Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems

The tuned mass damper inerter (TMDI) couples the classical tuned mass damper (TMD) with an inerter, a mechanical device whose generated force is proportional to the relative acceleration between its terminals, thus providing beneficial mass‐amplification effects. This paper deals with a dynamic layout in which the TMDI is installed below the isolation floor of base‐isolated structures in order to enhance the earthquake resilience and reduce the displacement demand. Unlike most of the literature studies that assumed a linearized behavior of the isolators, the aim of this paper is to investigate the effectiveness of the TMDI while accounting for the nonlinearity of the isolators. Two nonlinear constitutive behaviors are considered, a Coulomb friction model and a Bouc‐Wen hysteretic model, representative of friction pendulum and of lead‐rubber‐bearing isolators, respectively. Optimal design is based on the stochastic dynamic analysis of the system, by modeling the base acceleration as a Kanai‐Tajimi filtered stationary random process and resorting to the stochastic linearization technique to handle the nonlinear terms. Different tuning criteria based on displacement, acceleration, and energy‐based performance indices are defined, and their implications in a design process are discussed. It is proven that the improved robustness of the TMDI reduces its performance sensitivity to the tuning frequency and to the earthquake frequency content, which are well‐known shortcomings of TMD‐like systems. This important feature makes the TMDI particularly suitable for nonlinear base‐isolated structures that are affected by unavoidable uncertainties in the isolators' properties and that may experience changes of isolators effective stiffness depending on the excitation level.     

Optimal design and performance evaluation of systems with Tuned Mass Damper Inerter (TMDI)

The paper concerns the optimal design and performance evaluation of a Tuned Mass Damper Inerter (TMDI) to reduce dynamic vibrations. The system exploits properties of the inerter, a two‐terminal mechanical device able to produce a force proportional to the relative acceleration between terminals, with the ability of generating an apparent mass even two orders of magnitude greater than its own physical mass. A primary single‐degree‐of‐freedom structure is equipped with a classical linear Tuned Mass Damper (TMD), the secondary structure, whose mass is connected to the ground via an inerter. The optimal design of the TMDI is conducted by assuming a white noise process as base input and utilizing three different design methodologies: displacement minimization, acceleration minimization and maximization of the ratio between the energy dissipated in the secondary system and the total input energy. Optimal results obtained with the different methodologies are carried out and compared. Two limit cases are also considered when the inerter is not contemplated: conventional and non‐conventional TMDs, characterized by a low and a large mass ratio, respectively. The TMDI performance is evaluated and compared with conventional and non‐conventional TMDs; moreover, its robustness is assessed with a sensitivity analysis varying the design parameters. Attention is focused not exclusively on the primary structure response but also on the secondary one. Finally, the effectiveness of the optimally designed TMDI is evaluated having considered earthquake base excitation. Results demonstrate the effectiveness of TMDI systems for dynamic response reduction with superior performances and robustness than classical TMDs. Copyright © 2017 John Wiley & Sons, Ltd.     

Using an inerter‐based device for structural vibration suppression

This paper proposes the use of a novel type of passive vibration control system to reduce vibrations in civil engineering structures subject to base excitation. The new system is based on the inerter, a device that was initially developed for high‐performance suspensions in Formula 1 racing cars. The principal advantage of the inerter is that a high level of vibration isolation can be achieved with low amounts of added mass. This feature makes it an attractive potential alternative to traditional tuned mass dampers (TMDs). In this paper, the inerter system is modelled inside a multi‐storey building and is located on braces between adjacent storeys. Numerical results show that an excellent level of vibration reduction is achieved, potentially offering improvement over TMDs. The inerter‐based system is compared to a TMD system by using a range of base excitation inputs, including an earthquake signal, to demonstrate how the performance could potentially be improved by using an inerter instead of a TMD. Copyright © 2013 John Wiley & Sons, Ltd.     

