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.     

Design of multiple tuned mass dampers by using a numerical optimizer

A new method to design multiple tuned mass dampers (multiple TMDs) for minimizing excessive vibration of structures has been developed using a numerical optimizer. It is a very powerful method by which a large number of design variables can be effectively handled without imposing any restriction before the analysis. Its framework is highly flexible and can be easily extended to general structures with different combinations of loading conditions and target controlled quantities. The method has been used to design multiple TMDs for SDOF structures subjected to wide‐band excitation. Some novel results have been obtained. To reduce displacement response of the structure, the optimally designed multiple TMDs have distributed natural frequencies and distinct damping ratios at low damping level. The obtained optimal configuration of TMDs was different from the earlier analytical solutions and was proved to be the most effective. A robustness design of multiple TMDs has also been presented. Robustness is defined as the ability of TMDs to function properly despite the presence of uncertainties in the parameters of the system. Numerical examples of minimizing acceleration structural response have been given where the system parameters are uncertain and are modeled as independent normal variates. It was found that, in case of uncertainties in the structural properties, increasing the TMD damping ratios along with expanding the TMD frequency range make the system more robust. Meanwhile, if TMD parameters themselves are uncertain, it is necessary to design TMDs for higher damping ratios and a narrower frequency range. Copyright © 2004 John Wiley & Sons, Ltd.     

Tuned mass dampers for structures with closely spaced natural frequencies

Analytical results are developed for vibration control of structures with one or more Tuned Mass Dampers (TMDs). The input is a harmonic load with a range of possible frequencies. The control objective is to reduce the maximum amplitude of the structural response. Perturbation theory is used with three sets of small parameters: the ratio of TMD and structural modal masses, the damping of the system, and the differences between the structural and loading frequencies. It is shown analytically that for structures with widely spaced natural frequencies, the response can be approximated accurately by the response of the well-known single-mode structure/TMD system. For structures with p closely spaced natural frequencies, more general analytical results are developed to describe the coupling between the motions of the p modes of the structure and the multiple TMDs. The results show that at least p TMDs with properly placed attachments to the structure are necessary to control the response. If fewer TMDs are used, the maximum frequency response has a lower bound which is independent of the properties of the TMDs. The TMD placement is shown to be always important, regardless of the spacing of the structure's natural frequencies. The results are illustrated for both lumped-mass and continuous structures.     

A METHOD OF ESTIMATING THE PARAMETERS OF TUNED MASS DAMPERS FOR SEISMIC APPLICATIONS

The optimum parameters of tuned mass dampers (TMD) that result in considerable reduction in the response of structures to seismic loading are presented. The criterion used to obtain the optimum parameters is to select, for a given mass ratio, the frequency (tuning) and damping ratios that would result in equal and large modal damping in the first two modes of vibration. The parameters are used to compute the response of several single and multi-degree-of-freedom structures with TMDs to different earthquake excitations. The results indicate that the use of the proposed parameters reduces the displacement and acceleration responses significantly. The method can also be used in vibration control of tall buildings using the so-called ‘mega-substructure configuration’, where substructures serve as vibration absorbers for the main structure. It is shown that by selecting the optimum TMD parameters as proposed in this paper, significant reduction in the response of tall buildings can be achieved. © 1997 John Wiley & Sons, Ltd.     

Ant colony optimization of tuned mass dampers for earthquake oscillations of high-rise structures including soil–structure interaction

This paper investigates the optimized parameters for tuned mass dampers (TMDs) to decrease the earthquake vibrations of tall buildings; involving soil–structure interaction (SSI) effects. The time domain analysis based on Newmark method is employed in this study. To illustrate the results, Tabas and Kobe earthquakes data are applied to the model, and ant colony optimization (ACO) method is utilized to obtain the best parameters for TMD. The TMD mass, damping coefficient and spring stiffness are assumed as design variables, and the objective is to reduce both the maximum displacement and acceleration of stories. It is shown that how the ACO can be effectively applied to design the optimum TMD device. It is also indicated that the soil type greatly affects the TMD optimized parameters and the time response of structures. This study helps the researchers to better understanding of earthquake vibrations, and leads the designers to achieve the optimized TMD for high-rise buildings.     

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.     

