Modelling of tuned mass damper for wind tunnel tests on a full-bridge aeroelastic model
人群简化模型与人行桥 TMD 参数设计研究
人群简化模型与人行桥 TMD 参数设计研究孙昊;周叮;刘伟庆;李枝军【摘要】用两段连续弹性杆模拟静立人体，建立人群－人行桥－调谐质量阻尼器（TMD）振动系统。
将静立人群简化建模为单个的广义人体，研究广义人体－人行桥－调谐质量阻尼器振动系统的动力特性及 TMD 参数设计。
运用最小二乘原理确定广义人体的相关参数，通过与已有的实验数据对比，验证了将静立人群简化为广义人体模型的正确性。
以均方根加速度作为人体舒适度的优化准则，分析了人行桥 TMD 的最优频率比和最优阻尼比。
%Here,a continuous-elastic bar with two segments was used to model bodies standing on a footbridge and the crowd-footbridge-tuned mass damper (TMD) vibration system was built.By simplifying the static crowd as a generalized human body,the dynamic characteristics of the generalized human body-footbridge-TMD system and the parameter design of TMD were studied.The parameters of the generalized human body were identified with the principle of least paring with the data available from tests,the correctness of the simplified generalized human body was verified.The root-mean-square acceleration was taken as the optimization criterion to assess the human body comfort,the optimal parameters of the TMD were analyzed.【期刊名称】《振动与冲击》【年(卷),期】2016(000)004【总页数】8页(P217-223,240)【关键词】人群 -人行桥 -TMD 系统;广义人体 -人行桥 -TMD 系统;最小二乘;最优频率比;最优阻尼比【作者】孙昊;周叮;刘伟庆;李枝军【作者单位】南京工业大学土木工程学院，南京 211816;南京工业大学土木工程学院，南京 211816;南京工业大学土木工程学院，南京 211816;南京工业大学土木工程学院，南京 211816【正文语种】中文【中图分类】TU3;TB1随着建筑结构技术的迅速发展和高性能建筑材料的广泛运用，人行桥正向大跨轻柔低阻尼的方向发展，人行桥的人致振动问题也因此日益突出。
风浪联合作用下分布式调谐质量阻尼器对海上半潜漂浮式风机的减振控制
第 37 卷第 4 期2024 年4 月振 动 工 程 学 报Journal of Vibration EngineeringVol. 37 No. 4Apr. 2024风浪联合作用下分布式调谐质量阻尼器对海上半潜漂浮式风机的减振控制罗一帆1，2，孙洪鑫1，2，王修勇1，2，陈安华3，彭剑1，2，左磊4（1.湖南科技大学土木工程学院，湖南湘潭 411201； 2.湖南科技大学结构抗风与振动控制湖南省重点实验室，湖南湘潭 411201； 3.湖南科技大学机电工程学院，湖南湘潭 411201；4.美国密歇根大学船舶海洋工程系，美国安娜堡 48109）摘要: 海上半潜漂浮式风机在复杂深海环境下产生有害振动会威胁风机的安全性和耐久性，针对该问题并结合美国NREL的5 MW样机的漂浮平台几何结构构造，提出利用分布式调谐质量阻尼器（Tuned Mass Dampers，TMDs），即分别在漂浮平台的3根浮筒中布置TMD，形成等边三角形布置，对随机风浪联合作用下海上半潜漂浮式风机的平台纵摇振动进行控制。
为了更好地描述分布式TMDs对海上半潜漂浮式风机的减振效果，基于拉格朗日方程和模态叠加法，对海上半潜漂浮式风机‑TMDs耦合系统提出并建立了9自由度多体动力学模型。
基于H∞算法，即以平台纵摇频响函数的峰值为优化目标，对分布式TMDs的参数进行优化设计，优化设计中考虑了3个TMDs之间的耦合关系。
对风机‑TMDs耦合系统开展了风浪联合作用下的数值模拟，分析了分布式TMDs对平台纵摇响应的减振效果。
结果表明：最优设计下的分布式TMDs对海上半潜漂浮式风机平台纵摇振动具有良好的减振性能；在三种不同工况的随机风浪荷载作用下，分布式TMDs对平台纵摇固有频率附近的功率谱密度曲线峰值减振率和标准差减振率能分别达到39%和52%以上。
关键词:振动控制；海上半潜漂浮式风机；多体耦合动力学模型；分布式调谐质量阻尼器；参数优化中图分类号: TB535；TK83 文献标志码: A 文章编号: 1004-4523（2024）04-0565-13DOI：10.16385/ki.issn.1004-4523.2024.04.004引言随着全球变暖的加速和人们环境保护意识的增强，可再生清洁能源的生产和使用变得越来越重要，其中海上风能因其风速高、风力稳定、对环境影响小等优点受到广泛关注。
Tuned Mass Dampers (2 D.O.F)
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Lecture 20-Tuned Mass Damper
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Lecture 20-Tuned Mass Damper
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摩缇马帝multimatic底盘及调教简介
Objective Testing
Multimatic’s unique multi-post rig testing and vehicle characterisation techniques offer an easily interpreted objective-based methodology for assessing a vehicle’s ride and handling performance. Using in-house developed servo-hydraulic actuators in conjunction with a proprietary controller and software suite, a vehicle’s dynamic signature can be identified. The analysis returns data on the dynamic characteristics of the vehicle’s structure, suspension and tires as well as an overall assessment of performance.