调谐惯容系统的混合隔震体系一致性优化设计

基础隔震技术广泛应用于建筑结构以减轻结构的地震响应.值得注意的是,在隔震体系中减小主结构的加速度响应是以牺牲隔震器变形为代价的.调谐惯容系统(TID)和隔震器组成的混合隔震体系可减小隔震层的位移响应.与传统调谐质量阻尼器(TMD)结构类似,TID 由惯容、调谐弹簧和阻尼元件组成.因此,可直接利用 TMD减震系统的设计公式来确定 TID 的最优参数.首先基于单自由度体系(SDOF)附加 TID的运动方程,推导分析两种 TID和 TMD设计公式,对两者设计公式的前提条件和适用性进行深入的探讨.其后,借助基础隔震体系的benchmark模型来检验设计 TID的可行性和有效性.数值模拟结果表明,在不增加主结构绝对加速度响应的情况下, TID能够显著减小基础隔震结构的位移响应和基底剪力.     

Optimal design and effectiveness evaluation for inerter-based devices on mitigating seismic responses of base isolated structures

The optimal design and effectiveness of three control systems, tuned viscous mass damper(TVMD), tuned inerter damper(TID) and tuned mass damper(TMD), on mitigating the seismic responses of base isolated structures, were systematically studied. First, the seismic responses of the base isolated structure with each control system under white noise excitation were obtained. Then, the structural parameter optimizations of the TVMD, TID and TMD were conducted by using three different objectives. The results show that the three control systems were all effective in minimizing the root mean square value of seismic responses, including the base shear of the BIS, the absolute acceleration of structural SDOF, and the relative displacement between the base isolation floor and the foundation. Finally, considering the superstructure as a structural MDOF, a series of time history analyses were performed to investigate the effectiveness and activation sensitivity of the three control systems under far field and near fault seismic excitations. The results show that the effectiveness of TID and TMD with optimized parameters on mitigating the seismic responses of base isolated structures increased as the mass ratio increases, and the effectiveness of TID was always better than TMD with the same mass ratio. The TVMD with a lower mass ratio was more efficient in reducing the seismic response than the TID and TMD. Furthermore, the TVMD, when compared with TMD and TID, had better activation sensitivity and a smaller stroke.     

Second‐mode tuned mass dampers in base‐isolated structures for reduction of floor acceleration

To reduce floor acceleration of base‐isolated structures under earthquakes, a tuned mass damper (TMD) system installed on the roof is studied. The optimal tuning parameters of the TMD are analyzed for linear base isolation under a generalized ground motion, and the performance of the TMD is validated using a suite of recorded ground motions. The simulation shows that a TMD tuned to the second mode of a base‐isolated structure reduces roof acceleration more effectively than a TMD tuned to the first mode. The reduction ratio, defined as the maximum roof acceleration with the TMD relative to that without the TMD, is approximately 0.9 with the second‐mode TMD. The higher effectiveness of the second‐mode TMD relative to the first‐mode TMD is attributed primarily to the unique characteristics of base isolation, ie, the relatively long first‐mode period and high base damping. The modal acceleration of the second mode is close to or even higher than that of the first mode in base‐isolated structures. The larger TMD mass ratio and lower modal damping ratio of the second‐mode TMD compared to the first‐mode TMD increases its effect on modal acceleration reduction. The reduction ratio with the second‐mode TMD improves to 0.8 for bilinear base isolation. Because of the detuning effect caused by the change in the first‐mode period in bilinear isolation, the first‐mode TMD is ineffective in reducing roof acceleration. Additionally, the displacement experienced by the second‐mode TMD is considerably smaller than that of the first‐mode TMD, thereby reducing the installation space for the TMD.     

磁流变智能基础隔震系统研究

本文将磁流变(MR)阻尼器与普通橡胶隔震支座相结合,组成智能基础隔震系统应用到结构控制中。在详细介绍了系统的各部分与整体运行情况后,采用LQR经典线性最优控制算法对结构进行了振动台试验研究。试验结果表明,由MR阻尼器提供可调阻尼力的智能隔震控制系统,能有效克服被动隔震最优控制频带窄的缺点,对较宽频域范围地震激励能进行有效的振动控制。其相对一般被动隔震装置,能同时减小上部结构加速度和隔震层位移.     

