• Smart Structures and Systems
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• 제30권1호
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• pp.89-106
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• 2022

The negative stiffness of an active or semi-active damper system has been proven to be very effective in reducing dynamic response. Therefore, energy dissipation devices possessing negative stiffness, such as viscous inertial mass dampers (VIMDs), have drawn much attention recently. The control performance of the VIMD for cable vibration mitigation has already been demonstrated by many researchers. In this paper, a new optimal design procedure for VIMD parameters for taut cable vibration control is presented based on the fixed-points method originally developed for tuned mass damper design. A model consisting of a taut cable and a VIMD installed near a cable end is studied. The frequency response function (FRF) of the cable under a sinusoidal load distributed proportionally to the mode shape is derived. Then, the fixed-points method is applied to the FRF curves. The performance of a VIMD with the optimal parameters is subsequently evaluated through simulations. A taut cable model with a tuned VIMD is established for several cases of external excitation. The performance of VIMDs using the proposed optimal parameters is compared with that in the literature. The results show that cable vibration can be significantly reduced using the proposed optimal VIMD with a relatively small amount of damping. Multiple VIMDs are applied effectively to reduce the cable vibration with multi-modal components.

• Smart Structures and Systems
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• 제23권6호
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• pp.521-536
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• 2019

Using magnetorheological (MR) dampers in multiswitch open-loop control mode has been shown to be cost-effective for cable vibration mitigation. In this paper, a method for analyzing the damping performance of taut cables incorporating MR dampers in open-loop control mode is developed considering the effects of damping coefficient, damper stiffness, damper mass, and stiffness of the damper support. Making use of a three-element model of MR dampers and complex modal analysis, both numerical and asymptotic solutions are obtained. An analytical expression is obtained from the asymptotic solution to evaluate the equivalent damping ratio of the cable-damper system in the open-loop control mode. The individual and combined effects of the damping coefficient, damper stiffness, damper mass and stiffness of damper support on vibration control effectiveness are investigated in detail. The main thrust of the present study is to derive a general formula explicitly relating the normalized system damping ratio and the normalized damper parameters in consideration of all concerned effects, which can be easily used for the design of MR dampers to achieve optimal open-loop vibration control of taut cables.

• Structural Engineering and Mechanics
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• 제55권6호
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• pp.1261-1278
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• 2015

Due to their low intrinsic damping, stay cables in cable-stayed bridges have often exhibited unanticipated and excessive vibrations which result in increasing maintenance frequency and disruption to normal operations of the entire bridges. Mitigation of undesired cable vibration can be achieved by attaching an external damping device near the anchorage. High Damping Rubber (HDR) dampers have many advantages such as compact size, better aesthetics, easy maintenance, temperature stability, and cost benefits; therefore, they have been widely used to increase cable damping. Although a single damper has been shown to reduce cable vibrations, it is not the most effective method due to geometric constraints. This paper proposes the use of two HDR dampers to improve effectiveness and robustness in suppressing cable vibration. Oscillation parameters of the cable-dampers system were investigated in detail by modeling the stay cable as a taut string and each HDR damper as complex-valued impedance and by using an analytical formulation of the complex eigenvalue problem. The problem of two HDR dampers arbitrarily located along a cable is solved and the solution is discussed. Asymptotic formulas to calculate the damping ratios of the cable with two HDR dampers installed near the anchorage(s) are proposed and compared with the exact solutions. Further, a design example is presented in order to justify the methodology. The results of this study show that when the two HDR dampers are installed close to each other on the same end of the cable, some interaction between the dampers leads to reduced damping ratio. When the dampers are on the opposite ends of the cable, they are effective in increasing damping ratio and can provide better vibration reduction to multiple modes.

• Structural Engineering and Mechanics
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• 제86권2호
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• pp.221-235
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• 2023

To calculate the vibrations of a tout cable subjected to axial support excitations, a nonlinear relationship of cable force and the support displacement under static situations are employed to depict the quasi-static vibration of the cable. The dynamic components of quasi-static vibration are inputted as "direct loads" to cause the parametric vibrations on the cable. Both the governing equations of motion and deformation compatibility for parametric vibrations are then derived, which indicates the high coupling of cable parametric force and deformation. Numerical solutions, based on the finite difference method, are put forward for the parametric vibrations, which is validated by the finite element method under periodic axial support excitations. For the quasi-static response, the shorter cables are more sensitive to support excitations than longer ones at small cable force. The quasi-static cable force makes the greatest contribution to the total cable force, but the parametric cable force is responsible for the occurrence of cable loosening at large excitation amplitudes. Moreover, this study also revealed that the traditional approach, assuming a linear relationship between quasi-static cable force and axial support displacement, would result in some great error of the cable parametric responses.

