Title: Using Supplemental Damping Systems on High-Rise Buildings

Authors: Xiangdong Du, Director, RWDIJon K. Galsworthy, Project Director, RWDIChien-Shen Lee, Engineer, RWDIBujar Morava, Senior Consultant, RWDI

Subject: Wind Engineering

Keywords: DampingTuned Liquid DamperTuned Mass DamperVibrationsWind

Publication Date: 2014

Original Publication: CTBUH 2014 Shanghai Conference Proceedings

Paper Type: 1. Book chapter/Part chapter2. Journal paper3. Conference proceeding4. Unpublished conference paper5. Magazine article6. Unpublished

© Council on Tall Buildings and Urban Habitat / Xiangdong Du; Jon K. Galsworthy; Chien-Shen Lee; BujarMorava

ctbuh.org/papers

642 | CTBUH 2014 Shanghai Conference

Using Supplemental Damping Systems on High-Rise Buildings附加阻尼系统于高层建筑中的应用

Xiangdong Du Chien-Shen Lee

Xiangdong Du, Chien-Shen Lee, Bujar Morava & Jon Galsworthy

RWDI 650 Woodlawn Road West Guelph, Ontario Canada N1K 1B8

tel (电话): +1.519.823.1311 fax (传真): +1.519.823.1316 email (电子邮箱): Xiangdong.Du@rwdi.com; Tom.Lee@rwdi.com; Bujar.Morava@rwdi.com; Jon.Galsworthy@rwdi.com http://www.rwdi.com/

Xiangdong Du is director of RWDI China Inc. His areas of specialization in RWDI are the cladding, structural wind loads on tall buildings and large roofs. He received his Ph.D. from mechanical engineering, McGill University.

杜向东是RWDI中国公司的总监。他在RWDI的专业方向为高层建筑和大屋面的幕墙、结构风荷载，并于麦吉尔大学获得机械工程博士学位。

Chien-Shen Lee joined RWDI’s Structural Dynamics & Motion Control Division (Motioneering) in 2011. He received his Ph.D. from University of Western Ontario in the field of Structural Dynamics with emphasis on nonlinear finite element analysis.

李建生Chien-Shen Lee于2011年加入RWDI的结构动力及振动控制部门（Motioneering）。他于西安大略大学获得博士学位，专业方向为结构动力学非线性有限元分析。

Bujar Morava is a Senior Consultant at RWDI with extensive experience in applied structural dynamics. His experience includes research and consulting in seismic design, nonlinear response of structures, wind-induced loading, performance-based design and structural response control.

Bujar Morava是RWDI的高级咨询工程师，有着广泛的结构动力学应用经验。他的研究和咨询经验包括抗震设计、结构非线性响应、风荷载、性能设计和结构响应控制。

Jon Galsworthy joined RWDI in 2009 as a Project Director. He is a wind engineering expert, with recognized contributions to the response of tall chimneys subjected to wind loads.

Jon Galsworthy于2009年作为项目总监加入RWDI。他是风工程专家，在高大烟囱的风荷载响应有着公认的贡献。

Abstract

A considerable number of supplemental damping system implementations are for wind-induced motion control of skyscrapers and their performance has been validated through full scale monitoring during wind storms or seismic events. Among the passive supplemental damping systems, the most popular concepts that have been widely implemented in tall buildings and other wind- or seismically-sensitive structures around the world are the Tuned Mass Dampers (TMDs) and Tuned Sloshing Dampers (TSDs). In this paper, the implementation of supplemental damping systems will be discussed, with specific attention to their recent notable applications in actual wind-sensitive buildings. The objective of this paper is to discuss the implementation of TMD and TSD systems in recently designed high-rise buildings and briefly review the performance of the TMD system installed in the Taipei 101 tower.

Keywords: TMD, TLD, TSD, TLCD, Wind-Induced Vibration, Damper

摘要

附加阻尼系统用于对摩天大楼的风致的振动控制有相当多的案例。附加阻尼系统的性能已通过在风暴或地震事件中的实际监测得到了验证。在被动式阻尼系统中，众所周知的概念是调谐质量阻尼器 (TMD) 和调谐液体阻尼器（TSD），已广泛应用于世界各地的高层建筑和其他风或地震敏感的结构。在本文中，将讨论附加阻尼系统及其最近在风敏感的实际建筑物的应用。本文的目的是讨论最近TMD和TSD在高层建筑的设计应用，并讨论台北101TMD系统的性能。

关键词：TMD、TLD、TSD、TLCD、风致振动、阻尼器

Introduction

Supplemental damping systems have been in existence for well over forty years and have been thoroughly researched and tested. Furthermore, their performance has been also validated through full scale monitoring during wind storms or seismic events. A considerable number of supplemental damping system implementations are for wind-induced motion control of skyscrapers. Their implementation has gained much recognition as a workable and highly reliable solution to enhance the serviceability performance of tall buildings and other dynamically sensitive structures.