SEMI-ACTIVE TUNED MASS DAMPERS FOR SEISMIC PROTECTION OF CIVIL STRUCTURES

A semi-active tuned mass damper (TMD) which is capable of adjusting initial displacement and damping is applied to seismic protection of structures. Control algorithms are derived in closed forms using perturbation analysis on modal properties of the single degree of freedom (SDOF) structure/TMD system. Because perturbation solutions are given in a relatively simple form, the control algorithms are developed in a physically intuitive manner. In the first half of the paper, the control algorithms are introduced using numerical simulations of the impulse response. Then the algorithms are applied to seismic protection of civil structures using the strategy of multiple releasing and capturing of TMDs. The control strategy for seismic control is summarized in a flow chart. Numerical studies with the El Centro earthquake record show that the proposed semi-active method has higher performance than conventional passive TMDs.     

Seismic fragility assessment of existing sub-standard low strength reinforced concrete structures

An analytical seismic fragility assessment framework is presented for the existing low strength reinforced concrete structures more common in the building stock of the developing countries.For realistic modelling of such substandard structures,low strength concrete stress-strain and bond-slip capacity models are included in calibrating material models.Key capacity parameters are generated stochastically to produce building population and cyclic pushover analysis is carried out to capture inelastic behaviour.Secant period values are evaluated corresponding to each displacement step on the capacity curves and used as seismic demand.A modified capacity demand diagram method is adopted for the degrading structures,which is further used to evaluate peak ground acceleration from back analysis considering each point on the capacity curve as performance point.For developing fragility curves,the mean values of peak ground acceleration are evaluated corresponding to each performance point on the series of capacity curves.A suitable probability distribution function is adopted for the secant period scatter at different mean peak ground acceleration values and probability of exceedance of limit states is evaluated.A suitable regression function is used for developing fragility curves and regression coefficients are proposed for different confidence levels.Fragility curves are presented for a low rise pre-seismic code reinforced concrete structure typical of developing countries.     

Optimal design of tuned mass dampers for a multi‐storey cross laminated timber building against seismic loads

In this paper, the effectiveness of different design solutions for tuned mass dampers (TMD) applied to high‐rise cross‐laminated (X‐Lam) timber buildings as a means to reduce the seismic accelerations was investigated. A seven‐storey full‐scale structure previously tested on shaking table was used as a reference. The optimal design parameters of the TMDs, i.e. damping and frequency ratios, were determined by using a genetic algorithm on a simplified model of the reference structure, composed by seven masses each representing one storey. The optimal solutions for the TMDs were then applied to a detailed finite element model of the seven‐storey building, where the timber panels were modelled with shell elements and the steel connectors with linear spring. By comparing the numerical results of the building with and without multiple TMDs, the improvement in seismic response was assessed. Dynamic time‐history analyses were carried out for a set of seven natural records, selected in accordance with Eurocode 8, on the simplified model, and for Kobe earthquake ground motion on the detailed model. Results in terms of acceleration reduction for different TMD configurations show that the behaviour of the seven‐storey timber building can be significantly improved, especially at the upper storeys. Copyright © 2016 John Wiley & Sons, Ltd.     

Velocity adjustable TMD and numerical simulation of seismic performance

A new type of velocity adjustable tuned mass damper (TMD) consisting of impulse generators and clutches is presented. The force impulse is generated by a joining operation of electromagnets and springs and MR dampers are used as clutches. Rules for velocity adjustment are established according to the working mechanism of TMD. The analysis program is developed on a VB platform. Seismic response of SDOF structures with both passive TMD and velocity adjustable TMD are analyzed. The results show that (1) the control effectiveness of passive TMDs is usually unstable; (2) the control effectiveness of the proposed semi-active TMDs is much better than passive TMDs under typical seismic ground motions; and (3) unlike the passive TMD system, the proposed velocity adjustable TMDs exhibit good control effectiveness even when the primary structure performance becomes inelastic during severe earthquakes.     