• Smart Structures and Systems
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• 제24권1호
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• pp.83-94
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• 2019

Passive negative stiffness dampers (NSDs) that possess superior energy dissipation abilities, have been proved to be more efficient than commonly adopted passive viscous dampers in controlling stay cable vibrations. Recently, inertial mass dampers (IMDs) have attracted extensive attentions since their properties are similar to NSDs. It has been theoretically predicted that superior supplemental damping can be generated for a taut cable with an IMD. This paper aims to theoretically investigate the impact of the cable sag on the efficiency of an IMD in controlling stay cable vibrations, and experimentally validate superior vibration mitigation performance of the IMD. Both the numerical and asymptotic solutions were obtained for an inclined sag cable with an IMD installed close to the cable end. Based on the asymptotic solution, the cable attainable maximum modal damping ratio and the corresponding optimal damping coefficient of the IMD were derived for a given inertial mass. An electromagnetic IMD (EIMD) with adjustable inertial mass was developed to investigate the effects of inertial mass and cable sag on the vibration mitigation performance of two model cables with different sags through series of first modal free vibration tests. The results show that the sag generally reduces the attainable first modal damping ratio of the cable with a passive viscous damper, while tends to increase the cable maximum attainable modal damping ratio provided by the IMD. The cable sag also decreases the optimum damping coefficient of the IMD when the inertial mass is less than its optimal value. The theoretically predicted first modal damping ratio of the cable with an IMD, taking into account the sag generally, agrees well with that identified from experimental results, while it will be significantly overestimated with a taut-cable model, especially for the cable with large sag.

• 대한토목학회논문집
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• 제28권1A호
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• pp.125-133
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• 2008

사장교의 장대화로 주탑 및 보강형과 더불어 사장 케이블의 동적 안정화에 많은 노력이 요구된다. 사장 케이블에서 동적 불안정은 주로 대칭 1모드와 역대칭 1모드에서 발생되며 대칭 1모드는 역대칭 1모드와 다르게 새그의 영향이 명확하게 나타나므로 기본진동수는 팽팽한 스트링으로부터 얻은 것과 상이한 결과를 제공하게 된다. 이러한 현상에 관해 Irvine, Triantafyllou, 안상섭 등은 해석적 기법을 통해 동적거동 분석을 수행하였다. 이들의 연구는 광범위한 영역의 Irvine Parameter에 대해 중요한 결과를 제시하였으나 특성점(Cross-Over Point 혹은 복합모드 형성점) 이후 영역에 대해서는 상이한 결과를 제시하였고 진동수방정식의 높은 비선형성으로 인해 해가 매우 민감한 난점이 있다. 본 연구는 사장 케이블 동적안정 문제에 주요한 모드들 중 새그의 영향이 가장 높은 대칭 1모드의 기본진동수에 초점을 맞추었으며 일반화된 역학적에너지에 경계조건을 만족시키는 진동형상을 적용하고 Rayleigh-Ritz 방법으로 해석적인 해를 제시하였다. 선행연구들과 다르게 본 연구는 선형적인 해를 제공하며 이에 따른 오차는 특성점 이내에서 3% 미만의 오차를 보였다. 또한, 사장 케이블이나 이에 준한 케이블은 특성점을 넘지 않으므로 공학적으로 충분한 가치를 갖는다고 볼 수 있다. 더불어 대칭 1모드에서 발생되는 갤로핑과 Parametric 공진대역을 분석하여 연구의 활용성을 확인하였다.

• Structural Engineering and Mechanics
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• 제20권3호
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• pp.363-380
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• 2005

The cable tension plays an important role in the construction, assessment and long-term health monitoring of cable structures. The cable vibration equation is nonlinear if cable sag and bending stiffness are included. The engineering implementation of a vibration-based cable tension evaluation is mostly carried out by the simple taut string theory. However, the simple theory may cause unacceptable errors in many applications since the cable sag and bending stiffness are ignored. From the practical point of view, it is necessary to have empirical formulas if they are simple and yet accurate. Based on the solutions by means of energy method and fitting the exact solutions of cable vibration equations where the cable sag and bending stiffness are respectively taken into account, the empirical formulas are proposed in the paper to estimate cable tension based on the cable fundamental frequency only. The applicability of the proposed formulas is verified by comparing the results with those reported in the literatures and with the experimental results carried out on the stay cables in the laboratory. The proposed formulas are straightforward and they are convenient for practical engineers to fast estimate the cable tension by the cable fundamental frequency.