Early Applications

Installation of viscoelastic dampers in the twin towers of World Trade Center in 1969 marks the beginning of the application of innovative technologies to tall building structures to achieve the desired performance in terms of occupant comfort (Mahmoodi, 1969; Mahmoodi et al., 1987; Caldwell, 1986). Approximately ten thousand viscoelastic damper units were installed in each tower, evenly distributed throughout the building from the 7th the 107th floor (Fanella et

引言

附加阻尼系统已经存在了四十多年，并进行了深入研究和测试。此外，其性能已通过在风暴或地震事件中的实际监测得到了验证。附加阻尼系统用于对摩天大楼的风致的振动控制有相当多的案例。作为一个可行且高度可靠的解决方案，以改善高层建筑和其他动力敏感结构的使用性能，附加阻尼系统的应用已经获得了很大的认可。

早期应用

1969年，世贸中心双塔的粘弹性阻尼器的安装，标志着创新技术在高层建筑结构中的应用，以实现在住户舒适性的预期性能（Mahmoodi, 1969; Mahmoodi et al., 1987; Caldwell, 1986）。每个塔楼安装了约一万个粘弹性阻尼器单元，从7到107层均匀地分布于整个建筑（Fanella et al., 2005）。阻尼器单元被安装在塔楼水平桁架和外围柱之间。阻尼器的选择、数量、形状和位置是根据风荷载下的塔的动力表现，以及达到性能标准所需的额外阻尼（Mahmoodi et al., 1987）。在这些早期的用于减少高楼风致振动的粘弹性阻尼器应用之后，出现了其他类型的附加阻尼系统，包括调谐质量阻尼器（TMD）、调谐液体阻尼器（TSD）、调

Bujar Morava Jon Galsworthy

2014年CTBUH上海会议 | 643

al., 2005). Damper units were installed between the lower struts of the horizontal trusses and the perimeter columns of the tower. The selection, quantity, shape and location of the dampers was based on the dynamic behavior of the towers under wind loading and on the amount of additional damping required to achieve the performance standards (Mahmoodi et al., 1987). These early applications of viscoelastic dampers to reduce wind-induced motions in tall buildings were followed by other types of supplemental damping systems such as tuned mass dampers (TMDs), tuned sloshing dampers (TSDs), tuned liquid column dampers (TLCDs), distributed damping systems and active dampers, etc. Some recent RWDI/Motioneering implementations of these damping systems in actual tall buildings and other dynamically sensitive structures will be discussed herein.

Tuned Mass Dampers

A TMD is a damped secondary inertial system which consists of a mass attached to the building (generally at a location with maximum motion) through a spring and damping mechanism, usually a viscous damping device. In practice the spring connecting the secondary mass to the main mass can be the stiffness arising from pendulum action when the TMD mass is hung from cables attached to the building structure. Accurate tuning of the frequency of the TMD to that of the building generates inertial forces on the TMD mass which counteract the lateral wind or seismic forces acting on the structural frame of the building, resulting in reduced wind-induced motions of the building. The effectiveness of a TMD is determined by its basic design parameters: mass ratio (the ratio of TMD mass to the generalized mass of the building in its target mode of vibration) and TMD mass displacement. Depending on the target performance and the space constraints, a mass ratio in the range of 0.5% to 2.0% is generally specified. The ratio of the TMD mass to the generalized mass of the structure has an inverse relationship to TMD displacements (i.e. with increased mass ratio, TMD displacements decrease). However, with the increase in TMD mass, larger forces will be imparted on the structure, creating the need for stronger supports.

There are a number of practical considerations in the design of a TMD. One of these is the need to limit the motions of the TMD mass under extreme wind or seismic. By employing a nonlinear viscous damping device with a higher exponent (say 2), the motions of the TMD mass can be greatly reduced under the extreme loading conditions. To properly simulate the response of a TMD with nonlinear dampers it is best to undertake time history simulations of the tower response in both wind and earthquake loading, (Breukelman, et al, 2001). The equations of motion for the oscillatory system can be presented in the general matrix formulation shown below, with a couple of specialized modifications as indicated:

