On tuned mass dampers for reducing the seismic response of structures

This paper presents an energy‐based theoretical model for a two degree‐of‐freedom mechanical system. After a general formulation in Appendix A, the model is specialized to study tuned mass dampers as a means to substantially increase modal damping in order to induce a consequential decrease of the seismic response of the structures thus provided. Although approximate since it neglects coupling due to damping, it is shown that the model yields a first‐order approximation to the exact frequencies, providing values of optimum damping that closely match exact results proposed by others. In view of this, it is proposed that the model be applied through an iterative numerical procedure that identifies the pertinent optimum parameters. It is also shown that for certain particular benchmark cases the model provides closed‐form equations for the parameters defining the dynamic states related to these special conditions. Despite its approximate nature the model presented in this paper is rational, and due to its explicit consideration of energy balance and overall simplicity, it provides a convenient platform for the study of tuned mass dampers, as well as for other methods of structural passive control. Copyright © 2005 John Wiley & Sons, Ltd.     

Tuned liquid dampers for controlling earthquake response of structures

Numerical simulations of a single‐degree‐of‐freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both real and artificially generated earthquake ground motions, show that a properly designed TLD can significantly reduce the structure's response to these motions. The TLD is a rigid, rectangular tank with shallow water in it. Its fundamental linear sloshing frequency is tuned to the structure's natural frequency. The TLD is more effective in reducing structural response as the ground excitation level increases. This is because it then dissipates more energy due to sloshing and wave breaking. A larger water‐depth to tank‐length ratio than previous studies suggested, which still falls within the constraint of shallow water theory, is shown to be more suitable for excitation levels expected in strong earthquake motions. A larger water‐mass to structure‐mass ratio is shown to be required for a TLD to remain equally effective as structural damping increases. Furthermore, the reduction in response is seen to be fairly insensitive to the bandwidth of the ground motion but is dependent on the structure's natural frequency relative to the significant ground frequencies. Finally, a practical approach is suggested for the design of a TLD to control earthquake response. Copyright © 2000 John Wiley & Sons, Ltd.     

非对称结构扭转振动多重调谐质量阻尼器(MTMD)控制的最优位置

研究了非对称结构扭转振动多重调谐质量阻尼器(MTMD)控制的最优位置。本文采用的MTMD具有相同的刚度、阻尼，但质量不同。基于导出的设置MTMD时非对称结构扭转角位移传递函数，建立了扭转角位移动力放大系数解析式。MTMD最优参数的评价准则定义为：非对称结构最大扭转角位移动力放大系数的最小值的最小化。MTMD的有效性评价准则定义为：非对称结构最大扭转角位移动力放大系数的最小值的最小化与未设置MTMD时非对称结构最大扭转角位移动力放大系数的比值。基于定义的评价准则，研究了非对称结构的标准化偏心系数(NER)和扭转对侧向频率比(TTFR)对不同位置MTMD最优参数和有效性的影响。     

A method for tuning tuned mass dampers for seismic applications

This paper studies tuned mass dampers (TMDs) resulting in high modal damping for mechanical systems incorporating such devices for the purpose of seismic response reduction. Focusing on the determination of damping and tuning, the proposed methodology identifies a point of multiplicity of complex eigenvalues and eigenvectors, resulting in different parameters for TMDs according to their location with respect to such multiplicity condition. It is shown that significant equal modal damping and average modal damping can be induced by properly tuning highly damped TMDs, obtaining parameters intrinsic to the mechanical systems, and excitation independent. Further, it is shown that the methodology yields, as particular cases, two proposals by others using TMDs for the same purpose of seismic response abatement. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental verification of torsional response control of asymmetric buildings using MR dampers

This paper proposes a semiactive control system to reduce the coupled lateral and torsional motions in asymmetric buildings subjected to horizontal seismic excitations. Magnetorheological (MR) dampers are applied as semiactive control devices and the control input determination is based on a clipped‐optimal control algorithm which uses absolute acceleration feedback. The performance of this method is studied experimentally using a 2‐story building model with an asymmetric stiffness distribution. An automated system identification methodology is implemented to develop a control‐oriented model which has the natural frequencies observed in the experimental system. The parameters for the MR damper model are identified using experimental data to develop an integrated model of the structure and MR dampers. To demonstrate the performance of this control system on the experimental structure, a shake table is used to reproduce an El Centro 1940 N–S earthquake as well as a random white noise excitation. The responses for the proposed control system are compared to those of passive control cases in which a constant voltage is applied to the MR damper. Copyright © 2003 John Wiley & Sons, Ltd.     

