An experimental study on active tendon control of cable-stayed bridges

Active tendon control of cable-stayed bridges subject to a vertical sinusoidal force is experimentally and analytically studied. Emphasis is placed on the effects of linear and non-linear internal resonances on the control (due to the presence of the cable vibration). A simple cable-supported cantilever beam is used as a model. It is found that active tendon control is very effective in vertical girder motion with small cable vibration (girder dominated motion), whereas it is not effective in vertical girder motion with large cable vibration (cable dominated motion). Analytical prediction is very satisfactory except for the latter case.     

拉索端部弹性约束振动控制研究(Ⅱ)——试验验证

在索端沿轴向设置弹性约束,对拉索振动轴向被动控制进行了试验研究。研究了支座移动对拉索振动频率的影响;验证了弹性约束对拉索振动的减振效果,讨论了阻尼系数和弹簧刚度对减振效果的影响;最后验证文献[10]中理论研究的正确性。     

ACTIVE TENDON CONTROL OF CABLE-STAYED BRIDGES

This paper considers the active vibration control of cables and cable/structure systems with an active tendon controlling the axial displacement of the cable anchor point. It is demonstrated that a force feedback based on a collocated force sensor measuring the tension in the cable is feasible and that this control configuration can be associated with control laws with guaranteed stability properties. Experimental results are presented on a cable with small sag and on a cable/structure system. They show that the control algorithm can provide the structure with several percent of active damping and that the parametric resonance does not occur when the natural frequency of the structure is twice that of the cable.     

Dynamic loading test and simulation analysis of full‐scale semi‐active hydraulic damper for structural control

A semi‐active hydraulic damper (SHD) for a semi‐active damper system, which is useful for practical structural control especially for large earthquakes, has been developed. Its maximum damping force is set to 1 or 2 MN, and it is controlled by only 70 W of electric power. An SHD with a maximum damping force of 1 MN was applied to an actual building in 1998. This paper first presents the results of a dynamic loading test to confirm the control performance of the SHD. Next, an analytical model of SHDs (SHD model) is constructed with the same concept for two kinds of SHDs based on the test results. Through simulation analyses of the test results using the proposed SHD model, the dynamic characteristics of the SHD can be well represented within practical conditions. Simulation analyses are also carried out using a simple structure model with the SHD model. It is shown that this SHD model can be used to precisely evaluate the control effect of the semi‐active damper system and is useful in practical SHD design under the applied conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

A mathematical hysteretic model for elastomeric isolation bearings

An analytical model for high damping elastomeric isolation bearings is presented in this paper. The model is used to describe mathematically the damping force and restoring force of the rubber material and bearing. Ten parameters to be identified from cyclic loading tests are included in the model. The sensitivity of the ten parameters in affecting the model is examined. These ten parameters are functions of a number of influence factors on the elastomer such as the rubber compound, Mullins effect, scragging effect, frequency, temperature and axial load. In this study, however, only the Mullins effect, scragging effect, frequency and temperature are investigated. Both material tests and shaking table tests were performed to validate the proposed model. Based on the comparison between the experimental and the analytical results, it is found that the proposed analytical model is capable of predicting the shear force–displacement hysteresis very accurately for both rubber material and bearing under cyclic loading reversals. The seismic response time histories of the bearing can also be captured, using the proposed analytical model, with a practically acceptable precision. Copyright © 2002 John Wiley & Sons, Ltd.     

拉索端部弹性约束振动控制研究(I)——理论模型

本文建立了拉索振动的轴向被动控制理论模型。在拉索端部沿轴向设置弹性约束,通过影响索端支座的移动,从而改变拉索的振动特性,最终达到减振效果。通过D’Alembert原理建立拉索-弹性约束系统振动方程,通过Galerkin方法将偏微分方程转化为常微分方程,应用龙格-库塔积分法求解方程;经过仿真分析,验证了该振动控制具有明显的减振效果,并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响;最后给出了计算最优阻尼参数的近似解析式,为工程师提供了简便有效的参考依据及设计方法。     

Hybrid seismic protection of cable‐stayed bridges

This paper proposes a hybrid control strategy combining passive and semi‐active control systems for seismic protection of cable‐stayed bridges. The efficacy of this control strategy is verified by examining the ASCE first‐generation benchmark problem for a seismically excited cable‐stayed bridge, which employs a three‐dimensional linearized evaluation bridge model as a testbed structure. Herein, conventional lead–rubber bearings are introduced as base isolation devices, and semi‐active dampers (e.g., variable orifice damper, controllable fluid damper, etc.) are considered as supplemental damping devices. For the semi‐active dampers, a clipped‐optimal control algorithm, shown to perform well in previous studies involving controllable dampers, is considered. Because the semi‐active damper is a controllable energy‐dissipation device that cannot add mechanical energy to the structural system, the proposed hybrid control strategy is fail‐safe in that the bounded‐input, bounded‐output stability of the controlled structure is guaranteed. Numerical simulation results show that the performance of the proposed hybrid control strategy is quite effective in protecting seismically excited cable‐stayed bridges. Copyright © 2004 John Wiley & Sons, Ltd.     

