Passive hybrid technique for the vibration mitigation of systems of interconnected stays

Struct Control Health Monit

Hong

Chen

2019

Summary Connecting stay cables with cross‐ties is the most promising solution for vibration control of long cables in cable‐stayed bridges. Existing studies have been focusing on the influences of the cross‐tie configurations and properties on the dynamics of the formed cable networks, mostly based on the taut‐string model of cables. However, the cross‐ties are particularly aimed at long cables whose in‐plane vibrations can be significantly affected by the sag effect. This paper therefore presents an analytical method to investigate free in‐plane vibrations of shallow cable networks with cross‐ties, using the linear theory of shallow cables. A two‐shallow‐cable network with one viscoelastic cross‐tie is studied in detail to appreciate the sag effect on the dynamics of the cable network. It is shown that the sag effect couples vibrations of the cable segments divided by the cross‐ties and changes the modal interactions substantially. When the cross‐tie is rigid, curve veering occurs between frequency curves of the system with respect to varying cross‐tie location, as compared with curve intersection in the absence of the sag effect. When the cross‐tie is flexible, generally, mode shapes of the cable segments and the whole cable are not antisymmetric nor symmetric, and the sag then affects nearly all the vibration modes. Furthermore, taking into account the damping effect of the cross‐tie, the frequency loci in the complex plane regarding the increment of cross‐tie damping coefficient can still be categorized by the corresponding undamped and clamped frequencies while the modal interaction becomes more complicated. Quantitatively speaking, when the sag parameter is in the practical range of existing cable‐stayed bridges, the first and second vibration modes of the cable networks are considerably affected and need to be considered for practice.

\sin false(β l false/ 2 false) = 0

and βl /2−4/ λ 2 ( βl /2) 3 =0.…”

Section: A Two‐shallow‐cable System With One Cross‐tiesupporting

confidence: 75%

Section: A Two‐shallow‐cable System With Two Cross‐tiesmentioning

confidence: 76%

In‐plane free vibrations of shallow cables with cross‐ties

Struct Control Health Monit

Hong

Chen

2019

“…Considering continuity of displacement, Y j , p ( x j , p ) can be expressed as

Y_{j, p} ((), x_{j p}) = A_{j, p} \frac{normalsinh ((), π f_{j} λ x_{j, p} true/ L_{j})}{normalsinh ((), π f_{j} λ l_{j, p} true/ L_{j})} + B_{j, p} \frac{normalcosh ((), π f_{j} λ x_{j, p} true/ L_{j})}{normalcosh ((), π f_{j} λ l_{j, p} true/ L_{j})}

Where f j = ω 01 / ω 0 j is the j th cable frequency ratio ,

ω_{0 j} = π true/ L_{j} \sqrt{T_{j} true/ m_{j}}

, and A j , p and B j , p are complex parameters; two terms of hyperbolic functions are retained because of the presence of nonzero end displacements of cable segment .…”

Section: General Problem Formulationmentioning

confidence: 99%

Free vibrations of a two-cable network with near-support dampers and a cross-link

Zhou

Xia

Struct. Control Health Monit.

et al. 2015

SUMMARYVibration mitigation of cables is a crucial problem for cable-supported bridges. A hybrid method for cable vibration mitigation that combines cross-ties and dampers has been applied in engineering practice; however, the damping and frequency of this kind of system needs to be further assessed. In this paper, a system of two parallel cables with a cross-link and dampers located near the cable anchorage is proposed and analyzed. Based on displacement continuity and force equilibrium at the damper and spring locations, the characteristic equation of the system is derived by applying the transfer matrix method. The complex characteristic equation is then numerically solved to obtain the modal damping and frequencies. The damping and frequency characteristics are discussed in detail for the case when the two cables are identical. Special attention is given to the case when only one damper is installed, and the approximate damping evaluation formulations are proposed when spring stiffness approaches infinity. Effects of mass-tension ratio, cable length ratio and frequency ratio on damping are also addressed. Finally, a case study of multimode damping optimization for bridge hangers is given. The results of this paper could be useful for vibration mitigation of two parallel cables and further development of design guidelines for cable networks with attached dampers.

“…It can be found that it is easy to optimize the odd or even mode separately ( l 2 / L approximately from 0.5 to 0.63 for the first and the third modes; l 2 / L approximately from 0.4 to 0.48 for the second and the fourth modes); however, it is unpractical to find spring locations for multiple modes optimization considering both odd and even modes together. And it should be noted that the optimized damper constant is also different for each specific vibration mode as Caracoglia and Jones have discussed [].…”

Section: Asymptotic Solutionsmentioning

confidence: 99%

Free vibration of taut cable with a damper and a spring

Zhou

Struct. Control Health Monit.

Xing

2013

SUMMARY The damping and frequency of taut cable with a damper and a spring are investigated in this paper, which is motivated by cross‐ties and damper that are both utilized in mitigation of oscillation of the stays in cable‐stayed bridges or damper located near cable anchorage with rubber bushing. The dynamic characteristics of the cable‐damper‐spring system are analyzed on the basis of the taut string theory and considering the compatibility requirements on each constraint point. By using a transfer matrix method, the complex frequency equation of the cable‐damper‐spring system is derived. The complex frequency equation is further re‐written in terms of real and imaginary parts. The special limiting solutions are presented. Asymptotic approximate solutions for damper and spring close to cable ends are developed with small frequency shifts between free cable and damped system mode. The effects of spring stiffness and location to maximum cable vibration damping, optimum damper constant, and frequency are also addressed when spring is not located near cable anchorage. The mode behaviors when damper and spring is parallel connected are given. The general solutions for arbitrary location of damper and spring along the cable are further discussed. The results of this study are helpful to understanding the damper parameter optimization of cable‐damper‐rubber‐bushing system and the basic dynamics of the complex cable‐cross‐ties‐damper system. Copyright © 2013 John Wiley & Sons, Ltd.