Active multiple tuned mass dampers for structures under the ground acceleration

Active multiple tuned mass dampers (AMTMD) consisting of many active tuned mass dampers (ATMDs) with a uniform distribution of natural frequencies have been, for the first time, proposed for attenuating undesirable vibrations of a structure under the ground acceleration.The multiple tuned mass dampers (MTMD) in the AMTMD is manufactured by keeping the stiffness and damping constant and varying the mass. The control forces in the AMTMD are generated through keeping the identical displacement and velocity feedback gain and varying the acceleration feedback gain. 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 AMTMD are investigated to delineate the influence of the important parameters on the effectiveness and robustness of the AMTMD by conducting a numerical searching technique. The parameters include the frequency spacing, average damping ratio, tuning frequency ratio, total number and normalized acceleration feedback gain coefficient. The criterion, which can be stated as the minimization of the minimum values of the maximum dynamic magnification factors (i.e. Min.Min.Max.DMF), is chosen for the optimum searching. Additionally, for the sake of comparison, the results of the optimum MTMD (the passive counterpart of AMTMD) and ATMD are also taken into account in the present paper. It is demonstrated that the proposed AMTMD can be expected to significantly reduce the oscillations of structures under the ground acceleration. It is also shown that the AMTMD can remarkably improve the performance of the MTMD and has higher effectiveness than ATMD. Copyright © 2002 John Wiley & Sons, Ltd.     

Controlling seismic response of eccentric structures by friction dampers

Previous studies have demonstrated the good performance of friction dampers in symmetric frame structures subjected to earthquake excitation. This paper examines their effectiveness in asymmetric structures where lateral-torsional coupling characterizes the behaviour. A parametric study is first performed employing an idealized single-storey structure; this is followed by the example of a three-dimensional 5-storey prototype structure equipped with friction dampers. The parametric results show that it is necessary to tune the friction damped braces with respect to both the stiffness of the braces and the slip load of the devices. For properly tuned structures, maximum response for all magnitudes of eccentricity between the centres of stiffness and mass is reduced to levels equal to or less than that of the corresponding symmetric structure. Compared to this prediction, the prototype structure with friction damped bracing exhibits the desired improvement in performance; namely, the devices slip at all storey levels while the frames remain elastic.     

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。     

结构主动与被动调谐质量阻尼器的减震性能

使用Kanai-Tajimi地震动模型,建立了主动调谐质量阻尼器(ATMD)结构系统的传递函数。将ATMD最优参数的评价准则定义为：设置ATMD结构均方根位移(解析式)的最小值的最小化。将ATMD有效性的评价准则定义为：设置ATMD结构均方根位移的最小值的最小化与未设置ATMD结构的均方根位移之比。根据逃择的评价准则,评价了地震卓越频率系数(EDFR)对ATMD抗震控制性能的影响。同时也评价了EDFR对被动调谐质量阻尼器(PTMD)抗震控制性能的影响。     

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.     

土木工程结构的双层多重调谐质量阻尼器控制策略

为能得到用尽可能少的调谐质量阻尼器(TMD)组成有效性和鲁棒性高的多重调谐质量阻尼器控制系统，本文提出了一种适用于土木工程结构的新控制策略——双层多重调谐质量阻尼器(DMT—MD)。使用定义的优化目标函数，评价了双层多重调谐质量阻尼器(DMTMD)的控制性能。数值结果表明，双层多重调谐质量阻尼器(DMTMD)比多重凋谐质量阻尼器(MTMD)具有更好的有效性和对频率调谐的鲁棒性。DMTMD比双重调谐质量阻尼器(DTMD)具有更好的有效性，而DMTMD和DT—MD对频率调谐的鲁棒性近似相同。因此，双层多重调谐质量阻尼器是一种先进的结构控制策略。     

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.     

