Active viscous damping system for control of MDOF structures

The development and applications of a supplemental viscous damping device with active capacity are described. The system of the dampers defined as active viscous damping system (AVDS) is presented herein. Structural control principles defined here as active control theory (ACT) are used to obtain the control forces at each time step during an excitation. Control of the damping forces is possible due to a mechanical structure of the proposed AVDS and do not require the input of large power and energy. This system can be efficiently used to enhance the damping of a structure without adding in stiffness and strength. The added damping forces can be adjusted in a wide range. Its efficiency is demonstrated by a numerical simulation of a seven‐storey building subjected to earthquakes. The simulation shows that the behaviour of the damped structure with the AVDS is significantly improved compared to that of an uncontrolled system. Moreover, the response is better than that of adding either passive viscous dampers or electrorheological damping devices. Copyright © 2001 John Wiley & Sons, Ltd.     

多维地震作用下大跨空间结构的减震控制分析

考虑到多维地震输入对网架结构的不利影响,基于形状记忆合金超弹性,研制出一种兼具自复位、高耗能及放大功能于一体的形状记忆合金复合黏滞阻尼器(Hybrid Shape Memory Alloy Viscous Dampers,简称HSMAVD),并通过试验研究该阻尼器在循环荷载作用下的力学性能;然后以平面四角锥网架模型为基础,将该阻尼器替换部分网架结构杆件,并分析该阻尼器减震控制效果。结果表明形状记忆合金与黏滞阻尼器复合后具有良好的协同工作能力,可有效发挥形状记忆合金的超弹性和黏滞阻尼器的速度相关特性,使其具有稳定的滞回性能和良好的耗能能力;采用阻尼杆件替换原杆件的方法既能对结构进行有效的减震控制,又不改变原有的结构形式,是一种优越的减震控制方法,并为HSMAVD被动控制系统在结构抗震中的实际应用提供新思路。     

Damping reduction factors and code‐based design equation for structures using semi‐active viscous dampers

This study uses a semi‐active viscous damper with three different control laws to reshape the structural hysteresis loop and mitigate structural response, referred to as 1–4, 1–3 and 2–4 devices, respectively. The 1–4 control law provides damping in all four quadrants of the force‐displacement graph (it behaves like a standard viscous damper), the 1–3 control law provides resisting forces only in the first and third quadrants, and the 2–4 control law provides damping in the second and fourth quadrants. This paper first outlines the linear single degree of freedom structural performance when the three types of semi‐active viscous dampers are applied. The results show that simultaneous reduction in both displacement and base‐shear demand is only available with the semi‐active 2–4 device. To enable guidelines for adding a 2–4 device into the design procedure, damping reduction factors (RF_ξs) are developed, as they play an important role and provide a means of linking devices to design procedures. Three methods are presented to obtain RF_ξ and equivalent viscous damping of a structure with a 2–4 semi‐active viscous damper. In the first method, the relationship between RF_ξ and the damping of a semi‐active structure can be obtained by calculating the area under the force‐deformation diagram. The second and third method modified the Eurocode8 formula of RF_ξ and smoothed results from analysis, respectively. Finally, a simple method is proposed to incorporate the design or retrofit of structures with simple, robust and reliable 2–4 semi‐active viscous dampers using standard design approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Predictive active control of MDOF structures

This paper presents a theoretical study of a predictive active control system used to improve the response of multi‐degree‐of‐freedom (MDOF) structures to earthquakes. As an example a building frame equipped with electrorheological (ER) dampers is considered. The aim of the design is to find a combination of forces that are produced by the ER dampers in order to obtain an optimal structural response. The mechanical response of ER fluid dampers is regulated by an electric field. Linear auto‐regressive model with exogenous input (ARX) is used to predict the displacements and the velocities of the frame in order to overcome the time‐delay problem in the control system. The control forces in the ER devices are calculated at every time step by the optimal control theory (OCT) according to the values of the displacements and of the velocities that are predicted at the next time step at each storey of the structure. A numerical analysis of a seven‐storey ER damped structure is presented as an example. It shows a significant improvement of the structural response when the predictive active control system is applied compared to that of an uncontrolled structure or that of a structure with controlled damping forces with time delay. The structure's displacements and velocities that were used to obtain the optimal control forces were predicted according to an ‘occurring’ earthquake by the ARX model (predictive control). The response was similar to that of the structure with control forces that were calculated from a ‘known’ complete history of the earthquake's displacement and velocity values, and were applied without delay (instantaneous control). Copyright © 2000 John Wiley & Sons, Ltd.     

