Experimental study on multiple tuned mass dampers to reduce seismic responses of a three‐storey building structure

In this study, several mass dampers were designed and fabricated to suppress the seismic responses of a ¼‐scale three‐storey building structure. The dynamic properties of the dampers and structure were identified from free and forced vibration tests. The building structure with or without the dampers was, respectively, tested on a shake table under the white noise excitation, the scaled 1940 El Centro earthquake and the scaled 1952 Taft earthquake. The dampers were placed on the building floors using the sequential procedure developed by the authors in previous studies. Experimental results indicated that the multiple damper system is substantially superior to a single tuned mass damper in mitigating the floor accelerations even though the multiple dampers are sub‐optimal in terms of tuning frequency, damping and placement. These results validated the sequential procedure for placement of the multiple dampers. The structure was also analysed numerically based on the shake table excitation and the identified structure and damper parameters for all test cases. Numerical and experimental results are in good agreement, validating the dynamic properties identified. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimum strength ratio of hysteretic damper

This paper deals with steel moment frames combined with hysteretic dampers. Specifically, it examines the strength of dampers required to minimize damage to moment frames under earthquake loading. The important structural variables are the ratio of the dampers' shear strength to the maximum resistance, termed β in this study, and the relative stiffness between the damper and the main frame, termed k. The equivalent viscous damping ratio of the entire structural system is affected by the quantities β and k and the ductility ratio of the main frame. The optimum dampers' strength ratio (β_opt), which maximizes the equivalent viscous damping ratio, was formulated as a function of k, and it was found that β_opt is independent of the ductility ratio of the main frame. Earthquake response analysis confirmed that damage to the main frame can be significantly reduced by hysteretic dampers and minimized at the value of β_opt. © 1998 John Wiley & Sons, Ltd.     

Performance of multiple tuned mass dampers for attenuating undesirable oscillations of structures under the ground acceleration

Multiple tuned mass dampers (MTMDs) consisting of many tuned mass dampers (TMDs) with a uniform distribution of natural frequencies are considered for attenuating undesirable vibration of a structure. The MTMD is manufactured by keeping the stiffness and damping constant and varying the mass. The structure is represented by its mode‐generalized system in the specific vibration mode being controlled using the mode reduced‐order method. The optimum parameters of the MTMD are investigated to delineate the influence of the important parameters on the effectiveness and robustness of the MTMD by conducting a numerical searching technique in two directions. The parameters include: the frequency spacing, average damping ratio, mass ratio and total number. The criterion selected for the optimization is the minimization of the maximum value of the dynamic magnification factor (DMF) of the structure with MTMD (i.e. Min.Max.DMF). In this paper, for the sake of comparison, the MTMD(II), which is made by keeping the mass constant and varying the stiffness and damping coefficient, and a single TMD are also taken into account. It is demonstrated that the optimum frequency spacing of the MTMD is the same as that of the MTMD(II) and the optimum average damping ratio of the MTMD is a little larger than that of the MTMD(II). It is also found that the optimum MTMD is more effective than the optimum MTMD(II) and the optimum single TMD with equal mass. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal design of viscoelastic dampers using eigenvalue assignment

In this study a procedure for determining the optimum size and location of viscoelastic dampers is proposed using the eigenvalue assignment technique. Natural frequencies and modal damping ratios, required to realize a given target response, are determined first by the convex model. Then the desired dynamic structural properties are realized by optimally distributing the damping and stiffness coefficients of viscoelastic dampers using non‐linear programming based on the gradient of eigenvalues. This optimization method provides information on the optimal location as well as the magnitude of the damper parameters. The proposed procedure is applied to the retrofit of a 10‐story shear frame, and to a three‐dimensional structure with an asymmetric plan. The analysis results confirm that the responses of model structures retrofitted by the proposed method correspond well with the given target response. Copyright © 2003 John Wiley & Sons, Ltd.     

Supporting brace sizing in structures with added linear viscous fluid dampers: A filter design solution

Viscous fluid dampers have proved to be effective in suppressing unwanted vibrations in a range of engineering structures. When dampers are fitted in a structure, a brace is typically used to attach them to the main structure. The stiffness of this brace can significantly alter the effectiveness of the damper, and in structures with multiple dampers, this can be a complex scenario to model. In this paper, we demonstrate that the effects of the brace compliance on the damper performance can be modelled by way of a first‐order filter. We use this result to formulate a procedure that calculates the stiffness required by the supporting brace to provide a specified effectiveness of the damping action. The proposed procedure assumes that viscous dampers have been sized in a previous design step based on any optimal methodology in which, as is usually the case, the presence of supporting braces and their dynamic effects were neglected. Firstly considering a one degree‐of‐freedom system, we show that the proposed method ensures a desired level of damper efficiency for all frequencies within a selected bandwidth. Then the analysis is extended to the case of multi‐degree‐of‐freedom systems to show that the design criteria can be applied in a straightforward and successful manner to more complex structures. © 2014 The Authors. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.     