谐液柱阻尼器（TLCD）以及分布式阻尼系统等。本文将讨论RWDI/Motioneering最近在一些高层建筑和其他动力敏感结构中应用的阻尼系统实际案例。

调谐质量阻尼器

TMD是有阻尼的次级惯性系统，包括通过弹簧和阻尼装置连接于建筑的质量（通常位于最大振动处），阻尼装置一般为粘性阻尼设备。实际上，连接主质量和次级质量的弹簧可以是单摆运动产生的刚度，即TMD质量由吊索悬挂于建筑结构中。将TMD频率准确调谐到建筑频率将产生TMD质量的惯性力，以抵消作用于建筑结构体系的侧向风荷载或地震荷载，从而使建筑的风致振动降低。TMD的有效性是通过其基本设计参数确定的：质量比（目标振型中TMD质量与建筑广义质量的比值）和TMD质量位移。根据目标性能和空间约束，质量比一般为0.5%到2.0%。TMD质量与结构广义质量的比值与TMD位移成反比（即质量比增加，TMD位移减少）。然而，TMD质量的增加，将对结构造成更大的荷载，引起更大的支撑结构需求。

设计TMD过程中有一些考虑，其中之一是需要限制TMD质量在极端风或地震下的运动。通过使用较高指数（如2）的非线性粘滞阻尼器，可以在极端荷载工况下大幅降低TMD质量的运动。为适当地模拟TMD与非线性阻尼器的响应，最好的方法是以时程分析模拟塔楼在风荷载和地震荷载下的响应（Breukelman, et al, 2001）。大楼振动体系的运动方程可由下列矩阵形式表述，其中进行了一些特别的修改：

这里:

x为表示层间平移（xn 和 yn）和扭转（rzn）坐标的向量，也包括TMD的两个平移坐标（相对于TMD楼层，xTMD 和 yTMD）；

[M]为包括每层的质量和质量惯性矩，和TMD质量（根据向量x调整）的矩阵。该矩阵在TMD楼层和TMD的坐标之间有几个稀疏分布的耦合项；

[C]为对角带状矩阵，基本为链状结构，包含建筑模型适当的阻尼特性；

[K]为对角带状矩阵，类似于阻尼矩阵，给出建筑和TMD的回复趋势（刚度）；

{FTMD(x)}是用于在TMD楼层与TMD之间，传递粘滞阻尼杆引起的非线性耦合力的向量，为x的瞬时函数；

{Fenv(t)}是环境作用于建筑和TMD系统的力向量，风荷载和地震荷载有所不同，具体如下：

• 对于风荷载，广义力由风洞时程数据计算得出。这些力作用于模拟时的每个时间点；

• 对于地震荷载，参考体系固定于建筑的地面层。因此，由D’Alembert’s原理，荷载作用于每层的平移方向，根据坐标体系分布。

方程系统之后代入状态空间形式，使其相比原来的二阶微分方程组，有两倍多的一阶微分方程。这样做是为了方便数值积分程序状态变量的传递（通常位移和速度起始为零）。考虑理想的精度和计算速度的组合，我们使用常用的四阶Runge-Kutta和Kutta-Merson（多时间点）方法。

[ ] [ ] [ ] ( ){ } ( ){ }tFxFxKxCxM envTMD +=++ &&&

[ ] [ ] [ ] ( ){ } ( ){ }tFxFxKxCxM envTMD +=++ &&&

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Where:

x is the vector representing the floor-by-floor translation (xn and y

n),

and rotation (rzn

) coordinates, as well as two translation coordinates (relative to the TMD floor) for the TMD (x

TMD and y

TMD);

[M] is a matrix which contains the mass and mass moment of inertia of each floor, as well as the mass of the TMD, organized according to the vector x. This matrix also has several sparsely distributed coupling terms between the coordinates of the TMD floor and the TMD;

[C] is a diagonally banded matrix, with terms representing the appropriate structural damping properties of the building model;

[K] is a diagonally banded matrix, similar to the damping matrix, with terms representing the appropriated restoring force characteristics of the building and the TMD;

{FTMD(x)} is a vector which takes into account the nonlinear coupling forces developed in the viscous damping devices between the TMD floor and the TMD, as an instantaneous function of x; and,

{Fenv(t)} is the force vector which takes a different form depending on whether wind or seismic excitation is being considered, as follows:

• For wind, the generalized forces are calculated from the time domain wind tunnel records. These forces are applied at each time step of the simulation; and

• For seismic excitation, the frame of reference is fixed to the ground floor of the building. Thus, by D’Alembert’s principle, forces are applied to the translation coordinate of every floor distributed according to the coordinate system.