Seismic retrofitting of braced frame buildings by RC rocking walls and viscous dampers

A design procedure for seismic retrofitting of concentrically and eccentrically braced frame buildings is proposed and validated in this paper. Rocking walls are added to the existing system to ensure an almost uniform distribution of the interstorey displacement in elevation. To achieve direct and efficient control over the seismic performance, the design procedure is founded on the displacement‐based approach and makes use of overdamped elastic response spectra. The top displacement capacity of the building is evaluated based on a rigid lateral deformed configuration of the structure and on the ductility capacity of the dissipative members of the braced frames. The equivalent viscous damping ratio of the braced structure with rocking walls is calculated based on semi‐empirical relationships specifically calibrated in this paper for concentrically and eccentrically braced frames. If the equivalent viscous damping ratio of the structure is lower than the required equivalent viscous damping ratio, viscous dampers are added and arranged between the rocking walls and adjacent reaction columns. The design internal forces of the rocking walls are evaluated considering the contributions of more than one mode of vibration. The proposed design procedure is applied to a large set of archetype braced frame buildings and its effectiveness verified by nonlinear dynamic analysis.     

Effect of viscous damping devices on the response of seismically isolated structures

Viscous and other damping devices are often used as elements of seismic isolation systems. Despite the widespread application of nonlinear viscous systems particularly in Japan (with fewer applications in the USA and Taiwan), the application of viscous damping devices in isolation systems in the USA progressed intentionally toward the use of supplementary linear viscous devices due to the advantages offered by these devices. This paper presents experimental results on the behavior of seismically isolated structures with low damping elastomeric (LDE) and single friction pendulum (SFP) bearings with and without linear and nonlinear viscous dampers. The isolation systems are tested within a six‐story structure configured as moment frame and then again as braced frame. Emphasis is placed both on the acquisition of data related to the structural system (drifts, story shear forces, and isolator displacements) and on non‐structural systems (floor accelerations, floor spectral accelerations, and floor velocities). Moreover, the accuracy of analytical prediction of response is investigated based on the results of a total of 227 experiments, using 14 historic ground motions of far‐fault and near‐fault characteristics, on flexible moment frame and stiff braced frame structures isolated with LDE or SFP bearings and linear or nonlinear viscous dampers. It is concluded that when damping is needed to reduce displacement demands in the isolation system, linear viscous damping results in the least detrimental effect on the isolated structure. Moreover, the study concludes that the analytical prediction of peak floor accelerations and floor response spectra may contain errors that need to be considered when designing secondary systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Design formulations for supplemental viscous dampers to highway bridges

Design formulas for supplemental viscous dampers to building structures are readily available in FEMA provisions and MCEER research reports. However, for the design of supplemental viscous dampers corresponding to a desired system damping ratio of highway bridges, there exist, if any, few design guidelines. This is particularly true if the bridge components such as elastomeric bearings, piers and abutment possess different damping ratios, stiffnesses, and lumped masses. In this paper, the design formulas for supplemental viscous dampers to highway bridges have been derived based on the concept of ‘composite damping ratio’. The design formulas can be used to determine the damping coefficients of the dampers corresponding to a desired system damping ratio of the bridge in which different component damping ratios may be assumed for the elastomeric bearings, piers and abutments. The proposed design formulas are numerically validated by comparing the seismic responses of a three‐span bridge equipped with viscous dampers with those of the same bridge without viscous dampers but with an assigned inherent system damping ratio equal to the target system damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

The effect of coulomb damping on multidegree of freedom elastic structures

This paper is based on the premise that the damping mechanism of a multidegree of freedom structure can be represented by viscous and coulomb dampers. A closed form solution for the structure subjected to a sinusoidal forcing function is presented. The solution is used as the basis of a method for determining relative amounts of viscous and coulomb damping from vibration tests. The method was applied to the results of a series of vibration tests on a five storey reinforced concrete structure and approximate values of viscous and coulomb damping obtained. A comparison of the effect of various combined damping values on the earthquake response of the structure was made. It was concluded that the use of the equivalent viscous damping concept to approximate the combined effect of viscous and coulomb damping results in a low estimate of the elastic response of the structure.     