Non-monotonic optimal damper placement via steepest direction search

An efficient and systematic procedure is proposed for finding the optimal damper positioning to minimize the dynamic compliance of a 3-D shear building model. The dynamic compliance is expressed in terms of the transfer function amplitudes of the local interstorey drifts evaluated at the undamped fundamental natural frequency. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added dampers. Optimality criteria are derived and the optimal damper positioning is determined via an original steepest direction search algorithm. This algorithm enables one to find an optimal damper positioning sequentially for gradually increasing damper capacity levels. A non-monotonic design path with respect to the total damper capacity level often appears in the application of this algorithm. A new augmented algorithm via parameter switching is devised to find this non-monotonic design path. Copyright © 1999 John Wiley & Sons, Ltd.     

用于高压电气设备的剪切型铅减震器性能影响研究

作为重要的电气设备抗震技术产品,剪切型铅减震器能够有效降低电气设备的地震响应。但随着电气设备电压等级的提高,设备结构规格不断增大,其地震作用力显著增大,对电气设备安装的减震器性能提出了更高要求。通过剪切型铅减震器的低周反复加载试验研究,分析其受力模型,对比减震器在不同加载频率下的力学和阻尼耗能性能,并根据试验结果提出优化工艺,进一步提高减震器性能,为电气设备抗震能力的提高提供更可靠的技术保障     

考虑阻尼器极限状态的耗能减震体系 斜拉桥抗震性能分析

在大震或特大震下,黏滞阻尼器可能因某个极限状态的出现而发生破坏。现有在斜拉桥上设置黏滞阻尼器的研究多集中在阻尼器的参数优化上,很少考虑到阻尼器失效对斜拉桥抗震性能的影响。针对这一问题,以某三塔斜拉桥为背景,利用OpenSees平台建立斜拉桥有限元模型和可以考虑承载力及行程极限的黏滞阻尼器模型;分析黏滞阻尼器的阻尼系数和阻尼指数对斜拉桥地震响应的影响,确定阻尼器参数的取值;对不安装阻尼器、安装不考虑极限状态及考虑极限状态阻尼器等多种工况的斜拉桥进行非线性时程分析,对比各工况斜拉桥的地震响应。分析结果表明,在大震下,考虑极限状态阻尼器的耗能能力及减震效果将显著降低;不考虑阻尼器达到极限状态后失效的情况将高估耗能减震设计斜拉桥的抗震能力。     

Optimum viscous damper for connecting adjacent SDOF structures for harmonic and stationary white‐noise random excitations

The dynamic behaviour of two adjacent single‐degree‐of‐freedom (SDOF) structures connected with a viscous damper is studied under base acceleration. The base acceleration is modelled as harmonic excitation as well as stationary white‐noise random process. The governing equations of motion of the connected system are derived and solved for relative displacement and absolute acceleration responses of connected structures. The response of structures is found to be reduced by connecting with a viscous damper having appropriate damping. For undamped SDOF structures, the closed‐form expressions for optimum damping of viscous damper for minimum steady state as well as minimum mean square relative displacement and absolute acceleration of either of the connected SDOF structures are derived. The optimum damper damping is found to be functions of mass and frequency ratio of two connected structures. Further, numerical results had indicated that the damping of the connected structures does not have noticeable effects on the optimum damper damping and the corresponding optimized response. This implies that the derived closed‐form expressions for optimum damper damping of undamped structures can also be used in practical applications for damped structures. Copyright © 2006 John Wiley & Sons, Ltd.     

Damper placement optimization in a shear building model with discrete design variables: a mixed‐integer second‐order cone programming approach

Supplemental damping is known as an efficient and practical means to improve seismic response of building structures. Presented in this paper is a mixed‐integer programming approach to find the optimal placement of supplemental dampers in a given shear building model. The damping coefficients of dampers are treated as discrete design variables. It is shown that a minimization problem of the sum of the transfer function amplitudes of the interstory drifts can be formulated as a mixed‐integer second‐order cone programming problem. The global optimal solution of the optimization problem is then found by using a solver based on a branch‐and‐cut algorithm. Two numerical examples in literature are solved with discrete design variables. In one of these examples, the proposed method finds a better solution than an existing method in literature developed for the continuous optimal damper placement problem. Copyright © 2013 John Wiley & Sons, Ltd.     