The system of equations is then expanded into state space form, such that there are twice as many first order differential equations, as compared to the original set of second order equations. This is done to facilitate the propagation of state variables, subject to initial conditions (typically both displacement and velocity coordinates all start at zero), with any of a number of common numerical integration procedures. For a desirable combination of accuracy and speed, we have made extensive use of the popular 4th order Runge-Kutta, and Kutta-Merson (variable time step) methods.

In the dynamic analysis, it is necessary to investigate both the wind- and seismic-induced motions of the TMD. Given that the TMD is being designed to reduce wind-induced accelerations, the optimization of the physical parameters relating to its behavior in wind events takes the lead in this analysis task.

Upon determining a set of parameters that satisfy the conditions for both short and long return period wind events, the TMD must also respond favorably to several intensities of design seismic event. If a response quantity (e.g. relative TMD amplitude compared to the building surrounding it) is deemed undesirable in a seismic simulation, and thus necessitates a change in some physical aspect of the system, the entire analysis must return to the first step to ensure that the target return period wind response is suitable. These iterative steps are logged, and performance trends as functions of design parameters are developed to facilitate finding a design which satisfies the combined requirements of acceleration reduction and reasonable response to both strong wind and seismic events.

在动力分析中，有必要对风致振动和地震导致的振动都进行研究。由于该阻尼器的设计旨在降低风致加速度，因此对有关风致响应的物理参数进行优化是分析中的首要任务。

在使一组参数满足不同回归期风速情况的同时，该阻尼器还要满足不同设计地震烈度下的要求，如果阻尼器在地震模拟中有不利的响应（即TMD相对振幅过大），则设计必须进行改变，整个分析必须重新从第一步进行并保证设计回归期风速下的响应满足要求。这些迭代步骤会被记录下来，阻尼器性能的变化趋势与设计参数的变化研究会将帮助找出同时满足降低风致加速度、强风和地震情况下的控制要求。

单级摆TMD

目前已投入服务用于控制摩天大楼风致振动的单级摆TMD其中之一是安装于台湾台北101大厦顶部的660吨球形调谐质量阻尼器（图1）（Haskett, et al., 2003; Joseph, et al., 2006）。其中八根速度平方限制阻尼器（VDD）由意大利FIP Industriale S.p.A.公司设计制造，并于TMD质量相连。VDD的安装长度为3.4m，外直径为330mm。VDD的风力系数为1000 kN/(m/s)2，其估计的最大持续耗散功率为25kW。这也是第一个作为建筑中关键视觉元素而设计制造的TMD。尽管TMD在风和地震荷载工况下要求有很大的振幅空间，建筑师仍将该振动吸收器纳入最高使用层的建筑方案中（图2a）。从TMD穿过中心的餐厅和酒吧中，在每年有小风的许多天里，人们可以看到金色的铁球轻微摇摆（图2b）。根据台湾舒适度标准，TMD设计为减少6个月重现期的峰值加速度到5 milli-g左右（1 milli-g为1/1000的重力加速度）（Haskett, et al., 2003）。自从TMD调谐和运行测试后，数个台风和地震袭击了台北101现场，观测到的阻尼器和塔楼的性能与分析预计的情况和设计目标一致。图3显示了台风罗莎（2007年10月5-6日）接近台北时TMD与建筑响应的同步采样数据。从该图可以看出建筑在两个方向的加速度响应满足5 milli-g要求。

双级摆TMD

在某些情况下，建筑中所分配的用于安装附加阻尼系统的空间高度不足以使用简单形式的吊索单摆TMD。在该情况下，为达到建筑的调谐频率，可以使用折叠摆，也称之为多级摆。双级摆TMD已被证明在指定楼层安装附加阻尼系统时，是减少竖向空间要求而同时占用基本相同的水平空间的有效解决方案。

图4显示了一个双级摆TMD实例，是中国某超高层建筑2009年的原始设计。主要质量是1200公吨。该塔楼详细的风洞试验研究预计10年峰值加速度为19 milli-g，超过了中国建筑规范的住宅舒适度标准，15 milli-g。因此考虑使用附加阻尼系统来降低10年峰值加速度至11 milli-g，其等效的阻尼比为3%。由于后来TMD空间调整，该设计改为单级摆TMD。

可变回复力单摆TMD

一般来说，附加阻尼系统安装的水平和竖向空间十分有限，使达到期望的舒适度性能变得非常具有挑战性。在这些情况下，考虑使用更复杂的TMD形式。图5显示了RWDI/Motioneering研发的一种可变回复力单摆，这种单摆的周期相比上述单级摆所能达到的周期有很大延长。通过这种设计，对单级摆施加一个反向的与振幅成正比的回复力，其形式为一个相连接的质量为m2（次要质量）的反向摆，从而得到比原本单摆更低的频率。该单摆系统的频率可以通过调整主要和次要质量比，以及/或调整主要质量吊索（或连接件）长度与次要质量支撑构件长度的比值来实现。