Design of dampers for structures based on optimal control theory

The aim of this paper was to propose a design guideline for using visco‐elastic dampers for the control of building structures subjected to earthquake loading as well as suspension roof structures subjected to wind loading. The active control algorithm was used to calculate the control forces. Based on the single‐mode approach the control forces were transformed to the forces which visco‐elastic dampers can provide. Application of the method to the design of the building structure with passive damping devices in the bracing system and to the suspension roof with dampers was studied. Through the application of optimal control theory a systematic design procedure to implement dampers in structures is proposed. Copyright © 2000 John Wiley & Sons, Ltd.     

THE FORMATION OF VISCOUS DAMPING MATRICES FOR THE DYNAMIC ANALYSIS OF MDOF SYSTEMS

The paper deals with the representation of dissipative effects by means of equivalent viscous forces. A brief review of the classical analytical treatment of the subject is first presented devoting particular attention to the topics of hysteretic and modal damping. The problem of forming viscous matrices in the case of systems which are non-homogeneous from the point of view of dissipation is then addressed; soil–structure systems are first considered and some accepted techniques for forming the structure contribution to the viscous matrix are reviewed. A different technique is then proposed which avoids some of the drawbacks of the previously quoted methods. In the final section of the paper it is shown how this technique is easily applicable also in the case of systems having internal concentrated dampers of viscous type, this being a situation which is difficult to tackle with usual criteria.     

台湾某钢框架大楼采用阻尼器补强结构减震效果评析

阻尼器是一种效果良好的减震装置,将阻尼器安装于结构中能够适时为结构体系提供阻尼力,从而减小地震作用对结构的破坏。黏滞阻尼器对振动的反应比较敏感,在结构受到较小振动时就可以发挥其减震效果,其阻尼力会随着振动周期和使用状态温度的不同而变化。当地震发生时,安装在结构中的阻尼器会消减地震作用,降低传导到主结构体系的地震能量,减小结构相对位移。本文介绍了黏滞阻尼器的工作原理和安装有黏滞阻尼器的结构体系的阻尼比的计算方法,对减震结构的减震效果的评析方法做出探讨,并以一安装有黏滞阻尼器的台湾某既有钢框架结构为例,分析了(1)该结构在遭受地震作用时的地震反应;(2)该结构体系在不同地震作用水平时的阻尼比,包括主体结构阻尼比和黏滞阻尼器阻尼比;(3)结构安装黏滞阻尼器后的减震效果。实例对本文的减震评析方法和减震效果进行了说明和分析,计算及分析结果表明利用黏滞阻尼器加固既有结构能够取得较好的减震效果,本文所提减震效果评析方法是一种实用有效的评析方法,对类似工程的减震评析具有一定的参考价值。     

Equivalent damping of SDOF structure with Maxwell damper

To predict the maximum earthquake response of an SDOF structure with a Maxwell fluid damper or supplemental brace-viscous damper system using the seismic design response spectrum technique, a new approach is presented to determine the first- and second-order equivalent viscous damping and stiffness, the peak responses, and the damper force of the above structure. Based on the fact that the dynamic characteristics of a general linear viscoelastically damped structure are fully determined by its free vibration properties and the relaxation time constants of a Maxwell fluid damper and supplemental brace-viscous damper system in engineering practice are all small, the method of improved multiple time scales and the equivalent criterion in which all free vibration properties are the same are used to obtain the first- and second-order equivalent viscous damping and stiffness of the above structure in closed form. The accuracy of the proposed method is higher and significantly better than that of the modal strain energy method. Furthermore, in the parametric range of the requirements of the Chinese "Code for Seismic Design of Buildings", the error of the proposed second-order equivalent system for the above-mentioned engineering structure is not more than 0.5%.     