双座串联大跨度斜拉桥粘滞阻尼器参数分析

以双座串联大跨度斜拉桥-珠海洪鹤大桥为背景,根据桥梁自振特性及场地效应,生成了三组人工波,采用纵向+2/3竖向的地震作用组合输入方式,通过非线性时程分析,系统的研究了粘滞阻尼器对双座串联大跨度斜拉桥减震性能的影响。同时为了确定粘滞阻尼器的最优参数,对粘滞阻尼器的阻尼系数C和速度指数α进行了参数敏感性分析。结果表明:设置纵向粘滞阻尼器能够显著减小双座串联斜拉桥的纵向位移响应,减小主梁在串联处发生碰撞的概率,同时改善主塔塔底结构受力情况,具有良好的耗能减震效果。综合考虑安全性、适用性和经济性等方面,最后给出针对洪鹤大桥的最优粘滞阻尼器参数:速度指数α为0.3,阻尼系数C为3 000kN/（m/s）^0.3。     

Particle swarm optimization of TMD by non‐stationary base excitation during earthquake

There are many traditional methods to find the optimum parameters of a tuned mass damper (TMD) subject to stationary base excitations. It is very difficult to obtain the optimum parameters of a TMD subject to non‐stationary base excitations using these traditional optimization techniques. In this paper, by applying particle swarm optimization (PSO) algorithm as a novel evolutionary algorithm, the optimum parameters including the optimum mass ratio, damper damping and tuning frequency of the TMD system attached to a viscously damped single‐degree‐of‐freedom main system subject to non‐stationary excitation can be obtained when taking either the displacement or the acceleration mean square response, as well as their combination, as the cost function. For simplicity of presentation, the non‐stationary excitation is modeled by an evolutionary stationary process in the paper. By means of three numerical examples for different types of non‐stationary ground acceleration models, the results indicate that PSO can be used to find the optimum mass ratio, damper damping and tuning frequency of the non‐stationary TMD system, and it is quite easy to be programmed for practical engineering applications. Copyright © 2008 John Wiley & Sons, Ltd.     

Application of semi‐active tuned mass dampers to base‐excited systems

A continuously variable semi‐active damper is used in a tuned mass damper (TMD) to reduce the level of vibration of a single‐degree‐of‐freedom system subjected to harmonic base excitations. The ground hook dampers as have been used in the auto‐industry are being studied here. Using these dampers a new class of tuned mass dampers, named as ground hook tuned mass dampers (GHTMD) is being introduced. In order to generalize the design properties of the GHTMDs, they are defined in terms of non‐dimensional parameters. The optimum design parameters of GHTMDs for lightly damped systems are obtained based on the minimization of the steady‐state displacement response of the main mass. These parameters are computed for different mass ratios and main system damping ratios. Frequency responses of the resulting systems are compared to that of equivalent TMDs using passive dampers. In addition, other characteristics of this system as compared to the passive TMDs are discussed. A design guide to obtain the optimum parameters of GHTMD using the developed diagrams in this paper based on non‐dimensional values is presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimum tuned-mass dampers for minimizing steady-state response of support-excited and damped systems

A numerical searching procedure to find the optimum tuning frequency and damping ratio of the tuned-mass damper which can reduce the steady-state response of damped main systems to a minimum level is developed and applied to the two different harmonic excitation sources, support motion of fixed-displacement amplitude and support motion of fixed-acceleration amplitude. The explicit formulae for these optimum parameters are then derived through a sequence of curve-fitting schemes. It has been found that, as the error of the explicit formulae is negligible, they provide a convenient tool to compute the optimum parameters in engineering applications. The numerical results show that the tuned-mass damper is less effective in reducing the system's response when there is a high level of damping incorporated into the system. It is also found that the optimum tuning frequency is strongly influenced by the damping level of a system, especially in regard to the fixed-acceleration support motion, but the optimum damping ratio of the tuned-mass damper is not sensitive to the damping level of a system. The response of the damped system using the undamped optimum value as the damping of the tuned-mass damper is not much different from the response using the damped optimum value.     

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.     

Dynamic properties analysis of a stay cable-damper system in consideration of design and construction factors

A numerical solution based on the Steffensen stable point iterative method is proposed to resolve the transcendental frequency equation of a stay cable-damper system. The frequency equation, which considers clamped supports and fl exural rigidity of the cable, is intended to investigate the infl uence of the parameters of the cable damper system on its dynamic characteristics. Two factors involved in the design and construction phases, the damping coeffi cient induced by external dampers and the cable tension, are the focus of this study. Their impact on modal frequencies and damping ratios in these two phases of cable-damper systems are investigated by resolving the equation with the proposed solution. It is shown that the damping coeffi cient and cable tension exert more noticeable effects on the modal damping ratios than on the modal frequencies of stay cable-damper systems, and the two factors can serve as design variables in the design phase and as adjustment factors in the construction phase. On the basis of the results, a roadmap for system-level optimal design of stay cable-damper systems that can achieve global optimal vibration suppression for the entire bridge is proposed and discussed.     