Semi‐active control of sliding isolated bridges using MR dampers: an experimental and numerical study

Sliding base‐isolation systems used in bridges reduce pier drifts, but at the expense of increased bearing displacements under near‐source pulse‐type earthquakes. It is common practice to incorporate supplemental passive non‐linear dampers into the isolation system to counter increased bearing displacements. Non‐linear passive dampers can certainly reduce bearing displacements, but only with increased isolation level forces and pier drifts. The semi‐active controllable non‐linear dampers, which can vary damping in real time, can reduce bearing displacements without further increase in forces and pier drifts; and hence deserve investigation. In this study performance of such a ‘smart’ sliding isolation system, used in a 1:20 scaled bridge model, employing semi‐active controllable magneto‐rheological (MR) dampers is investigated, analytically and experimentally, under several near‐fault earthquakes. A non‐linear analytical model, which incorporates the non‐linearities of sliding bearings and the MR damper, is developed. A Lyapunov control algorithm for control of the MR damper is developed and implemented in shake table tests. Analytical and shake table test results are compared. It is shown that the smart MR damper reduces bearing displacements further than the passive low‐ and high‐damping cases, while maintaining isolation level forces less than the passive high‐damping case. Copyright © 2005 John Wiley & Sons, Ltd.     

三维隔震单层球面网壳结构频率相关变阻尼半主动控制

在不同频率特征的地震动作用下,三维隔震单层球面网壳结构隔震层最优阻尼设计不同.文中基于单自由度体系加速度传递率函数,提出一种地震动主频相关的加速度阈值变阻尼半主动控制方法以及地震动主频分区识别方法.基于ABAQUS软件的DLOAD子程序,开展了三维隔震单层球面网壳被动控制与半主动控制有限元计算,对节点加速度、杆件轴力进...     

Semiactive variable stiffness control for parametric vibration of cables

In this paper, a semiactive variable stiffness （SVS） device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented. The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect. From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.     

长型大截面地下结构的横向自由振动方程

文中综合考虑了内阻尼、外阻尼、剪切变形、横截面转动惯性、轴力和地基模型参数的影响,推得了弹性地基梁的一般自由振动方程。由这一方程可以得到一系列特殊情况下地下结构的自由振动方程。这一方程不仅能从理论上扩展了Timoshenko粱理论,而且在后续的研究中,为研究上述因素对于地下结构的自由振动和强迫振动的影响奠定了理论基础。     

Passive and active control of three‐dimensional buildings

The majority of the recent research effort on structural control considers two‐dimensional plane structures. However, not all buildings can be modelled as plane structures, thus limiting the capability of the proposed procedures only to regular and symmetrical structures. A new procedure is developed in this paper to analyse three‐dimensional buildings utilizing passive and active control devices. In the building model, the floors are assumed rigid in their own plane resulting in three degrees of freedom at each floor. Two types of active control devices utilizing an active tuned mass damper and an active bracing system are considered. The effect of passive mass dampers and active control force in the equations of motion is incorporated by using the Hamilton's principle. The passive parameters of the dampers as well as the controller gain is then optimized using a genetic based optimizer where the H₂, H_∞ and L₁ norms are taken as the objective functions. Copyright © 2000 John Wiley & Sons, Ltd.     

Effectiveness of structural control based on control energy perspectives

A computational algorithm for maximizing the control efficiency in actively controlling the elastic structural responses during earthquake is proposed. Study of optimal linear control using a single degree of freedom shows that applying active control is very effective in reducing the structural displacement and velocity responses for long‐period structures, but at the same time it has an adverse effect in increasing the absolute acceleration response. The extent of this adverse effect reduces the effectiveness of the control system, and therefore it poses a limit on the maximum control force in order to provide maximum control efficiency. In view of this shortcoming, maximum control energy dissipation is used to define the most effective optimal linear control law. Less displacement and velocity response are expected as larger control force is applied, but there is always a limit that maximum control energy can be dissipated. This study shows that this limit depends on the structural characteristics as well as the input ground motion, and a general trend is that the maximum control energy decreases as damping increases. Finally, application of the proposed algorithm on a six‐storey hospital building is presented to show the effectiveness of using optimal linear control on a multi‐degree‐of‐freedom system from the control energy perspectives. Copyright © 2001 John Wiley & Sons, Ltd.     

Horizontal dynamic response of a large-diameter pipe pile considering the second-order effect of axial force

The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated. Governing equations of the pile-soil system are established based on elastodynamics. Three-dimensional wave equations of soil are decoupled through differential transformation and variable separation. Consequently, expressions of soil displacements and horizontal resistances can be obtained. An analytical solution of the pile is derived based on continuity conditions between the pile and soil, subsequently from which expressions of the complex impedances are deduced. Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile. Some conclusions can be summarized as follows: stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.     