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Simple-Pendulum TMD

One of simple-pendulum TMDs in service to control wind-induced motions of a skyscraper is the 660 tonne ball-shaped tuned mass damper (Figure 1) installed at the top of the Taipei 101 building in Taipei, Taiwan (Haskett, et al., 2003; Joseph, et al., 2006). Eight velocity-squared viscous damping devices (VDDs), designed and manufactured by FIP Industriale S.p.A., Italy, are attached to the TMD mass. The installed length of the VDDs is 3.4 m and their external diameter is 330 mm. The force coefficient of the VDDs is 1000 kN/(m/s)2 and their estimated maximum continuous power dissipation is 25 kW. This TMD is also the first one designed and constructed as a key architectural and visual element in the building. The design team was able to incorporate this vibration absorber into the architectural scheme of the uppermost occupied floors (Figure 2a) despite the significant amplitude requirements of the TMD under extreme wind and seismic loading scenarios. From the restaurant and bar, through the center of which the TMD penetrates, patrons are able to see the golden steel ball slightly swinging, many days of the year, under light winds (Figure 2b). The TMD is designed to reduce 6-month return period peak accelerations to approximately 5 milli-g (1 milli-g is 1/1000 of gravity acceleration), as required by Taiwanese criteria for occupant comfort (Haskett, et al., 2003). Since tuning and commissioning of the TMD, several typhoons and earthquakes have hit the Taipei 101 site. The observed performance of both, the damper and the tower have been reported to be in line with analytical predictions and design objectives. Sample traces of simultaneous TMD and building response as Typhoon Krosa was approaching Taipei (October 5-6, 2007) are shown in Figure 3. From this figure it can be seen that building acceleration responses in both directions are in line with 5 milli-g.

Figure 1. The ball-shaped TMD installed in Taipei 101 building图1： 安装于台北101大厦的球形调谐质量阻尼器a. (above) Aerial view of the building 大厦鸟瞰图b. (right top) 3-D rendering of the TMD TMD三维渲染图c. (right bottom) TMD after completion 安装后的TMD系统

Figure 2. Integration of the TMD into architectural design scheme of the uppermost floors图2： 将TMD纳入最高使用层的建筑方案a. (top) Architectural design concept 建筑设计方案b. (bottom) Implementation 方案的实施

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Dual-Stage Pendulum TMD

In some situations, the height of the allocated space for the installation of a supplemental damping system in the building is insufficient to allow a simple type, cable-pendulum TMD to fit. In such a case, to match the tuning frequency of the building a folded pendulum, also known as multi-stage pendulum, can be used. Dual-stage pendulum TMDs have proven to be an effective solution in reducing vertical space requirements while occupying nearly the same horizontal space at the designated floor for supplemental damping system installation.

An example of dual-stage pendulum TMD is shown in Figure 6, which was an original design in 2009 for a high-rise building in China. The primary mass is 1200 tonne. Detailed wind tunnel studies for this tower predicted 10-year peak acceleration of 19 milli-g, which exceeded the occupant comfort criteria of China Building Code of 15 milli-g for residential. Therefore implementation of a supplemental damping system was considered to reduce commonly occurring acceleration levels experienced in the upper floors. This TMD was designed to reduce 10-year peak acceleration to approximately 11 milli-g by achieving a total equivalent damping ratio of 3% of critical. This design was changed to simple pendulum TMD later due to revision of TMD space.

该形式TMD的设计案例参见图6。对某塔楼进行的详细风致结构响应研究预计其1年的峰值加速度为24 milli-g。计划在有限的可用空间（约14.5m高）采用两个质量分别为600公吨（总质量1200公吨）的调谐质量阻尼器以减少上部楼层的常遇加速度。如果采用单级摆TMD，所需的高度将大于40m。由于需要超长的吊索，无法在分配的竖向空间中使用传统的单级摆或双级摆TMD。为纳入预留空间，建议“可变回复力单摆”是最为可行的方案。在该形式TMD系统中，主要质量从顶部悬挂于吊索上，而次要质量从底部支撑。该次要质量与主要质量相连，使它们共同侧向运动，但两个质量之间的相对竖向运动是自由的。该摆机构的频率可通过调整主要质量和次要质量的摆长比和质量比来调节。

TMD系统由6类构件组成：

1. 吊索;

2. 质量块组件;

3. 机械连接件;

4. 关节式支撑杆;

5. 粘滞阻尼杆 以及,

6. 限位系统.