核电厂考虑结构参数不确定的 地震易损性分析

为考虑核电厂结构参数不确定对结构地震易损性的影响,基于一次二阶矩法(First-Order Second-Moment, FOSM)进行地震易损性分析。以核电结构中混凝土材料的密度、弹性模量,泊松比和抗拉强度为不确定参数,建立有限元模型,并与试验结果对比,以验证模型的准确性。基于有限元数值模拟方法,通过增量动力法计算核电厂模型在多条地震记录下不同峰值加速度的动力响应,同时基于FOSM得到参数不确定下的对数标准差,进而得到核电厂结构考虑参数不确定的地震易损性曲线。结果表明,结构参数的不确定对核电结构有一定的影响,未考虑参数不确定的地震易损性结果会低估结构的失效概率。该方法可为核电结构基于参数不确定下的易损性分析提供一定的理论依据与实用价值。     

结构最优主动调谐质量阻尼器风致振动控制的研究

基于我国现行的风荷载规范,建立了在风荷载作用下结构-主动调谐质量阻尼器(ATMD)系统的动力方程。定义ATMD最优参数准则为:结构-ATMD系统的位移或加速度响应方差的最小化。ATMD有效性的评价准则为:设置ATMD结构的最小化位移或加速度响应方差与未设置ATMD结构的位移或加速度响应方差之比(分别称为位移和加速度减振系数)。根据上述准则,在频域内数值研究了结构自振频率、标准化加速度反馈增益系数、质量比对ATMD系统的最优参数(包括最优频率比和阻尼比)、有效性和冲程的影响。此外,为了比较的目的,论文同时考虑了结构TMD风致振动控制的情况。     

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.     

Influence of ground motion intensity on the effectiveness of tuned mass dampers

The effectiveness of Tuned Mass Dampers (TMD) on buildings subjected to moderate and high-intensity motions is analysed. First, the response of a 22-storey four-bay reinforced concrete non-linear frame with a TMD is studied for motions with different intensities. Several values of the relevant parameters are assumed in the analyses. Then, equivalent single-degree-of-freedom systems with TMDs and without them are defined and analysed under the action of ground motions with intensities associated with different return intervals at the site where the structures are located. Vulnerability curves for the systems are obtained based on the probabilities of reaching two different performance limit states. The expected annual rate of exceedance of each limit state is calculated. The results show that the effectiveness of TMDs is higher for systems with small non-linearity produced by small and moderate earthquakes, than for systems with high non-linear behaviour, generally associated with high-intensity motions. Some recommendations about the applicability of TMD are given. Copyright © 1999 John Wiley & Sons Ltd.     

Intensity measure conversion of fragility curves

In seismic risk assessment of structures, fragility functions are the probabilistic characterization of vulnerability at the component and/or structural level, expressing the probability of failure as a function of a ground motion intensity measure (IM). Fragility curves, in general, are structure- and site-specific, thus a comparison of fragility curves, then of vulnerability, is not straightforward across multiple structures. Also, it could be the case that hazard at a site of interest is not available for the IM originally considered in the fragility assessment. These situations require to convert fragility curves from an original IM to a target one. The present study addresses a hazard-consistent probabilistic framework for converting spectral acceleration-based IMs from an original IM to a target IM at a given site. In particular, three conversion cases, under different assumptions on the explanatory power of the involved IMs with respect to structural failure, are discussed: (a) a vector-valued IM consisting of the original and target IMs, magnitude, and source-to-site distance; (b) a vector-valued IM consisting of the original and target IMs; and (c) the original (scalar) IM only, assuming that structural response, given the IM, is statistically independent of the other ground motion variables. In this framework, the original fragility functions are characterized using the state-of-the-art methods in performance-based earthquake engineering, then the fragility curves as a function of the target IM are evaluated through applications of the probability calculus rules, ensuring consistency with the seismic hazard at the site of interest. The conversion strategy is illustrated through the applications to three-, six-, and nine-story Italian code-conforming reinforced concrete buildings designed for a high-hazard site in Italy. The study shows that, in most of the cases, the converted fragility curves have agreement with the reference curves directly developed in terms of the target IM. Cases in which least agreement was found are likely due to the models used to obtain the terms required by the conversion equations.     