Dynamic characteristics of multiple substructures with closely spaced frequencies

This paper considers a main structure supporting a large number of substructures. The substructures have closely spaced natural frequencies, and the combined main structure/multiple substructures system is subjected to harmonic or wide-band forces. The goal is to characterize the effects of the substructures on the response of the main structure. A special, fundamental case is studied in detail, where the substructures are oscillators with equal stiffnesses and equally spaced natural frequencies. The exact response expressions for the combined system are in terms of a complicated rational polynomial. However, by taking the limit where the number of substructures becomes large, the response expressions reduce to simple, physically meaningful results. It is found that the multiple substrutures are equivalent to a single viscous damping which is added to the damping of the main structure. An example illustrates how the results can be applied to passive vibration control of large structures.     

Active control of the seismic response of structures by combined use of base isolation and absorbing boundaries

The relative advantages of several control strategies to reduce the seismic response of multi-storey structures are studied. The strategies involve the separate or combined use of passive base isolation mechanisms and active control forces. The base isolation mechanism is modelled as an equivalent linear soft storey with high damping. The active control forces are selected so that an absorbing boundary is obtained at the top of the structure and non-reflecting or reflecting boundaries are obtained at the base of the building. It is found that the best results are obtained when a passive base isolation system is combined with an active absorbing boundary placed at the top of the building. However, the incremental gains resulting from adding a base isolation system to a structure already controlled by a roof-top active absorbing boundary are significant only for relatively soft base isolation systems. Also, the incremental gains appear to decrease as the number of storeys of the structure increases.     

大底盘多塔楼结构的混合隔震控制

结合某实际工程,针对大底盘多塔楼结构提出混合隔震的控制策略,即对大底盘上的一栋或多栋塔楼采用隔震技术,并在隔震层附设一定数量的被动、主动或半主动的减震控制装置。建立了这种大底盘多塔楼结构混合隔震控制体系的运动方程,方程中各塔楼与下部结构及隔震层之间的刚度解耦,并考虑了隔震层的非线性。研究中比较了被动非线性粘滞阻尼器,半主动变孔隙阻尼器与理想主动控制时的减震控制效果。结果表明,这种混合隔震体系可以有效地减小上部塔楼与下部结构的地震反应,提高大底盘多塔楼结构的抗震安全性,取得明显的经济和社会效益。半主动变孔隙阻尼器可以极好地追踪理想主动控制力,取得与理想主动控制相近的减震控制效果。被动非线性粘滞阻尼器也能取得较好的减震效果,且易于维护,经济性较好,从工程应用的角度来看更为现实可行,具有较好的应用推广价值。     

Amplification system for concentrated and distributed energy dissipation devices

Recent analytic, experimental, and practical studies are developing energy dissipation devices combined with amplifying mechanisms (AM) to enhance structural behavior. This research presents the theoretical and experimental development of the eccentric lever‐arm system (ELAS), a new system generically called amplified added damping (AAD), which is a combination of an AM with one or more dampers capable of supporting large deformations. The proposed AM device is a variant of the well‐known lever‐arm system. This work is divided in four parts: (1) kinematics of the ELAS and definition of an equivalent AAD; (2) parametric analysis of a linear single‐story structure with ELAS; (3) numerical analysis of a multi‐degree‐of‐freedom structure with frictional damping with and without AM; and (4) pseudo‐dynamic tests of a full scale asymmetric one story steel structure with and without frictional AAD. Parametric analyses demonstrate that using high‐amplification ratios and low supplemental damping could be a good practice. On the other hand, similar to systems without AMs, dissipation efficiency increases conformably with the stiffness of the secondary structure. As expected, it was observed that deformation was highly concentrated in the flexible edge of the asymmetric test model without damper. Conversely, the structure with frictional AAD clearly showed uniform plane deformation. The implemented AM, which has a large amplifying ratio of α≈11, performed with close accordance with numerical simulations and a high mechanical efficiency (≈95%) using a frictional damper with a very low force capacity. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of soil–structure interaction on the dynamic properties and seismic response of piled structures