Statistical performance analysis of seismic‐excited structures with active interaction control

This paper presents a statistical performance analysis of a semi‐active structural control system for suppressing the vibration response of building structures during strong seismic events. The proposed semi‐active mass damper device consists of a high‐frequency mass damper with large stiffness, and an actively controlled interaction element that connects the mass damper to the structure. Through actively modulating the operating states of the interaction elements according to pre‐specified control logic, vibrational energy in the structure is dissipated in the mass damper device and the vibration of the structure is thus suppressed. The control logic, categorized under active interaction control, is defined directly in physical space by minimizing the inter‐storey drift of the structure to the maximum extent. This semi‐active structural control approach has been shown to be effective in reducing the vibration response of building structures due to specific earthquake ground motions. To further evaluate the control performance, a Monte Carlo simulation of the seismic response of a three‐storey steel‐framed building model equipped with the proposed semi‐active mass damper device is performed based on a large ensemble of artificially generated earthquake ground motions. A procedure for generating code‐compatible artificial earthquake accelerograms is also briefly described. The results obtained clearly demonstrate the effectiveness of the proposed semi‐active mass damper device in controlling vibrations of building structures during large earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Displacement reduction effect and simplified evaluation method for SDOF systems using a clutching inerter damper

This study evaluates the response reduction effect of linear single degree of freedom systems with a clutching inerter damper (CID) via parametric analysis under harmonic excitations and real earthquake records. The cause of the displacement reduction effect of a CID is inherited from the inertial mass damper (IMD)—reducing the nominal load intensity by increasing the mass by inertance. Additionally, the displacement reduction effect is further enhanced by the clutching effect, which speeds up the decreasing of the velocity response from an instantaneous extremum to 0. Thus, the CID is more effective than the IMD at reducing displacement responses. For example, the displacement response for a long‐period structure with a CID can be reduced by approximately 53%, while for an IMD, it can only be reduced by approximately 24%. Additionally, the linear single degree of freedom system with a CID is a weak nonlinear system reserving homogeneity, indicating that the response reduction factor will provide enough information to reveal the seismic reduction effect of the CID and that there is no need to consider the amplitude of the input excitations. To simplify the analysis of such nonlinear systems, an equivalent linearization method and a simplified formula of displacement reduction factors for code‐based designs are proposed and validated by another independent set of records from the European Strong‐motion Database.     

Optimal displacement feedback control law for active tuned mass damper

Optimal displacement feedback control law is derived for a vibration control of a single‐degree‐of‐freedom structure with an active tuned mass damper (ATMD). Analytical expressions of the linear quadratic regulator (LQR) feedback gains for the ATMD are derived by solving the Ricatti equation straightforwardly. Based on these solutions, it is found that if the stiffness of the tuned mass damper (TMD) is calibrated to satisfy a certain condition, the control law is simplified to be composed of the feedback gains only for the displacement of the structure and the velocity of the auxiliary mass stroke, which is referred to as ‘optimal displacement feedback control’. The mean‐square responses of the structure as well as the auxiliary mass against Gaussian white noise excitations are evaluated by solving the Lyapunov equation analytically based on the stochastic optimal control theory. Using these analytical solutions, the optimal damping parameter for the auxiliary mass is also derived. Finally, the optimal displacement feedback control law is presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Semi‐active tuned mass damper building systems: Design

Passive and semi‐active tuned mass damper (PTMD and SATMD) building systems are proposed to mitigate structural response due to seismic loads. The structure's upper portion self plays a role either as a tuned mass passive damper or a semi‐active resetable device is adopted as a control feature for the PTMD, creating a SATMD system. Two‐degree‐of‐freedom analytical studies are employed to design the prototype structural system, specify its element characteristics and effectiveness for seismic responses, including defining the resetable device dynamics. The optimal parameters are derived for the large mass ratio by numerical analysis. For the SATMD building system the stiffness of the resetable device design is combined with rubber bearing stiffness. From parametric studies, effective practical control schemes can be derived for the SATMD system. To verify the principal efficacy of the conceptual system, the controlled system response is compared with the response spectrum of the earthquake suites used. The control ability of the SATMD scheme is compared with that of an uncontrolled (No TMD) and an ideal PTMD building systems for multi‐level seismic intensity. Copyright © 2009 John Wiley & Sons, Ltd.     