Multiple active–passive tuned mass dampers for structures under the ground acceleration

An Erratum has been published for this article in Earthquake Engineering and Structural Dynamics 2003; 32(15):2451. Multiple active–passive tuned mass dampers (MAPTMD) consisting of many active–passive tuned mass dampers (APTMDs) with a uniform distribution of natural frequencies have been, for the first time here, proposed for attenuating undesirable oscillations of structures under the ground acceleration. The MAPTMD is manufactured by keeping the stiffness and damping coefficient constant and varying the mass. The control forces in the MAPTMD are generated through keeping the identical displacement and velocity feedback gain and varying the acceleration feedback gain. The structure is represented by the mode‐generalized system corresponding to the specific vibration mode that needs to be controlled. Through minimization of the minimum values of the maximum dynamic magnification factors (DMF) of the structure with the MAPTMD (i.e. through implementation of Min.Min.Max.DMF), the optimum parameters of the MAPTMD are investigated to delineate the influence of the important parameters such as mass ratio, total number, normalized acceleration feedback gain coefficient and system parameter ratio on the effectiveness (i.e. Min.Min.Max.DMF) and robustness of the MAPTMD. The optimum parameters of the MAPTMD include the optimum frequency spacing, average damping ratio and tuning frequency ratio. Additionally, for the sake of comparison, the results for a single APTMD are also taken into account in the present paper. It is demonstrated that the proposed MAPTMD can be employed to significantly reduce the oscillations of structures under the ground acceleration. Also, it is shown that the MAPTMD can render high robustness and has better effectiveness than a single APTMD. In particularly, if and when requiring a large active control force, MAPTMD is more promising for practical implementations on seismically excited structures with respect to a single APTMD. Copyright © 2003 John Wiley & Sons, Ltd.     

土木工程结构不同多重调谐质量阻尼器的控制策略

提出了双层多重调谐质量阻尼器（DMTMD）和多重双重调谐质量阻尼器（MDTMD）控制策略。利用定义的优化目标函数,评价了最易制作DMTMD和MDTMD模型的性能。数值结果表明,DMTMD和MDTMD比基于任意整数或基于奇数的多重调谐质量阻尼器（AI-MTMD和ON-MTMD）具有更好的有效性和鲁棒性。MDTMD和DMTMD具有近似相同的有效性,但MDTMD比DMTMD具有更好的鲁棒性。总的来说,MDTMD的冲程大于DMTMD的冲程;DMTMD中小质量块的冲程大于AI-MTMD和ON-MTMD的冲程。     

基于Maxwell型阻尼器的多重调谐质量阻尼器性能评价

研究了基于Maxwell型阻尼器的多重调谐质量阻尼器(MTD—MTMD)在控制结构地震反应方面的最优动力特性。利用建立的设置MTD-MTMD时结构的传递函数,定义了设置MTD—MTMD时结构的动力放大系数(DMF)。将MTD-MTMD的优化准则定义为结构最大动力放大系数的最小值的最小化(Min．Min．Max．DMF)。利用定义的优化准则,评价了Maxwell型阻尼器的松弛时间系数(RTC)对MTD—MTMD最优参数和有效性的影响。利用最大的MTD—MTMD动力放大系数(DMF),评价了RTC对MTD-MTMD冲程的影响。     

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.     

Optimum multiple tuned mass dampers for structures under the ground acceleration based on DDMF and ADMF

Multiple tuned mass dampers (MTMD) consisting of many tuned mass dampers (TMDs) with a uniform distribution of natural frequencies are taken into consideration for attenuating undesirable vibration of a structure under the ground acceleration. A study is conducted to search for the preferable MTMD which performs better and is easily manufactured from the five available models (i.e. MTMD‐1 – MTMD‐5), which comprise various combinations of the stiffness, mass, damping coefficient and damping ratio in the MTMD. The major objective of the present study then is to evaluate and compare the control performance of these five models. The structure is represented by its mode‐generalized system in the specific vibration mode being controlled by adopting the mode reduced‐order approach. The optimum parameters of the MTMD‐1 – MTMD‐5 are investigated to reveal the influence of the important parameters on their effectiveness and robustness using a numerical searching technique. The parameters include the frequency spacing, average damping ratio, tuning frequency ratio, mass ratio and total number. The criteria selected for the optimum searching are the minimization of the maximum value of the displacement dynamic magnification factor (DDMF) and that of the acceleration dynamic magnification factor (ADMF) of the structure with the MTMD‐1 – MTMD‐5 (i.e. Min.Max.DDMF and Min.Max.ADMF). It is demonstrated that the optimum MTMD‐1 and MTMD‐4 yield approximately the same control performance, and offer higher effectiveness and robustness than the optimum MTMD‐2, MTMD‐3, and MTMD‐5 in reducing the displacement and acceleration responses of structures. It is further demonstrated that for both the best effectiveness and robustness and the simplest manufacturing, it is preferable to select the optimum MTMD‐1. Copyright © 2002 John Wiley & Sons, Ltd.     