This paper presents a simple and stable procedure for the estimation of periods and dampings of piled shear buildings taking soil–structure interaction into account. A substructuring methodology that includes the three-dimensional character of the foundations is used. The structure is analyzed as founded on an elastic homogeneous half-space and excited by vertically incident S waves. The strategies proposed in the literature to estimate the period and damping are revised, and a modified strategy is proposed including crossed impedances and all damping terms. Ready-to-use graphs are presented for the estimation of flexible-base period and damping in terms of their fixed-base values and the system configuration. Maximum shear forces together with base displacement and rocking peak response are also provided. It is shown that cross-coupled impedances and kinematic interaction factors need to be taken into account to obtain accurate results for piled buildings.     

An alternative practical design method for structures with viscoelastic dampers

Viscoelastic dampers (VEDs) are one of the most common passive control devices used in new and retrofit building projects which reduce the structure responses and dissipate seismic energy during an earthquake. Various methods to design this kind of dampers have been proposed based on the desired level of additional damping, eigenvalue assignment, modal strain energy, linear quadratic regulator control theories, and other approaches. In the current engineering practice, the popular method is the one based on the modal strain energy that uses the inter-story lateral stiffness as one of the main variables for damper design. However, depending on the configuration of the structure, in some cases the resulting interstory lateral stiffness can be very large. Consequently, the dampers size would also be large producing much more damping than that effectively necessary, resulting in an increase of the overall cost of the supplemental damping system and causing excessive stress on the structural elements connected to the dampers. In this paper an alternative practical design method for structures with VEDs is proposed. This method uses the inter-story shear forces as one of the main variables to accomplish the damper design compared to what was done in previous studies. Nonlinear time-history analyses were conducted on a 7-story reinforced concrete (RC) structure to check the reliability and effectiveness of the proposed method. Comparisons on the seismic performance between the structure without dampers and that equipped with VEDs were carried out. It is concluded that the proposed method results in a very suitable size of dampers, which are able to improve the performance of the structure at all levels of earthquake ground motions and satisfying the drift requirement prescribed in the codes.     

基于AFSMC算法的结构非线性振动MR控制与仿真分析

作为最近发展起来的高性能半主动控制装置,磁流变阻尼器通过改变磁场强度来调节控制力,可靠度高,体积小,出力大,并且具有Fail-Safe的特点,是一种具有广泛应用前景的新型结构控制装置。本文主要研究结构非线性振动的磁流变阻尼半主动控制。首先采用我们提出的自适应模糊滑模控制(AFSMC)算法得到了结构非线性振动的主动控制力,然后参照主动控制力,提出和仿真实现了结构非线性振动的磁流变阻尼半主动控制。最后,针对3层和20层benchm ark非线性模型,每层均设置一个磁流变阻尼器,对在给定的地震动下的结构响应进行了计算,分析了半主动控制跟踪主动控制的效果,并且对于半主动控制下的结构位移响应、加速度响应等各项指标也进行了对比分析。仿真结果表明,由于自适应模糊滑模控制算法与半主动控制算法相结合可以很好地实现结构非线性振动的半主动控制,所以能够得到令人满意的控制结果。     

基于遗传算法的粘滞阻尼器减震结构优化设计研究

以线性粘滞阻尼器加固剪切型规则框架结构为研究对象,基于能量原理提出阻尼系数正比于层间位移（α+1）次方的分配方式,在此基础上提出了一种基于遗传算法的粘滞阻尼器减震结构优化设计方法。使得中震下结构最大层间位移角小于允许值,以满足"中震不坏"的设计目标,同时令附加总阻尼系数最小,满足经济性要求。以12层规则框架为例,分别采用优化方法和其他三种方案对结构进行减震设计,计算结果表明:基于优化方法进行粘滞阻尼器减震结构优化设计,既能保证结构层间位移角小于限值,又能满足经济性要求。