TMD包括两个质量块组件，它们被设计为互相连接、联合运动，但它们由不同的方式支撑（该项目中一个质量块由缆索悬挂支撑，另一个由关节式支撑杆支撑）。这种相关联运动的方式（通过分界面组件连接两个质量块）使得整个系统能够在接近结构自振频率的预计频率下运动。并且，此TMD系统与单质量块被动系统相比大量节约了空间。

TMD界面组件是一套机械连接件，用来连接主要和次要质量块，使这两个质量块能联合运动。为避免连接件变形，该界面组件必须精确地制造和安装以避免任何可能的碰撞或干扰，并应配备低摩擦球面轴承。

应安装支撑杆使次要质量块垂直并精确地与主要质量块对齐。支撑杆应具有在同一标高和相同平面尺寸的关节节点，并应在转动关节处具有低摩擦特性以便于次要质量块运动。

粘滞阻尼杆连接主要质量块和建筑结构。在TMD的相对运动导致

Figure 3. Sample traces of TMD and building response during Typhoon Krosa台风罗莎期间TMD与建筑响应的采样数据a. X-direction acceleration responses (in milli-g) X方向加速度响应 （单位为milli-g）b. Y-direction acceleration responses (in milli-g) Y方向加速度响应 （单位为milli-g）

Figure 4. Dual-stage pendulum TMD 图4： 双级摆TMD

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Simple Pendulum with Variable Restoring Force TMD

Quite often, the available horizontal and vertical space for a supplemental damping system installation is very limited and achieving the desired performance for occupant comfort becomes very challenging. In these situations, considerations have been given to more complex TMD configurations. An design concept of simple pendulum with variable restoring force TMD shown in Figure 5 was developed by RWDI/Motioneering to allow extension of the period of a pendulum beyond that which is capable based solely on the length of said simple pendulum. By this design, a negative restoring force proportional to amplitude is applied to said simple pendulum in the form of a coupled inverted pendulum of mass m2 (the secondary mass), and thereby results in an frequency lower than that of the original pendulum. The frequency of this system of pendulums can be adjusted by varying the ratio of primary to secondary masses and/or by varying the ratio of the primary mass’s suspension cables (or linkages) to length of the secondary mass’s supporting member(s).

A design example of this type of TMD is shown in Figure 6. Detailed wind-induced structural response studies conducted for a tower predicted 1-year peak acceleration of 24 milli-g. Two tuned mass dampers (TMD) with a mass of 600 tonnes each (total mass 1200 tonnes) have been planned to reduce commonly occurring acceleration levels experienced in the upper floors in the available limited space of approximately 14.5 m high. If a simple pendulum-type TMD were to be employed, a floor to ceiling height of greater than 40 m would be required. Due to the great cable length required, a traditional simple pendulum or a dual-stage pendulum TMD would not fit within the allotted vertical height. In order to fit into the reserved space, “simple pendulum with variable restoring force” TMD is recommended to be most feasible. In this type of TMD system, a primary mass is suspended on cables from above and a secondary mass supported from below. The secondary mass is connected to the primary mass so that they translate laterally together, but the masses are free to translate vertically relative to each other. The frequency of such a pendulum can be adjusted by varying the pendulum length ratio and the mass ratio between the primary and secondary masses.

The TMD system is comprised of 6 general component categories:

1. cables

2. mass block assemblies

3. mechanical linkages

4. articulating support columns

5. viscous damping devices (VDDs)

6. snubbing system

There are two mass block assemblies. These are designed to move in conjunction with each other, but are supported by different means (hanging cable support for one mass block, and articulating support column supports for the other in this project). This principle of motion dependence (by linking the mass blocks to each other with an interface assembly), allows the system to move at predictable natural frequencies near to the structures’ natural frequencies. However this TMD consumes much less space than a singular-mass passive TMD system.

The TMD interface assembly is a set of mechanical linkages that inter-connect the primary and secondary mass block assemblies so that these systems are motion dependent. In order to prevent distortion of the linkage arms, the interface assembly must be precisely fabricated and installed to negate any potential for binding/jamming, and shall be equipped and with very low friction spherical bearings.