An advanced analytical model for high damping rubber bearings

Base‐isolation technologies have been developed over the years in attempts to mitigate the effects of earthquakes on structures and potentially vulnerable contents in earthquake prone areas of the world. The high damping rubber bearing (HDRB) is a relatively recent and evolving technology of this kind. The isolator shifts the fundamental period of the base‐isolated structure to a value beyond the range of the plentiful energy‐containing periods of earthquake motions and supplies significant damping to dissipate energy caused by motions. Nevertheless, the highly non‐linear mechanical behaviour of the HDRB is so complex, especially at large strains, that it is difficult to model it analytically. In this paper, an extensive study of experimental tests for identifying the mechanical characteristics of the HDRB is presented. By modifying the Wen's model to include the rate‐dependent effects, an advanced analytical model in an incremental form for the HDRB is also proposed. A very good agreement between the analytical and experimental results has been obtained. It is illustrated that the proposed mathematical model can predict well the mechanical behaviour of HDRB bearings, even at large shear strain. Copyright © 2003 John Wiley & Sons, Ltd.     

Design approaches for active, semi-active and passive control systems based on analysis of characteristics of active control force

In this paper,the characteristics of forces in active control systems connected to adjacent levels of a building are analyzed.The following characteristics are observed:(1) active control can provide signifi cantly superior supplemental damping to a building,but causes a small frequency shift;(2) the linear quadratic regulator(LQR)-based control force is composed of an elastic restoring force component and a damping force component,where the damping force is almost identical to the total control force,howev...     

Forced vibration test of a building with semi‐active damper system

The authors developed a semi‐active hydraulic damper (SHD) and installed it in an actual building in 1998. This was the first application of a semi‐active structural control system that can control a building's response in a large earthquake by continuously changing the device's damping coefficient. A forced vibration test was carried out by an exciter with a maximum force of 100 kN to investigate the building's vibration characteristics and to determine the system's performance. As a result, the primary resonance frequency and the damping ratio of a building that the SHDs were not jointed to, decreased as the exciting force increased due to the influence of non‐linear members such as PC curtain walls. The equivalent damping ratio was estimated by approximating the resonance curves using the steady‐state response of the SDOF bilinear hysteretic system. After the eight SHDs were jointed to the building, the system's performance was identified by a response control test for steady‐state vibration. The elements that composed the semi‐active damper system demonstrated the specified performance and the whole system operated well. Copyright © 2000 John Wiley & Sons, Ltd.     

Actual seismic response controlled building with semi-active damper system

This paper presents the first application of a semi-active damper system to an actual building. The Semi-active Hydraulic Damper (SHD) can produce a maximum damping force of 1000 kN with an electric power of 70 W. It is compact, so a large number of them can be installed in a single building. It is thus possible to control the building's response during a severe earthquake, because a large control force is obtained in comparison with a conventional active control system. This paper outlines the building, the control system configuration, the SHD, the control method using a Linear Quadratic Regulator, the response analysis results of the controlled building, and the dynamic loading test results of the actual SHD. The simulation analysis shows that damage to buildings can be prevented in a severe earthquake by SHD control. The dynamic loading test results of the SHD are reported, which show that the specified design values were obtained in the basic characteristic test. The control performance test using simulated response time histories, also shows that the damping force agrees well with the command. Finally, it is confirmed that the semi-active damper system applied to an actual building effectively controls its response in severe earthquakes. Copyright © 1999 John Wiley & Sons Ltd.     

Smart base isolated buildings with variable friction systems: H∞ controller and SAIVF device

A new control algorithm is developed for reducing the response of smart base isolated buildings with variable friction semiactive control systems in near‐fault earthquakes. The central idea of the control algorithm is to design a H_∞ controller for the structural system and use this controller to determine the optimum control force in the semiactive device. The H_∞ controller is designed using appropriate input and output weighting filters that have been developed for optimal performance in reducing near‐fault earthquake responses. A novel semiactive variable friction device is also developed and with the H_∞ controller shown to be effective in achieving response reductions in smart base isolated buildings in near‐fault earthquakes. The new variable friction device developed consists of four friction elements and four restoring spring elements arranged in a rhombus configuration with each arm consisting of a friction–stiffness pair. The level of friction force can be adjusted by varying the angle of the arms of the device leading to smooth variation of friction force in the device. Experimental results are presented to verify the proposed analytical model of the device. The H_∞ algorithm is implemented analytically on a five storey smart base isolated building with linear elastomeric isolation bearings and variable friction system located at the isolation level. The H_∞ controller along with the weighting filters leads to the smooth variation of friction force, thus eliminating the disadvantages associated with rapid switching. Several recent near‐fault earthquakes are considered in this study. The robustness of the H_∞ controller is shown by considering a stiffness uncertainty of ±10%. Copyright © 2006 John Wiley & Sons, Ltd.     

Initial versus tangent stiffness‐based Rayleigh damping in inelastic time history seismic analyses

In the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with useful analytical tools to design Rayleigh damping model with good control on the damping ratios throughout inelastic analysis. To that end, a review of the literature dedicated to Rayleigh damping within these last two decades is first presented; then, practical tools to control the modal damping ratios throughout the time history analysis are developed; a simple example is finally used to illustrate the differences resulting from the use of either initial or tangent stiffness‐based Rayleigh damping model. Copyright © 2013 John Wiley & Sons, Ltd.