Real‐time hybrid testing of a smart base isolation system

Real‐time hybrid testing is a very effective technique for evaluating the dynamic responses of rate‐dependent structural systems subjected to earthquake excitation. A smart base isolation system has been proposed by others using conventional low‐damping isolators and controllable damping devices such as magnetorheological (MR) dampers to achieve specified control target performance. In this paper, real‐time hybrid tests of a smart base isolation system are conducted. The simulation is for a base‐isolated two‐degrees‐of‐freedom building model where the superstructure and the low‐damping base isolator are numerically simulated, and the MR damper is physically tested. The target displacement obtained from the step‐by‐step integration of the numerical substructure is imposed on the MR damper, which is driven by three different control algorithms in real‐time. To compensate the actuator delay and improve the accuracy of the test, an adaptive phase‐lead compensator is implemented. The accuracy of each test is investigated by using the root mean square error and the tracking indicator. Experimental results demonstrate that the hybrid testing procedure using the proposed actuator compensation techniques is effective for investigating the control performance of the MR damper in a smart base isolation system. Copyright © 2013 John Wiley & Sons, Ltd.     

基于碰撞调谐质量阻尼器的矮塔斜拉桥减震研究

以一座矮塔斜拉桥为研究对象,分析碰撞调谐质量阻尼器对于该结构的抑震效果。首先介绍了新型碰撞调谐质量阻尼器（Pounding Tuned Mass Damper,PTMD）的减震机理及基于接触单元的非线性碰撞力模型;之后,通过ANSYS软件中的APDL语言实现了PTMD减震系统的时域分析方法,并通过三条实际地震记录验证了PTMD的抑震效果。数值分析结果表明:（1）传统调谐质量阻尼器（tuned mass damper,TMD）及新型PTMD对于矮塔斜拉桥的位移、加速度及塔身弯矩响应均有较好的抑制效果;（2）PTMD相比传统TMD多了一种碰撞耗能模式,其减震效果略高于传统TMD。     

Seismic vibration control of building structures with multiple tuned mass damper floors integrated

Floor isolation system (FIS) achieving very small floor accelerations has been used to ensure human comfortability or protect important equipments in buildings. Tuned mass damper (TMD) with large mass ratios has been demonstrated to be robust with respect to the changes in structural properties. This paper presents the concept of a TMD floor vibration control system, which takes advantages of both the FIS and TMD. Such a system is called ‘TMD floor system’ herein. The TMD floor system (TMDFS) in which building floors serve as TMDs can achieve large mass ratio without additional masses. Furthermore, multiple TMD floors installed in a building can control multimode vibrations. Then, an optimal design process, where the objective function is set as the maximum magnitude of the frequency response functions of inter‐storey drifts, is proposed to determine the TMD floor parameters. Additionally, the multimode approach is applied to determine the optimal locations of TMD floors if not all of the floors in a building can serve as TMDs. In addition to the numerical simulations, a scaled model shaking table experiment is also conducted. Both the numerical and experimental results show that the absolute accelerations of the TMD floors are smaller than those of the main structural storeys, which indicates the TMDFS maintains the merit of FIS while greatly reducing seismic responses of main structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of a passive gap damper to control displacements in a shaking test of a seismically isolated three‐story frame

Recent studies have indicated uncertainty about the performance limit states of seismically isolated buildings in very large earthquakes, especially if the isolator displacement demands exceed the seismic gap and induce pounding. Previous research has shown the benefit of providing phased supplemental damping that does not affect the isolation system response in a design event. A phased passive control device, or gap damper, was designed, fabricated, and experimentally evaluated during shake table testing of a quarter scale base‐isolated three‐story steel frame building. Identical input motions were applied to system configurations without a gap damper and with a gap damper, to directly assess the influence of the gap damper on displacement and acceleration demands. The gap damper was observed to reduce displacement demands by up to 15% relative to the isolated system without the gap damper. Superstructure floor accelerations increased substantially because of damper activation, but were limited to a peak of about 1.18 g. The gap damper reduces displacement most effectively if the ground motion contains one or more of the following characteristics: the spectral displacement increases with increasing period near the effective period of the isolation system, the motion is dominated by a single large pulse rather than multiple cycles at a consistent intensity, and the motion has a dominant component aligned with a major axis of the structure. Copyright © 2016 John Wiley & Sons, Ltd.     

