Cable Dampers Research Articles

Seismic fragility assessment for highway bridges incorporating multi-level shape memory alloy cable dampers

An innovative multi-level shape memory alloy (SMA) cable damper is proposed for bridges in near-fault seismic regions. This study commences with the introduction of a constitutive material model for simulating SMA cables. The proposed model not only considers the self-centering hysteretic property but also accounts for the strength degradation and residual strain accumulation effects. Subsequently, the layout and working mechanism of the proposed multi-level SMA cable damper is presented. A seismic fragility analysis framework involving Box-Cox transformation and Bayesian inference is subsequently presented. The Box-Cox transformation is utilized to establish the nonlinear probabilistic seismic demand models (PSDMs), and the Bayesian-based logistic regression is employed to formulate fragility functions. Finally, a three-span continuous reinforced concrete (RC) girder bridge incorporating the multi-level SMA dampers is selected as an example to demonstrate the proposed framework. A total of 160 near-fault ground motions, containing pulse and non-pulse motions, are applied along the longitudinal direction of the bridge. To investigate the influences of different parameter values of the SMA cable damper on fragility functions, various parameters are generated with respect to a central composite design philosophy. Based on the seismic fragility analysis, it is found that the SMA isolation damper reduces the damage probabilities of the bearing and pier for all four damage states. In addition, the failure probability of the bearing decreases with the increase of the axial stiffness of the SMA damper, which is opposite to the pier. Moreover, the optimum designed SMA damper can significantly reduce the damage probability of the case study bridge, and the parameter values of the damper should be carefully selected to achieve the desired seismic performance.

Semi-Active Cable Damping to Compensate for Damping Losses Due to Reduced Cable Motion Close to Cable Anchor

The relative motion of transverse cable dampers is smaller than predicted by the taut string model because of the effects of bending stiffness and fixed support conditions. As a result of the reduced damper motion, the dissipated energy per cycle is reduced as well, which may explain why damping measurements on real stay cables with transverse dampers often show lower cable damping ratios than expected from the taut string theory. To compensate for the reduced damper motion and damper efficiency, respectively, a semi-active cable damper is proposed. The controllable damper is realized by a hydraulic oil damper with real-time controlled bypass valve whereby the resulting damper force is purely dissipative. The proposed control law is clipped viscous damping with negative stiffness. The viscous coefficient is adjusted in real time to the actual frequency of vibration to generate optimum modal damping while the negative stiffness component partially compensates for the reduced damper motion due to the flexural rigidity and fixed support conditions of the cable. The measurements of the prototype semi-active hydraulic damper are used to derive a precise model of the semi-active damper force including the control force constraints due to the fully open and fully closed bypass valve. This model is used to compute the cable damping ratios of the first four cable modes, for typical damper positions, for a taut string model and for a cable model with flexural rigidity and fixed supported ends. The obtained cable damping ratios are compared to those resulting from the passive linear viscous damper being optimized to the first four cable modes. The results demonstrate that the proposed semi-active cable damper with the consideration of the minimum and maximum control force constraints significantly enhances the cable damping of the first four modes compared to the linear viscous damper.

Modeling and Evaluation of Magnetorheological Dampers with Fluid Leakage for Cable Vibration Control

Magnetorheological (MR) dampers are common methods that are used to mitigate cable vibrations with high effectiveness. Under the long-term effect of external loads and harsh environment, MR dampers will probably suffer from various durability problems, especially fluid leakage. Hence, accurate modeling and evaluation of the effect of fluid leakage of MR dampers are of great significance for bridge maintenance. This paper will investigate the mechanical behavior of MR dampers with fluid leakage after long-term operation and will evaluate their residual performance for cable vibration control. First, three MR dampers with fluid leakage will be selected from a real bridge, followed by a laboratory test to illustrate their damping force characteristics. Based on the experimental results, a theoretical model will be proposed to predict the mechanical behavior of the leaked dampers. A parametric analysis will then be conducted to show the effect of fluid leakage on the damping capacity. Then, one full-scale cable will be idealized as a taut string and the equation of motion for the cable-leaked MR damper system will be formulated. Additional modal damping provided by the MR damper will be determined numerically. The results show that fluid leakage could cause considerable slipping in the damping force. This slipping could lead to a remarkable reduction of the achieved additional modal ratios for the cables. The results of this paper could be of practical significance for the assessment of cable dampers performance and their maintenance on real bridges.

Experimental Investigation on a Cable Structure Equipped with an Electrodynamic Damper and Its Monitoring Strategy through Energy Harvesting.

The vibration of cables in a cable-supported bridge affects its serviceability and safety. Therefore, cable dampers are essential for vibration control, monitoring, and the further maintenance of such bridges. In this study, the vibration control performance of an electrodynamic damper applied to a cable used in a footbridge was experimentally verified considering the major design variables of the damper. The damping performance was analyzed by varying the damping ratio according to the excitation condition and external circuit resistance. The acceleration and displacement at each measurement point and the frequency-domain response decreased. Considering the dominant response conditions of the cables in the bridge, an effective additional attenuation was observed. In addition, the harvesting power considering the measurement frequency and power loss was sufficient to operate a wireless measuring sensor by examining the energy harvesting performance from the cable measurement data of an actual bridge in service. Finally, a stepwise operation strategy for a cable vibration monitoring system was suggested and examined by analyzing the meteorological observation data and the power output according to the wind environment. The results demonstrate the feasibility of using an electrodynamic damper to build an integrated monitoring system capable of simultaneous cable vibration reduction and energy harvesting.