Closed-Loop Vehicle Closed-Loop Vehicle Dynamics Optimisation Dynamics Optimization
Multimatic provides development and tuning services that integrate three crucial testing and evaluation disciplines into a “Closed-Loop Vehicle Dynamics Optimisation” process.
一种新型调谐质量阻尼器的试验研究
一种新型调谐质量阻尼器的试验研究施卫星;何斌;李晓玮;鲁正【摘要】用填充颗粒群的盒子代替调谐质量阻尼器的质量块，形成一种新型调谐质量阻尼器。
通过对比单自由度排架不附加、附加该新型调谐质量阻尼器的自由振动，白噪声激励以及实际地震输入下的振动台试验，考察了该新型阻尼器对结构的减振控制效果。
试验研究表明：颗粒的填充率对振动衰减影响明显，表现出双峰值的曲线特征；颗粒质量对衰减率的影响不明显，实际工程可以采用轻质颗粒材料；输入地震波能量与衰减率呈抛物线形。
试验还从振型特性方面表明采用调谐颗粒阻尼器有利于减轻结构振动响应。
%A new type of tuned mass damper was generated by taking advantage of a box filled with particles instead of solid mass.The vibration reduction effects with or without this new damper under free vibration,white noise stimulation and onsite earthquake excitations were investigated by a series of shaking table tests.A bent frame with single degree of freedom was selected as the main structure in the experiments.It is shown that the filling ratio of particles has a significant influence on the vibration control,revealing the characteristics of bimodal curve;lightweight materials could be applied in practice owing to the slight effect of the particle mass on vibration reduction;a parabolic curve reveals the relationship between the input energy of seismic waves and the vibration damping.Also,the tests verify the effective vibration reduction performance of the new type of tuned mass damper from the aspect of vibration mode control.【期刊名称】《振动与冲击》【年(卷),期】2015(000)012【总页数】5页(P207-211)【关键词】新型调谐质量阻尼器;振动台试验;结构振动控制;影响因素【作者】施卫星;何斌;李晓玮;鲁正【作者单位】同济大学结构工程与防灾研究所，上海 200092;同济大学结构工程与防灾研究所，上海 200092;同济大学建筑设计研究集团有限公司，上海200092;同济大学结构工程与防灾研究所，上海 200092【正文语种】中文【中图分类】TU352;TB535单摆式调谐质量阻尼器（TMD）主要由摆绳、质量块和阻尼器组成。
高位卧式容器基础设计要点
变/应力关系、静态刚度等性能指标。
参考文献[1]和昆原.液压式摩擦阻尼器的研究[J].煤矿机械，2012（8）：60-62.[2]颜学渊，王璇，曹晨，等.复合型阻尼器研究进展[J].地震工程与工程振动，2020，40（3）：54-70.[3]Wang Z，Li H N，Song G.Aeolian vibration control of power transmi-ssion line using stockbridge type dampers—A review[J].International journal of structural stability and dynamics，2021，21（1）：2130001.[4]郑一峰，钱盛域.黏滞阻尼器与钢阻尼器在桥梁横向震动控制中的应用[J]. 华南理工大学学报（自然科学版），2021，49（12）：89-100.[5]Wang L，Shi W，Zhou Y.Adaptive-passive tuned mass damper for structural aseismic protection including soil–structure interaction[J].Soil dynamics and earthquake engineering，2022，158（7）：107298.[6]程扬，许卫晓，杨伟松，等.分阶段屈服金属阻尼器研究综述[J].青岛理工大学学报，2022，43（3）：83-92.[7]孔金震，钱亚鹏，贺枫，等.大型液压阻尼器仿真建模及静动态性能试验研究[J].噪声与振动控制，2021，41（1）：82-88.[8]Wang W L，Yu D S，Huang Y，et al.A locomotive ’s dynamic response to in-service parameter variations of its hydraulic yaw damper[J].Nonlinear dynamics，2014，77（4）：1485-1502.[9]范家俊，吴刚，冯德成，等.新型消能减震阻尼器滞回性能试验研究及有限元分析[J].东南大学学报（自然科学版），2019，49（3）：413-419.[10]侯和涛，仇锦，刘晓芳，等.带U 形板钢阻尼器拟静力试验与有限元分析[J].工业建筑，2017，47（10）：175-179，134.图2 “U”形头组件模型图3 框架模型0.00300.000.001000.00500.001500.002000.00150.00450.00600.00（mm）（mm）YYXXZZ由于原油处理量增加，新工艺的要求也相应增加，因此卧式容器的规模增大，放置高度也不断增加，高位卧式容器基础设计非常常见。
磁流变减振器的外特性及非线性特性