Convex model-based calculation of robust seismic fragility curves of isolated continuous girder bridge

The convex model approach is applied to derive the robust seismic fragility curves of a five-span isolated continuous girder bridge with lead rubber bearings (LRB) in China. The uncertainty of structure parameters (the yield force and the post-yield stiffness of LRB, the yield strength of steel bars, etc.) are considered in the convex model, and the uncertainty of earthquake ground motions is also taken into account by selecting 40 earthquake excitations of peak ground acceleration magnitudes ranging from 0.125 to 1.126 g. A 3-D finite element model is employed using the software package OpenSees by considering the nonlinearity in the bridge piers and the isolation bearings. Section ductility of piers and shearing strain isolation bearings are treated as damage indices. The cloud method and convex model approach are used to construct the seismic fragility curves of the bridge components (LRB and bridge piers) and the bridge system, respectively. The numerical results indicate that seismic fragility of the bridge system and bridge components will be underestimated without considering the uncertainty of structural parameters. Therefore, the failure probability P _f,max had better be served as the seismic fragility, especially, the fragility of the bridge system is largely dictated by the fragility of LRB. Finally, the probabilistic seismic performance evaluation of the bridge is carried out according to the structural seismic risk estimate method.     

Development of fragility functions as a damage classification/prediction method for steel moment‐resisting frames using a wavelet‐based damage sensitive feature

Fragility functions are commonly used in performance‐based earthquake engineering for predicting the damage state of a structure subjected to an earthquake. This process often involves estimating the structural damage as a function of structural response, such as the story drift ratio and the peak floor absolute acceleration. In this paper, a new framework is proposed to develop fragility functions to be used as a damage classification/prediction method for steel structures based on a wavelet‐based damage sensitive feature (DSF). DSFs are often used in structural health monitoring as an indicator of the damage state of the structure, and they are easily estimated from recorded structural responses. The proposed framework for damage classification of steel structures subjected to earthquakes is demonstrated and validated with a set of numerically simulated data for a four‐story steel moment‐resisting frame designed based on current seismic provisions. It is shown that the damage state of the frame is predicted with less variance using the fragility functions derived from the wavelet‐based DSF than it is with fragility functions derived from an alternate acceleration‐based measure, the spectral acceleration at the first mode period of the structure. Therefore, the fragility functions derived from the wavelet‐based DSF can be used as a probabilistic damage classification model in the field of structural health monitoring and an alternative damage prediction model in the field of performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

考虑填充墙影响的钢筋混凝土厂房结构地震易损性分析

采用对角斜撑模拟纵向填充墙的作用,建立考虑填充墙和不考虑填充墙厂房结构模型,采用拉丁超立方抽样技术建立考虑材料不确定性的结构分析样本,基于随机Pushover分析确定结构不同破坏状态下的统计参数。综合考虑结构材料强度及输入地震动不确定性的影响,通过非线性时程分析开展单层钢筋混凝土厂房结构易损性研究,在此基础上比较结构横、纵向易损性的差异,研究填充墙对结构易损性的影响。研究结果表明:钢筋混凝土厂房结构体系横向地震易损性显著大于纵向地震易损性;对纵向结构体系而言,加入填充墙会明显降低结构易损性,但在相同强度的地震动作用下,填充墙破坏程度比主体结构严重,这与厂房结构的实际震害特征相符。     

Lifecycle cost optimization of tuned mass dampers for the seismic improvement of inelastic structures

The seismic performance of tuned mass dampers (TMDs) on structures undergoing inelastic deformations may largely depend on the ground motion intensity. By estimating the impact of each seismic intensity on the overall cost of future seismic damages, lifecycle cost (LCC) proves a rational metric for evaluating the benefits of TMDs on inelastic structures. However, no incorporation of this metric into an optimization framework is reported yet. This paper presents a methodology for the LCC‐optimal design of TMDs on inelastic structures, which minimizes the total seismic LCC of the combined building‐TMD system. Its distinctive features are the assumption of a mass‐proportional TMD cost model, the adoption of an iterative suboptimization procedure, and the initialization of the TMD frequency and damping ratios according to a conventional linear TMD design technique. The methodology is applied to the seismic improvement of the SAC‐LA benchmark buildings, taken as representative of standard steel moment‐resisting frame office buildings in LA, California. Results show that, despite their limited performance at the highest intensity levels, LCC‐optimal TMDs considerably reduce the total LCC, to an extent that depends on both the building vulnerability and the TMD unit cost. They systematically present large mass ratios (around 10%) and frequency and damping ratios close to their respective linearly designed optima. Simulations reveal the effectiveness of the proposed design methodology and the importance of adopting a nonlinear model to correctly evaluate the cost‐effectiveness of TMDs on ordinary structures in highly seismic areas.