Bi‐directional coupled tuned mass dampers for the seismic response control of two‐way asymmetric‐plan buildings

This paper proposes bi‐directional coupled tuned mass dampers (BiCTMDs) for the seismic response control of two‐way asymmetric‐plan buildings subjected to bi‐directional ground motions. The proposed BiCTMD was developed from the three‐degree‐of‐freedom modal system, which represents the vibration mode of a two‐way asymmetric‐plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two‐way asymmetric‐plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. In addition, the investigation showed that the proposed BiCTMD is effective in reducing the seismic damage of inelastic asymmetric‐plan buildings. Therefore, the BiCTMD is an effective approach for the seismic response control of both elastic and inelastic two‐way asymmetric‐plan buildings. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal seismic response control with dampers

The usefulness of energy dissipation devices to reduce seismic response of structures is now well established. For a given installation of such devices in a structure, one can easily compute the level of response reduction achieved. However, the solution of an inverse problem of how many devices one would need to achieve a desired level of response reduction in a structure, or to achieve an expected level of performance from a structural system, is not quite as straightforward and well formulated. In this paper, a method is presented to obtain the amount of viscous and visco‐elastic damping one would need to obtain a desired level of response reduction. The needed supplemental devices are also optimally distributed in the structure to achieve the best performance. To solve the optimal problem, a gradient‐based optimization approach is used. To illustrate the application, numerical results for a 24‐storey building structure are presented where the objective is to achieve the maximum reduction in the performance functions expressed in terms of the inter‐storey drifts, base shear, or floor accelerations. Other forms of performance functions can also be treated similarly. Copyright © 2001 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.     

结构多重双重调谐质量阻尼器(MDTMD)的新控制策略

本文提出了一种新的控制策略——多重双重调谐质量阻尼器(以下简称为MDTMD)。MDTMD系统参数的可能组合形成十种MDTMD模型,本文评价其中最易制作的一种MDTMD模型。利用定义的优化目标函数,评价了MDTMD的控制性能。数值结果表明MDTMD比双重调谐质量阻尼器(DTMD)具有更好的有效性和对频率调谐的鲁棒性。但MDTMD的冲程大于DTMD的冲程。     

Optimal placement of dampers for passive response control

The effectiveness of viscous and viscoelastic dampers for seismic response reduction of structures is quite well known in the earthquake engineering community. This paper deals with the optimal utilization of these dampers in a structure to achieve a desired performance under earthquake‐induced ground excitations. Frequency‐dependent and ‐independent viscous dampers and viscoelastic dampers have been considered as the devices of choice. To determine the optimal size and location of these dampers in the structure, a genetic algorithm is used. The desired performance is defined in terms of several different forms of performance functions. The use of the genetic approach is not limited to any particular form of performance function as long as it can be calculated numerically. For illustration, numerical examples for different building structures are presented showing the distribution and size of different dampers required to achieve a desired level of reduction in the response or a performance index. Copyright © 2002 John Wiley & Sons, Ltd.     

Seismic response control with density-variable tuned liquid dampers

In this paper,the seismic effectiveness of a density-variable tuned liquid damper(DVTLD) with a sloping bottom is experimentally investigated through a series of shake table tests on a 1/4-scale,3-story frame structure and numerically simulated by a new semi-analytical model.Special attention was given to reducing the fi rst peak and maximum response under near-and far-fi eld ground motions,and the robustness of a density-variable control system consisting of multiple DVTLDs with closely-spaced frequencies....     