基于高阻尼纳米复合材料的直角型黏弹性阻尼器的数值模拟

为提高装配式钢结构梁柱节点的抗震性能,首先通过熔融共混法制备高阻尼性能纳米偏高岭土/氟橡胶(NanoGmetakaolin/Fluororubber,NMK/FKM)复合材料,并对该新型材料进行4种频率下的动态力学性能试验和静态力学试验,然后以 NMK/FKM 纳米复合材料为核心耗能材料,对所提出的直角型黏弹性阻尼器进行 ABAQUS有限元模拟分析.研究结果表明:当频率为1．5Hz 时,NMK/FKM 纳米复合材料宽阻尼温域和 TA 值皆达到峰值,该工况下材料的阻尼性能最佳;直角型黏弹性阻尼器表现出刚度随位移幅值的增大而增大的动力特性;当频率为0．5、1．0和1．5Hz 时,阻尼器滞回特性表现出非线性特征,当频率升至2．0Hz时,滞回特性则为线性.随着黏弹性材料层厚度的增大,滞回环面积、阻尼器刚度和最大阻尼力逐渐减小;随着高跨比的增大,阻尼器耗能性能提升.通过调整阻尼器的高跨比和阻尼材料层厚度,可以进一步提高直角型阻尼器的动态响应.     

结构附加粘滞阻尼器的抗震设计

本文结合抗震设计规范反应谱,给出了一个附加非线性流体粘滞阻尼器结构的抗震设计方法。研究了非线性阻尼器的力学特性,引入了非线性流体阻尼器的等效线性阻尼比,给出了计算最大加速度时刻附加非线性流体阻尼器结构反应的荷载组合系数,提出了按阻尼力的水平力分量与楼层剪力成正比的原则分配阻尼器阻尼系数的方法。同时给出了基于抗震规范设计反应谱附加非线性阻尼器结构的设计流程,通过一个算例说明了使用该方法设计附加非线性粘滞阻尼器结构的全过程。算例分析表明,这种设计方法适合于手算,便于设计人员掌握,在初步设计阶段可以快速、有效地设计满足给定性能水平的附加非线性流体阻尼器体系。     

Reliability-based optimal design of nonlinear viscous dampers for the seismic protection of structural systems

Viscous dampers are widely employed for enhancing the seismic performance of structural systems, and their design is often carried out using simplified approaches to account for the uncertainty in the seismic input. This paper introduces a novel and rigorous approach that allows to explicitly consider the variability of the intensity and characteristics of the seismic input in designing the optimal viscous constant and velocity exponent of the dampers based on performance-based criteria. The optimal solution permits controlling the probability of structural failure, while minimizing the damper cost, related to the sum of the damper forces. The solution to the optimization problem is efficiently sought via the constrained optimization by linear approximation (COBYLA) method, while Subset simulation together with auxiliary response method are employed for the performance assessment at each iteration of the optimization process. A 3-storey steel moment-resisting building frame is considered to illustrate the application of the proposed design methodology and to evaluate and compare the performances that can be achieved with different damper nonlinearity levels. Comparisons are also made with the results obtained by applying simplifying approaches, often employed in design practice, as those aiming to minimize the sum of the viscous damping constant and/or considering a single hazard level for the performance assessment.     

Damping identification of a full‐scale passively controlled five‐story steel building structure

A series of large‐scale dynamic tests was conducted on a passively controlled five‐story steel building on the E‐Defense shaking table facility in Japan to accumulate knowledge of realistic seismic behavior of passively controlled structures. The specimen was tested by repeatedly inserting and replacing each of four damper types, that is, the buckling restrained braces, viscous dampers, oil dampers, and viscoelastic dampers. Finally, the bare steel moment frame was tested after removing all dampers. A variety of excitations was applied to the specimen, including white noise, various levels of seismic motion, and shaker excitation. System identification was implemented to extract dynamic properties of the specimen from the recorded floor acceleration data. Damping characteristics of the specimen were identified. In addition, simplified estimations of the supplemental damping ratios provided by added dampers were presented to provide insight into understanding the damping characteristics of the specimen. It is shown that damping ratios for the specimen equipped with velocity‐dependent dampers decreased obviously with the increasing order of modes, exhibiting frequency dependency. Damping ratios for the specimen equipped with oil and viscoelastic dampers remained constant regardless of vibration amplitudes, whereas those for the specimen equipped with viscous dampers increased obviously with an increase in vibration amplitudes because of the viscosity nonlinearity of the dampers. In very small‐amplitude vibrations, viscous and oil dampers provided much lower supplemental damping than the standard, whereas viscoelastic dampers could be very efficient. Copyright © 2012 John Wiley & Sons, Ltd.