Influence of cable dampers on cable-stayed bridges

Cable-stayed bridges have seen a wider application in recent years, with many having longer and longer spans. Modern cable-stayed bridges use numerous cables to support the stiffening girders. Many cable dampers are installed to mitigate cable vibration. This paper focuses on the effect of a cable damper on the dynamic characteristics of the whole cable-stayed bridge, especially modal damping. A practical model comprising the cable, girder and damper is developed to analyse the relationship between system modal damping and the performance of a cable damper with the complex mode method. A test model with cable, girder and damper was made to verify the theoretical results. A finite-element model of a simplified cable-stayed bridge based on a test model is adopted to assess the effects of cable dampers on the anti-seismic performance and wind-resistant behaviour of the cable-stayed bridge. The results show that the cable dampers of a cable-stayed bridge can increase the modal damping of the whole bridge.

Semi Active Control of Civil Structures, Analytical and Numerical Studies

Abstract Structural control for civil structures was born out of a need to provide safer and more efficient designs with the reality of limited resources. The purpose of structural control is to absorb and to reflect the energy introduced by dynamic loads such as winds, waves, earthquakes, and traffic. Today, the protection of civil structures from severe dynamic loading is typically achieved by allowing the structures to be damaged. Semi-active control devices, also called “smart” control devices, assume the positive aspects of both the passive and active control devices. A semi-active control strategy is similar to the active control strategy. Only here, the control actuator does not directly apply force to the structure, but instead it is used to control the properties of a passive energy device, a controllable passive damper. Semi-active control strategies can be used in many of the same civil applications as passive and active control. One method of operating smart cable dampers is in a purely passive capacity, supplying the dampers with constant optimal voltage. The advantages to this strategy are the relative simplicity of implementing the control strategy as compared to a smart or active control strategy and that the dampers are more easily optimally tuned in- place, eliminating the need to have passive dampers with unique optimal damping coefficients. This research investigated semi-active control of civil structures for natural hazard mitigation. The research has two components, the seismic protection of buildings and the mitigation of wind-induced vibration in structures. An ideal semi-active motion equation of a composite beam that consists of a cantilever beam bonded with a PZT patch using Hamilton's principle and Galerkin's method was treated. A series R-L and a parallel R-L shunt circuits are coupled into the motion equation respectively by means of the constitutive relation of piezoelectric material and Kirchhoff's law to control the beam vibration. A numerical example of the parallel R-L piezoelectric vibration shunt control simulated with MATLAB® is presented. An analytical study of the resistor-inductor (R-L) passive piezoelectric vibration shunt control of a cantilever beam was undertaken. The modal and strain analyses were performed by varying the material properties and geometric configurations of the piezoelectric transducer in relation to the structure in order to maximize the mechanical strain produced in the piezoelectric transducer.

Full-scale measurements and system identification on Sutong cable-stayed bridge during Typhoon Fung-Wong.

The structural health monitoring system (SHMS) provides an effective tool to conduct full-scale measurements on existing bridges for essential research on bridge wind engineering. In July 2008, Typhoon Fung-Wong lashed China and hit Sutong cable-stayed bridge (SCB) in China. During typhoon period, full-scale measurements were conducted to record the wind data and the structural vibration responses were collected by the SHMS installed on SCB. Based on the statistical method and the spectral analysis technique, the measured data are analyzed to obtain the typical parameters and characteristics. Furthermore, this paper analyzed the measured structural vibration responses and indicated the vibration characteristics of the stay cable and the deck, the relationship between structural vibrations and wind speed, the comparison of upstream and downstream cable vibrations, the effectiveness of cable dampers, and so forth. Considering the significance of damping ratio in vibration mitigation, the modal damping ratios of the SCB are identified based on the Hilbert-Huang transform (HHT) combined with the random decrement technique (RDT). The analysis results can be used to validate the current dynamic characteristic analysis methods, buffeting calculation methods, and wind tunnel test results of the long-span cable-stayed bridges.

Influence of Cable Dampers on Cable-Stayed Bridges

Cable-stayed bridges have seen a wider application in recent years, with many having longer and longer spans. Modern cable-stayed bridges are using numerous cables to support the stiffing girders. Many cable dampers are installed to mitigate cable vibration. This paper focuses the attention on the effect of cable damper on the dynamic characteristics of the whole cable-stayed bridge, especially the modal damping. A practical model comprised of the cable, girder, and damper is developed to analyze the relationship between system modal damping and the performance of cable damper with complex mode method. A test model with cable, girder and damper was made to verify the theoretical results. A finite element model of a simplified cable-stayed bridge based on test model is adopted to assess the effects of cable dampers on the anti-seismic performance and wind-resistant behavior of the cable-stayed bridge. The results show that the cable dampers of cable-stayed bridge can increase the modal damping of the whole bridge.