磁流变减振器的外特性及非线性特性王靖岳;郭胜;王浩天【摘要】In order to study the motion state of the Magnetorheological (MR) damper, the influence of the cur-rent and the piston velocity on the external characteristics of the MR damper is investigated by using the test data of the MTS849 damper test bench .Considering the nonlinear characteristics of magnetorheological damping force , Using LabVIEW software to design the program diagram of the polynomial and the front panel , and the damping force of MR damper polynomial fitting simulation , accurate polynomial mathematical model is established , and in comparison with the use of MATLAB software to establish a polynomial model and the data of test bench test .The results show that when the speed is constant , the damping force increases with the increase of the control current . The damping force increases relatively slowly when the current is small , and the damping force increases rapidly when the current is larger .When the current is constant , the damping force increases with the increase of piston speed .The polynomial model fitted by LabVIEW software is more close to the experimental data curve , which shows that the polynomial mathematical model can well describe the hysteretic and nonlinear characteristics of the damping force of the MR damper .%为了更好地研究控制磁流变减振器的运动状态,运用MTS849减振器试验台测试的试验数据来探究电流和活塞运动速度对磁流变减振器外特性的影响.考虑到磁流变阻尼力非线性的特性,运用LabVIEW软件设计出了多项式的程序框图和前面板,并进行了磁流变减振器阻尼力的多项式拟合仿真,准确地建立了多项式数学模型,并与利用MATLAB软件建立的多项式模型和试验台测试的数据相比较.结果表明:当速度一定时,随着控制电流的增加,减振器阻尼力也随着增加,电流较小时阻尼力增加相对较慢,电流较大时阻尼力增加相对较快;当电流一定时,减振器阻尼力随着活塞速度的增加而增加.运用LabVIEW软件拟合的多项式模型更接近试验数据曲线,说明该多项式数学模型能很好地描述磁流变减振器阻尼力的滞回特性和非线性特性.【期刊名称】《科学技术与工程》【年(卷),期】2017(017)034【总页数】5页(P332-336)【关键词】磁流变阻尼器;LabVIEW;多项式模型;滞回特性;非线性【作者】王靖岳;郭胜;王浩天【作者单位】沈阳理工大学汽车与交通学院,沈阳 110159;沈阳理工大学汽车与交通学院,沈阳 110159;沈阳航空航天大学自动化学院,沈阳110136【正文语种】中文【中图分类】U461.4磁流变液(MRF)是一种低磁滞性、高磁导率的微小软磁性颗粒，与非导磁性液体混合组成的智能材料[1]。
振动控制优化质量布置
Optimal Mass Distribution of Multiple Tuned Mass DampersJingning Wu 1, student member and Genda Chen 2, memberDepartment of Civil Engineering, University of Missouri-Rolla, Rolla, MO 65409-0030Email: 1jingning@, 2gchen@IntroductionTuned Mass Dampers (TMD) have received wide applications in reducing the wind-induced vibration of buildings. For earthquake application, however, they are not as effective mainly because earthquakes generate the ground motions of a wide spectrum of frequency components. A single damper tuned to the fundamental frequency of a structure is unable to suppress the vibration of higher modes. These higher modes sometime significantly contribute to the total response of the structure. In fact, it was reported that the single damper could even amplify the higher mode responses due to coupling between the fundamental and the higher modes [1].Recognizing the above shortcomings, several investigators introduced the multiple mass dampers to improve the seismic performance [2-5]. In this paper, a distributed Multi-Stage Tuned Mass Dampers (MSTMD) scheme is proposed. It consists of several groups of small mass dampers. Each group is tuned to one mode of the structure and distributed uniformly along the building height. It is referred to as one-mode MSTMD herein. The distributed dampers in one group