Design of bilinear hysteretic isolation systems

This paper concerns the design of passive base isolation systems characterized by a bilinear hysteretic behaviour. The study refers to the case where the structure to be isolated (superstructure) vibrates according to the first mode. In this case the whole isolated structure can be modelled by a two‐degree‐of‐freedom system. The base isolation effectiveness has been evaluated for different characteristics of the device, namely mass, strength, elastic and plastic stiffness, by using mainly energetic quantities. The optimum values for the base device have been obtained by minimizing the input energy and the displacement of the superstructure. Conclusions are drawn for superstructures with a fundamental period of 0.5s, a damping ratio of 5% and for three different kinds of earthquake ground motions. The study showed that the seismic input greatly affects the behaviour of the isolated structure, and therefore the design ground motion must be carefully chosen, dependent on the characteristics of the site. A simple procedure that involves mainly linear dynamic analyses is proposed for the design of base devices used in conjunction with superstructures of any fundamental vibration period. The procedure produces good results in spite of its simplicity, and therefore it is suitable for practical use by design engineers. Copyright © 2003 John Wiley & Sons, Ltd.     

拉索式旋转电涡流阻尼器的理论模型及频域响应分析

惯容器是一种新型的振动控制装置,该装置可以将螺杆的轴向运动转换为黏滞材料和旋转质量的高速旋转运动,使阻尼器的阻尼效应和质量效应得到放大。基于惯容器原理以及电涡流原理,提出一种新型的拉索式旋转电涡流阻尼器,为结构被动控制提供了新的设计思路。为研究这种新型惯容系统的减振机理,对安装拉索式旋转电涡流阻尼器单层框架的力学模型进行了探讨。推导出了配置惯容系统单质点体系的动力表达式,并基于此表达式探讨在频域内该惯容系统关键参数对单质点体系位移、速度和加速度响应的影响。结果表明:这种拉索式旋转电涡流阻尼器可以起到放大质量的效果,惯容系统可以有效地减少单质点体系的位移、速度和加速度响应幅值。     

高阶单步法控制MR智能隔震系统的试验研究

高阶单步法已成功地应用于结构非线性分析及考虑时滞的主动控制等，显示了它的稳定、精度高和计算迅速等特点。磁流变阻尼器是一种性能优良的智能阻尼器，它具有阻尼力可调范围宽、响应迅速且所需能量很少的特点。本文将磁流变（MR）阻尼器与普通橡胶隔震支座相结合，采用高阶单步算法和两种控制策略对结构进行振动控制。数值模拟分析与振动台试验结果表明：由MR阻尼器提供可调阻尼力的智能隔震控制系统能有效克服被动隔震最优控制频带窄的缺点，对较宽频域范围不同大小的地震激励均能提供最优控制。同时也表明该控制算法是一种能用于结构实际控制的变阻尼有效算法。     

Optimum design and application of non‐traditional tuned mass damper toward seismic response control with experimental test verification

A variant type of tuned mass damper (TMD) termed as ‘non‐traditional TMD (NTTMD)’ is recently proposed. Mainly focusing on the employment of TMD for seismic response control, especially for base‐isolated or high‐rise structures, this paper aims to derive design formulae of NTTMDs based on two methodologies with different targets. One is the fixed points theory with the performance index set as the maximum magnitude of the frequency response function of the relative displacement of the primary structure with respect to the ground acceleration, and the other is the stability maximization criterion (SMC) to make the free vibration of the primary structure decay in the minimum duration. Such optimally designed NTTMDs are compared with traditional TMDs by conducting both numerical simulations and experiments. The optimum‐designed NTTMDs are demonstrated to be more effective than the optimum‐designed traditional TMDs, with smaller stroke length required. In particular, the effectiveness of the TMDs combined with a base‐isolated structure is investigated by small‐scale model experimental tests subjected to a time scaled long period impulsive excitation, and it is demonstrated that the SMC‐based NTTMD can suppress structural free vibration responses in the minimum duration and requires much smaller accommodation space. Additionally, a small‐scale shaking table experiment on a high‐rise bending model attached with a SMC‐based NTTMD is conducted. This study indicates that NTTMD has a high potential to apply to seismic response control or retrofit of structures such as base‐isolated or central column‐integrated high‐rise structures even if only a limited space is available for accommodating TMDs. Copyright © 2015 John Wiley & Sons, Ltd.