的粘滞阻尼杆伸长和缩短的过程中，一部分建筑振动的能量被吸收，吸收的这部分能量最终以热能形式耗散。

长重现期的地震和风会使TMD产生较大位移，这种位移需要被控制以保证没有局部破坏发生。限位系统使用辅助吸振器来限制TMD的过大运动。使用该TMD系统预计可以降低该塔楼顶部使用层1年峰值加速度约54%，即从24 milli-g到11 milli-g。该TMD目前正在施工中。

调谐液体阻尼器

在土木工程结构中应用调谐液体阻尼器减振的想法始于19世纪80年代（Bauer, 1984; Modi and Welt, 1987）。对比调谐质量阻尼器，调谐液体阻尼器的优点包括初步费用低、运行几乎不需维护和调频简便。然而，也有一些缺点，如关于水的质量抵消建筑振动的参与效果、对非线性响应效果的不确定、与TMD相比水的密度较低、以及一般为达到适当调谐的水箱尺寸需要较大的楼面空间。

2007年，一个大尺寸单向TSD（Morava et al., 2010）被安装于曼哈顿市中心的巴克利街10号塔楼屋顶（图7）。该柔性建筑方案设计阶段的风洞试验研究预计最高使用层的峰值加速度接近23 milli-g，比常用住宅楼的10年舒适度标准，15到18 milli-g高出许多。传统的增加刚度的方法可以提供期望的性能但将减少有价值的建筑楼面空间并增加造价。另一个解决方案是通过使用经济有效的TSD来改善塔楼使用性能，该方案已被研究并作为塔楼最终设计

Figure 5. Concept of simple pendulum with variable restoring force TMD图5：可变回复力单摆TMD的概念设计

Figure 6. An design example of simple pendulum with variable restoring force TMD图6：可变回复力单摆TMD设计案例

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Columns shall be installed so that the secondary mass block is plumb and precisely aligned with the primary mass block. They shall have articulating joints to be at exactly the same elevation and plan dimensions relative to each other. They shall exhibit very low friction properties at rotational joints to allow for ease of motion of secondary mass block.

Viscous damping devices (VDDs) are linked between the primary mass of the TMD and the structure. A certain proportion of the vibration energy is absorbed by these units as they extend and contract due to the TMD’s relative motions. This absorbed energy is eventually dissipated as heat.

Larger TMD displacements during higher return period wind or seismic events must be controlled to ensure that local damage is not caused. The snubbing system limits the excessive TMD motions with the use of four auxiliary shock absorbers. Implementation of this TMD system is expected to reduce peak 1-year acceleration at the top occupied floor of the tower by approximately 54%, i.e. from 24 milli-g to 11 milli-g. The TMD is currently under construction.

Tuned Liquid Dampers

The idea of applying tuned liquid dampers to reduce vibrations in civil engineering structures began in the 1980’s (Bauer, 1984; Modi and Welt, 1987). In comparison with tuned mass dampers, the advantages associated with tuned liquid dampers include low initial cost, nearly maintenance free operation and simplicity in frequency tuning. However, there are disadvantages as well which relate to the effectiveness of water mass participation in counteracting the building motion, uncertainties associated with nonlinear behavior effects, lower density of water compared to steel used in TMDs, and generally higher floor space requirements dictated by the water tank geometry to achieve the proper tuning.

In 2007, a large size unidirectional TSD (Morava et al., 2010) was installed at the roof top level of 10 Barclay Street tower in downtown Manhattan (Figure 7). Wind tunnel studies performed at the schematic design stage of this slender building predicted peak accelerations at the top occupied floors close to 23 milli-g, considerably higher than the commonly used 10-year criteria of 15 to 18 milli-g for human comfort in a residential tower. The traditional approach of stiffness increase would have produced the desired performance but at the expense of reduced valuable real estate space of the floors and overall cost increase. As an alternative solution, the enhancement of the serviceability performance of the tower through the implementation of a cost-effective TSD was investigated and incorporated in the final detailed design of the tower. This TSD, with a water mass of 170 tonnes, is designed to achieve a total damping ratio of 3.5% of critical. This total damping ratio is required to maintain 10-year peak accelerations within the commonly used comfort criteria of 15 to 18 milli-g.

Concluding Remarks

In the last two decades, implementation of passive supplemental damping systems has gained considerable recognition around the world as a workable and reliable technology for the mitigation of wind-induced motions in tall buildings. The acceptance of these innovative systems as part of the structural design scheme is based on a well-maintained balance between the serviceability performance targets, construction cost and the complexity of the implementation in an actual building.

Figure 7. 10 Barclay street tower and a rendering of the TSD installed at the roof top level图7：巴克利街10号塔楼和安装于屋顶的TSD渲染图a. (top) Building view 建筑外观b. (bottom) 3-D rendering of the TSD designed and implemented 设计和实施的TSD三维渲染图

的一部分。该TSD水量为170公吨，设计总阻尼比达到3.5%。该要求的总阻尼比可以维持10年峰值加速度在常用舒适度标准15到18 milli-g以内。

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Every tall building or dynamically sensitive structure has unique characteristics and constraints that must be carefully investigated in order to determine which type of supplemental damping system can best achieve the target performance in terms of cost, construction schedule, implementation etc. The up-front assessment should consider a wide range of factors that are critical in achieving the desired performance, such as:

• The type of the external dynamic excitation (i.e. vortex shedding, buffeting, seismic, etc.)