A response spectrum approach for seismic performance evaluation of actively controlled structures

To evaluate and measure the effectiveness of active control schemes in reducing the response of structures subjected to earthquake excitations, it is common to use recorded or artificially generated earthquakes as input motions. This paper introduces the response spectrum analysis to evaluate linear control systems for seismic inputs defined by code‐prescribed or site‐specific ground response spectra. Using such a method one can evaluate a control system in a single analysis for the ensemble of time histories that are represented by the input response spectra. The response spectrum analysis can also facilitate the implementation of comprehensive parametric studies. A generalized response spectrum method is used to analyse systems with non‐symmetrical matrices that are caused by the general nature of the control actions imposed on the structure. The application of the method is demonstrated on several numerical examples of a building structure where the control force is applied through an active tuned‐mass damper. Copyright © 2000 John Wiley & Sons, Ltd.     

On the dimensioning of viscous dampers for the mitigation of the earthquake-induced effects in moment-resisting frame structures

The effectiveness of viscous dampers in mitigating the seismic excitation impacts upon building structures has been widely proved. Recently, with reference to the specific case of equal mass, equal stiffness, shear-type structures, the authors developed a direct practical procedure which gives the mechanical characteristics of the manufactured viscous dampers capable of providing the frame structure with a prescribed value of the first damping ratio. In this paper, a comprehensive rational framework is presented, which allows to formally extend the validity of the proposed procedure to the more realistic case of a generic moment-resisting frame structure. Also the influence of various lateral stiffness distributions is investigated.     

A novel semi-active TMD with folding variable stiffness spring

An innovative variable stiffness device is proposed and investigated based on numerical simulations. The device, called a folding variable stiffness spring (FVSS), can be widely used, especially in tuned mass dampers (TMDs) with adaptive stiffness. An important characteristic of FVSS is its capability to change the stiffness between lower and upper bounds through a small change of distance between its supports. This special feature results in lower time-lag errors and readjustment in shorter time intervals. The governing equations of the device are derived and simplified for a symmetrical FVSS with similar elements. This device is then used to control a single-degree-of-freedom (SDOF) structure as well as a multi-degree-of-freedom (MDOF) structure via a semi-active TMD. Numerical simulations are conducted to compare several control cases for these structures. To make it more realistic, a real direct current motor with its own limitations is simulated in addition to an ideal control case with no limitations and both the results are compared. It is shown that the proposed device can be effectively used to suppress undesirable vibrations of a structure and considerably improves the performance of the controller compared to a passive device.     

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.     

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。     

Tuned mass dampers for response control of torsional buildings

This paper presents an approach for optimum design of tuned mass dampers for response control of torsional building systems subjected to bi‐directional seismic inputs. Four dampers with fourteen distinct design parameters, installed in pairs along two orthogonal directions, are optimally designed. A genetic algorithm is used to search for the optimum parameter values for the four dampers. This approach is quite versatile as it can be used with different design criteria and definitions of seismic inputs. It usually provides a globally optimum solution. Several optimal design criteria, expressed in terms of performance functions that depend on the structural response, are used. Several sets of numerical results for a torsional system excited by random and response spectrum models of seismic inputs are presented to show the effectiveness of the optimum designs in reducing the system response. Copyright © 2002 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。     

Hysteretic dampers for earthquake-resistant structures

The earthquake resistance of many structures can be increased by the inclusion of special components which act as hysteretic dampers. During moderately severe earthquakes these dampers act as stiff members which reduce structural deformations, while during very severe earthquakes the dampers act as energy absorbers which limit the quasi-resonant build-up of structural deformations and forces. The hysteretic dampers are not required to withstand the main structural loads, and may therefore be optimized for their required stiffness and energy-absorbing features. On the other hand, the main structural components no longer require large energy-absorbing capacities and they may therefore be optimized for their required stiffnesses and load-bearing features. For many structures this separation of component functions should lead to increased reliability at a lower initial cost. Under earthquake attack structural damage should be reduced. Non-structural damage should be lower during moderately severe earthquakes, and for certain types of structure it should also be lower for very severe earthquakes. Various ways in which hysteretic dampers may be utilized in structures are discussed briefly. The development of several types of high-capacity, low-cost hysteretic damper, suitable for use in structures, is described. The dampers utilize solid steel beams deformed plastically in various combinations of torsional, flexural and shear deformations.