An alternative methodology for designing tuned mass dampers to reduce seismic vibrations in building structures

It is well established that small tuned mass dampers (TMDs) attached to structures are very effective in reducing excessive harmonic vibrations induced by external loads but are not as interesting within the context of earthquake engineering problems. For this reason, large mass ratio TMDs have been proposed with the objective of adding a significant amount of damping to structures, thus constituting a good means of reducing structural response in these cases. This solution has other important and attractive dynamic features such as robustness to system uncertainties and reduction of the motion of the inertial mass. In this context, this paper aims to describe an alternative methodology to existing procedures used to tune these devices to earthquake loads and to present some additional considerations regarding its performance in controlling seismic vibrations. The main feature of the proposed method consists of establishing a direct proportion between the damping ratios of the structure's first two vibration modes and the adopted mass ratio. By equalizing the damping ratios of the system's main vibration modes, this proposal also facilitates the use of simplified methods, such as modal analysis based on response spectra. To demonstrate the usefulness of this alternative methodology, an application example is presented, which was also used to perform a parametric study involving other tuning methods and to estimate mass ratio values from which there is no significant advantage in increasing the TMD mass. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic response control of frame structures using magnetorheological/electrorheological dampers

Semi‐active control of buildings and structures for earthquake hazard mitigation represents a relatively new research area. Two optimal displacement control strategies for semi‐active control of seismic response of frame structures using magnetorheological (MR) dampers or electrorheological (ER) dampers are proposed in this study. The efficacy of these displacement control strategies is compared with the optimal force control strategy. The stiffness of brace system supporting the smart damper is also taken into consideration. An extensive parameter study is carried out to find the optimal parameters of MR or ER fluids, by which the maximum reduction of seismic response may be achieved, and to assess the effects of earthquake intensity and brace stiffness on damper performance. The work on example buildings showed that the installation of the smart dampers with proper parameters and proper control strategy could significantly reduce seismic responses of structures, and the performance of the smart damper is better than that of the common brace or the passive devices. The optimal parameters of the damper and the proper control strategy could be identified through a parameter study. Copyright © 2000 John Wiley & Sons, Ltd.     

Seismic response of controlled structures with active multiple tuned mass dampers

Active multiple tuned mass dampers （referred to as AMTMD）, which consist of several active tuned mass dampers （ATMDs） with identical stiffness and damping coefficients but varying mass and control force, have recently been proposed to suppress undesirable oscillations of structures under ground acceleration. It has been shown that the AMTMD can remarkably improve the performance of multiple tuned mass dampers （MTMDs） and is also more effective in reducing structure oscillation than single ATMDs. Notwithstanding this, good performance of AMTMD （including a single ATMD illustrated from frequency-domain analysis） may not necessarily translate into a good seismic reduction behavior in the time-domain. To investigate these phenomena, a three-story steel structure model controlled by AMTMD with three ATMDs was implemented in SIMULINK and subjected to several historical earthquakes. Likewise, the structure under consideration was assumed to have uncertainty of stiffness, such as 4-15% of its initial stiffness, in the numerical simulations. The optimum design parameters of the AMTMD were obtained in the frequency-domain by implementing the minimization of the minimum values of the maximum dynamic magnification factors （DMF） of general structures with AMTMD. For comparison purposes, response analysis of the same structure with a single ATMD was also performed. The numerical analysis and comparison show that the AMTMD generally renders better effectiveness when compared with a single ATMD for structures subjected to historical earthquakes. In particular, the AMTMD can improve the effectiveness of a single ATMD for a structure with an uncertainty of stiffness of 4-15% of its initial stiffness.     