• Smart Structures and Systems
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• 제15권3호
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• pp.627-643
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• 2015

Negative stiffness, previously emulated by active or semi-active control for cable vibration mitigation, is realized passively using a self-contained highly compressed spring, the negative stiffness device (NSD).The NSD installed in parallel with a viscous damper (VD) in the vicinity of cable anchorage, enables increment of damper deformation during cable vibrations and hence increases the attainable cable damping. Considering the small cable displacement at the damper location, even with the weakening device, the force provided by the NSD-VD assembly is approximately linear. Complex frequency analysis has thus been conducted to evaluate the damping effect of the assembly on the cable; the displacement-dependent negative stiffness is further accounted by numerical analysis, validating the accuracy of the linear approximation for practical ranges of cable and NSD configurations. The NSD is confirmed to be a practical and cost-effective solution to improve the modal damping of a cable provided by an external damper, especially for super-long cables where the damper location is particularly limited. Moreover, mathematically, a linear negative stiffness and viscous damping assembly has proven capability to represent active or semi-active control for simplified cable vibration analysis as reported in the literature, while in these studies only the assembly located near cable anchorage has been addressed. It is of considerable interest to understand the general characteristics of a cable with the assembly relieving the location restriction, since it is quite practical to have an active controller installed at arbitrary location along the cable span such as by hanging an active tuned mass damper. In this paper the cable frequency variations and damping evolutions with respect to the arbitrary assembly location are then evaluated and compared to those of a taut cable with a viscous damper at arbitrary location, and novel frequency shifts are observed. The characterized complex frequencies presented in this paper can be used for preliminary damping effect evaluation of an adaptive passive or semi-active or active device for cable vibration control.

• 대한토목학회논문집
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• 제28권5A호
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• pp.657-664
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• 2008

사장교 케이블은 구조적으로 휨강성과 감쇠력이 작아 풍우에 의해 쉽게 유해진동이 발생한다. 이러한 풍우진동을 저감시키기 위한 효과적인 방법으로 부가댐퍼를 장착하여 케이블의 감쇠력을 증가시키는 제어시스템이 널리 사용되어왔다. 그러나 사장교의 장대화로 인해 구조적으로나 미적으로 충분한 감쇠력을 제공할 수 있는 위치에 부가댐퍼를 장착하기 어렵게 되었다. 최근 본 저자는 사장교의 미관을 해치지 않으면서 기존의 제어시스템보다 효과적으로 케이블의 진동을 저감시킬 수 있는 새로운 개념의 사장교 케이블 진동 제어시스템을 제안하였다. 본 논문에서는 기존의 연구를 확장하여 새그(Sag)를 고려한 Movable anchorage 시스템을 제안하였으며, 수치해석을 통한 제어성능을 평가하였다. 수치해석의 결과 제안된 시스템은 새그를 고려하였을 때에도 고려하지 않은 경우와 마찬가지로 베어링장치의 강성이 작을수록 기존의 비감쇠 시스템이나 일반적인 수동제어시스템보다 훨씬 좋은 성능을 나타내었다. 제안된 시스템에 있어서 최적의 제어성능을 제공하기 위해서는 새그의 크기를 고려해서 최적의 감쇠계수를 결정해야 할 것으로 사료된다.

• 대한토목학회논문집
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• 제26권5A호
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• pp.881-885
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• 2006

사장교 케이블은 구조적으로 휨강성과 감쇠력이 작아 풍우에 의해 쉽게 유해진동이 발생한다. 이러한 풍우진동을 저감시키기 위한 효과적인 방법으로 부가댐퍼를 장착하여 케이블의 감쇠력을 증가시키는 제어시스템이 널리 사용되어왔다. 그러나 사장교의 장대화로 인해 구조적으로나 미적으로 충분한 감쇠력을 제공할 수 있는 위치에 부가댐퍼를 장착하기 어렵게 되었다. 그러므로 본 논문은 사장교의 미관을 해치지 않으면서 기존의 제어시스템보다 효과적으로 케이블의 진동을 저감시킬 수 있는 새로운 개념의 제어시스템을 제안하였다. 제안된 시스템은 케이블 앵커리지에 적층고무베어링과 같은 유동이 가능한 장치와 내부댐퍼로 구성되었으며, 제어성능평가를 위해 해석모델을 개발하였다. 제안된 시스템의 제어성능 분석을 위해 수치해석을 수행하였으며 기존의 부가 댐퍼시스템과 진동 저감효과를 비교하였다. 제안된 제어시스템은 기존의 부가댐퍼 시스템 보다 효과적으로 진동을 저감시킬 수 있었으며 사장교 케이블의 풍우진동 저감을 위해 효과적인 시스템으로 사료된다.