, the cable flexural rigidity, and the boundary conditions on the control performance of the cable with the IMD are well investigated in this refined study. An analytical model of the cable-IMD system considering these effects is developed. The equation of motion of the cable-IMD system is transformed into a complex eigenvalue problem through the finite difference method. Experimental results from a scaled cable model with an IMD are then used to verify theoretical solutions. Three typical cables in actual cable-stayed bridges are selected for case studies. The results show that the theoretically predicted modal damping ratios of the cable with an IMD, taking into account the sag and the flexural rigidity, agree well with those identified from experimental results, while would be often overestimated with a taut-cable model. Moreover, experimental damping ratios of the cable always fall between those theoretically calculated with fixed ends or pinned ends for each case. Finally, to be conservative in actual design, it is recommended to use the cable-IMD system model with fixed ends to calculate the required damper size and predict the resulting modal damping ratio of the cable, since the corresponding theoretical solution often gives the lower bound of supplemental damping ratio of the cable.

Modal damping ratio analysis of dynamical system with non-stationary responses

2016 ◽  
Vol 59 ◽  
pp. 138-146 ◽  
Author(s):  
Da Tang ◽  
Ran Ju ◽  
Qianjin Yue ◽  
Shisheng Wang
Keyword(s):  
Dynamical System ◽  
Damping Ratio ◽  
Ratio Analysis ◽  
Modal Damping Ratio ◽  
Modal Damping

scholarly journals Coupling of Flexural and Longitudinal Damped Vibration in a Two-Layered Beam

1998 ◽  
Vol 5 (5-6) ◽  
pp. 337-341
Author(s):  
F. Pourroy ◽  
S. Shakhesi ◽  
P. Trompette
Keyword(s):  
Damping Ratio ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Layered Beam ◽  
Flexural Vibrations

In dynamics, the effect of varying the constitutive materials’ thickness of a two-layered beam is investigated. Resonance frequencies and damping variations are determined. It is shown that for specific thicknesses the coupling of longitudinal and flexural vibrations influences the global modal damping ratio significantly.

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.

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