Single- and multiple-tuned liquid column dampers for seismic applications

Design parameters for single- and multiple-tuned liquid column dampers for reducing the response of structures to seismic excitations are presented. A deterministic analysis is carried out using 72 earthquake ground motion records to determine the tuning ratio, tube width to liquid length ratio, and head loss coefficient corresponding to a given mass ratio for single-tuned liquid column dampers. A similar analysis is performed to determine the central tuning ratio, tuning bandwidth, and grouping of dampers for multiple-tuned liquid column dampers. The study indicates that by properly selecting the design parameters, single- and multiple-tuned liquid column dampers can reduce the response of structures to seismic excitation by up to 45 per cent. Design examples using single- and multiple-tuned liquid column dampers in a bridge and a ten-storey building are presented to illustrate how the parameters are selected and to demonstrate the performance of the devices under different ground excitations. The response of several structures with tuned liquid column dampers is compared with that using tuned mass dampers where it is shown that both devices result in comparable reductions in the response. © 1998 John Wiley & Sons, Ltd. This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.     

Optimum design and experimental study of multiple tuned mass dampers with limited stroke

This paper develops a two‐stage optimum design procedure for multiple tuned mass dampers (MTMD) to reduce structural dynamic responses with the limitation of MTMD's stroke. A new performance index, which is a linear combination of structural response ratio and MTMD stroke ratio by a weighting factor α, is proposed; α is in the range from 0 to 1.0. The larger the α, the more important the stroke. The case of α=1.0 indicates that MTMD is locked. The analytical results show that the MTMD's stroke can be significantly suppressed with little sacrifice of structural control effectiveness when an appropriate α is selected. To verify the design algorithm, a 360 kg‐MTMD composed of five TMD units arranged in parallel was fabricated. Shaking table tests of a large‐scale three‐story building with and without the MTMD under earthquake excitations were conducted at the National Center for Research on Earthquake Engineering (NCREE) in Taiwan. The experimental results show that MTMD is not only effective in mitigating the building responses but also is successful in suppressing its stroke. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Tuned vibration absorbers with dry friction damping

The response of a linear SDOF system subjected to harmonic excitation to which a Tuned Vibration Absorber with linear stiffness and dry friction damping is attached is considered. Based on an intuitive examination of the physical behaviour of the system, closed-form expressions for TMD optimum parameters and for the steady-state amplitudes of vibration are presented. Two examples allow the comparison between the predicted behaviour and that found by numerically integrating the equations of motion. Copyright © 1999 John Wiley & Sons, Ltd.     

结构双层多重调谐质量阻尼器(DMTMD)控制策略的鲁棒性评价

基于定义的二类优化目标函数,评价双层多重调谐质量阻尼器(DMTMD)控制策略对漂移频率系数(DFR)摄动的鲁棒性。数值研究表明,使用第二类优化准则设计的DMTMD、双重调谐质量阻尼器(DTMD)和多重调谐质量阻尼器(MTMD)比使用第一类优化准则设计的DMTMD、DTMD和MTMD具有更高的对DFR摄动的鲁棒性。而且,使用第二类优化准则设计的总数为4的DMTMD、DTMD和总数为11的MTMD具有近似相同的对DFR摄动的鲁棒性。     

Multiple‐tuned liquid column dampers for torsional vibration control of structures: theoretical investigation

This paper presents a theoretical investigation on the performance of multiple‐tuned liquid column dampers (MTLCD) for reducing torsional vibration of structures in comparison with single‐tuned liquid column dampers (STLCD). The analytical model is first developed for torsional vibration of a structure with an MTLCD under either harmonic excitation or white noise excitation. The experimental results are then used to verify the analytical model for coupled MTLCD‐structure systems under harmonic excitation. The performance of an MTLCD and its beneficial parameters for achieving the maximum torsional response reduction to white noise excitation are finally investigated through an extensive parametric study in terms of the distance from the centre line of the MTLCD to the rotational axis of the structure, the ratio of the horizontal length to the total length of liquid column, frequency bandwidth, head‐loss coefficient, the number of TLCD units in an MTLCD, frequency‐turning ratio and the spectral level of excitation moment. The results show that there is an optimal head‐loss coefficient and an optimal frequency bandwidth for an MTLCD to achieve the maximum torsional response reduction. It is also demonstrated that the sensitivity of an optimized MTLCD to the frequency‐tuning ratio is less than that of an optimized STLCD, and it can be further improved by increasing the bandwidth but at the cost of less torsional vibration reduction. Copyright © 2002 John Wiley & Sons, Ltd.