• Dynamic behavior of the structure

• Damper – structure interaction

• Available space

• Level of performance required based on the occupancy or usage (i.e. high end condominiums, hotel, office, rental, pedestrian bridge, sky-bridge etc.)

• Construction method

• Construction schedule

• Maintenance requirements

Careful consideration of the above factors at early design stages is key to a successful implementation of a supplemental damping system and to the achievement of the desired occupant comfort level.

结论

最近20年中，被动式附加阻尼系统作为减少高层建筑风致振动的一个可行且高度可靠的技术，其应用得到了世界范围内的很大认可。接受这些创新系统作为结构设计方案的一部分，是基于实际建筑中保持使用性能目标、施工造价和应用复杂性间的平衡。

每个高层建筑或动力敏感结构具有独特的特性和需要特别调查的约束条件，以确定何种附加阻尼系统可以在造价、施工计划和应用等条件下满足目标性能。预先评估应考虑要到达预期性能的很多因素，比如：

• 外部动力激励形式（即漩涡脱落、抖振、地震等）

• 结构动力响应

• 阻尼器-结构相互作用

• 可用空间

• 基于用途所需的性能水平（即高端公寓、酒店、办公、租住、行人桥、天桥等)

• 施工方法

• 施工计划

• 维护要求

在设计早期仔细考虑上述因素是成功应用附加阻尼系统并达到预期使用舒适度的关键。

References (参考书目): Bauer, H.F. (1984), Oscillations of Immiscible Liquids in a Rectangular Container: A New Damper for Excited Structures, Journal of Sound and Vibration, 93(1), 117-133.

Breukelman, B., Haskett, T.C., Gamble, S.L.,and Irwin,P.A., (2001), Analysis and Model Techniques for Determining Dynamic Behaviour of Civil Structures with Various Damping Systems, Proceedings Council on Tall Buildings and Urban, Habitat, 6th World Congress, Melbourne, Australia, Feb. 26 -Mar. 2.

Caldwell, D.B. (1986), Viscoelastic Damping Devices Proving Effective in Tall Buildings, AISC Engineering Journal, 23(4), 148-150.

Fanella, D.A, Derecho, A.T. and Ghosh, S.K. (2005), Design and Construction of Structural Systems, Federal Building and Fire Safety Investigation of World Trade Center Disaster, NIST NCSTAR 1-1A Report, Technology Administration, U.S. Department of Commerce.

Haskett, T., Breukelman, B., Robinson, J. and Kottelenberg, J. (2003), Tuned Mass Dampers Under Excessive Structural Excitation, Extreme Loading Conference, Toronto, Canada.

Irwin, P. and Breukelman, B. (2001), Recent Applications of Damping Systems for Wind Response, 6th World Congress of the Council on Tall Buildings and Urban Habitat, Melbourne, 26 February to 2 March, 2001, 645-655.

Joseph, L.M, Poon, D. and Shieh, S. (2006), Ingredients of High-Rise Design: Taipei 101 – the World Tallest Building, Structure Magazine, June 2006, 40-45.

Keel, C.J. and Mahmoodi, P. (1986), Designing of Viscoelastic Dampers for Columbia Center Building, Building Motion in Wind, ASCE New York, 66-82.

Mahmoodi, P. (1969), Structural Dampers, ASCE Journal of Structural Division, 95(8), 1661-1672.

Mahmoodi, P. and Keel, C.J. (1986), Performance of Viscoelastic Structural Dampers for the Columbia Center Building, Building Motion in Wind, ASCE New York, 83-106.

Mahmoodi, P., Robertson, L.E., Yontar, M., Moy, C. and Feld, I. (1987), Performance of Viscoelastic Dampers in World Trade Center Towers, Dynamic of Structures, Structures Congress ’87,Orlando, Florida.

Modi, V.J. and Welt, F. (1987), Vibration Control Using Nutation Dampers, International Conference on Flow Induced Vibrations, London, England: 369-376.

Morava, B., Alkhatib, R., Grossman, J., Klein, G. and Han, S. (2010), Tuned Sloshing Damper for Wind-Induced Motion Control of a Tall Residential Tower, 2010 Structures Congress, Orlando, Florida, May12-15, 2010.