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

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.

Semi-active control of three-dimensional vibrations of an inclined sag cable with magnetorheological dampers

Three-dimensional semi-active vibration control of an inclined sag cable with discrete magnetorheological (MR) dampers is investigated in this paper using the finite difference method (FDM). A modified Dahl model is used to describe the dynamic property of MR damper. The nonlinear equations of motion of cable–dampers system are first established, which accounts for coupling between in-plane and out-of-plane motions, and also for the displacement of the support points. A MR damper can be considered as a variable friction damper approximately, so a semi-active control strategy based on the modulated homogeneous friction algorithm is proposed. Taking a typical short cable as an example, the vibration reduction ability with optimally controlled MR dampers is verified numerically by comparison with the viscous damper tuned to a single mode response. The analysis show that, if the conditions are fulfilled at which the optimal tuned viscous damper is designed, the MR damper and the viscous damper are performing equally well; however, if the response of the cable is dominated by several modes, the MR damper can achieve better vibration reduction effect compared with viscous damper. Especially, if the amplitude of the support point motion less than a threshold value, MR damper can prevent subharmonic excitation caused by support point motion from taking place, consequently, MR damper achieves significant vibration reduction compared to viscous damper. In addition, the influence of measurement noise on control effect and the robustness of the proposed semi-active control rule are also examined.

Development of Cable-Exciting System for Evaluating Modal Damping of Stay Cables

One of the effective alternatives to suppress hazardous vibration of stay cables is to use cable dampers. In order to design the cable damper optimally, it is necessary to exactly estimate the dynamic characteristics of existing cables. To estimate more reliable dynamic properties of stay cables, precise excitations inducing forced vibration are needed. Hence, in this paper, a cable-exciting system (cable exciter) controlled digitally is developed. A design formula for the cable exciter is also derived by the solution of the equation of motion of a cable-exciter system. The performance of the cable exciter is verified by sine sweeping tests and resonance tests for a cable model in a laboratory. Also from those tests, more reliable dynamic properties of the cable model are obtained. Thus, it is ascertained that modal damping of stay cables is proportional to the amplitude of cable vibration.

사장교 케이블 동특성 평가를 위한 케이블 가진시스템 개발

사장교에서 케이블은 교량 전체에 있어서 매우 중요한 요소이다. 차량, 바람 혹은 풍우에 의한 케이블의 진동은 교량의 안전성과 사용성을 감소시키는 주요 원인이 되어왔으며 이러한 문제를 해결하는 효과적인 방법중의 하나는 케이블 댐퍼를 설치하는 것이다. 이 케이블 댐퍼를 최적으로 설계하기 위해서는 케이블의 동특성을 정확하게 평가해야 하며 케이블 동특성치를 얻기 위해서는 정확한 가진이 필요하다. 따라서 본 연구에서는 케이블 가진시스템을 개발하고 성능을 평가하기 위해 케이블 가진시스템의 운동방정식을 유도하였으며, 케이블 가진기를 케이블 모형에 설치하여 정현진동실험과 공진진동실험을 수행하여 케이블의 동특성을 효과적으로 구하였다. As a critical member of cable-stayed bridges, stay cables play on important role of supporting the entire structure. Traffic, wind or rain-wind induced vibrations of stay cables would be a major cause of degrading both safety and serviceability of the bridge. One of the effective alternatives to solve this problem is to employ the cable dampers. In order to design the cable damper optimally, it is necessary to exactly estimate the dynamic characteristics of the existing cables. To achieve more reliable dynamic properties of stay cables, precise excitations inducing forced vibration are needed. Therefore, in this study, a cable excitation system(exciter) controlled digitally was developed. And to evaluate the performance of the cable exciter developed, a solution of the differential equation of cable motion considering the exciter was derived, Using the cable exciter, sine sweeping and resonance tests on a cable model were carried out to obtain the dynamic characteristics effectively.

Aesthetic Design of Odawara Port Bridge

The Odawara Port Bridge is located at the mouth of Odawara Port. Selecting a bridge type that symbolized the entire project and blended well with the surrounding area was critical. To achieve this, an extra-dosed prestressed concrete box girder with a main span of 122 m was selected. Construction of this bridge type is the first in the world. Special characteristics of this bridge type are a lower tower height than that of a cable-stayed bridge, the use of a saddle at the top of the towers, and the incorporation of epoxy-coated strands for diagonal cables. The design of the various sections of the bridge was achieved by integrating the characteristic shape of the towers with cable profiles while establishing horizontal continuity with the main girder. As a result of the integration process, the following design objectives were adopted: (a) constant main girder depth; (b) inverted trapezoidal main girder cross section; (c) towers without a connecting beam at the top; (d) a fan-shaped saddle; (e) compact cable vibration dampers; (f) graded metallic coloring of cables; (g) integrated steel railing and road surface lighting; (h) nighttime bridge lighting, and (i) encased drainage pipes.