reserve the orthogonal condition between the vibration modes of the structure [6]. Several multi-stage dampers tuned to different frequencies of the structure can suppress the vibration of higher modes as well as the fundamental mode. The objective of this study is to determine the optimum mass distribution between various groups of mass dampers.MSTMD vs. single TMDTo illustrate the performance of MSTMD, the modal transfer functions of a structurecontrolled with MSTMD or TMD are compared. The equation of motion of the MSTMD- or TMD-controlled structure can be written as)]()([)()()()()(t X t X M t x E M E M t X K t X C t X M d s T d g 2d 1s s s s s s s &&&&&&&&&+−+−=++ΓΓΓ (1))]()([)()()(t X t x E M t X K t X C t X M s T g 2d d d d d d d &&&&&&&Γ+−=++ (2) in which M s , C s and K s are the mass, damping and stiffness matrices of the structure; M d ,C d and K d are the corresponding matrices of the MSTMD or TMD system; )(t xg && is the ground acceleration, X s (t ) is the structural displacement vector relative to the base, X d (t ) is the dampers’ displacement vector with respect to the structure, and E 1, E 2 and G are the location matrices.A six-story shear building structure is considered. Each story has the same floor mass of 4×104kg and the same interval stiffness of 4×107N/m. The frequencies of the 1st to 3rd modes of the structure are 7.624, 22.43 and 35.93rad/sec, respectively. A constant damping ratio of 3% is assumed for all modes of the structure. Shown in Fig.1 are the modal transfer functions of the structure controlled with TMD and MSTMD,respectively. The TMD and MSTMD are considered to have the same modal mass for the 1st vibration mode. The ratio of the total damper mass to the total structure mass is 3.3%for TMD and 6% for MSTMD. Two cases are considered for MSTMD. All the dampers are either tuned to the 1st mode only (MSTMD1) or tuned to both the 1st and the 2nd modes (MSTMD2). For the second case, the mass ratio between the oscillators tuned to the 1st and those to the 2nd modes is 3 to 2. The frequency and damping parameters of the MSTMD system are determined using the equations for a single TMD scheme [7,8].10-410-310-210-1100010203040Frequency (rad/sec)D i s p l a c e m e n tFig. 1 Modal transfer functions of the controlled structure It can be clearly seen that only when the dampers are tuned to higher modes, can the responses of the higher modes be reduced. The transfer functions of the structure controlled with MSTMD1 are almost the same as those with TMD except for the significant amplification of the higher-mode responses at the fundamental frequency in the latter case. The appreciable increase in response results from the coupling between the vibration modes of the structure due to the presence of a single mass damper. However, compared with the response magnitude of the 1st mode, the effect of the increase in higher mode response on the overall response is negligible for regularstructures. Therefore, the MSTMD1 control scheme is not as efficient as a single TMD in suppressing the peak response since it requires a significantly larger mass for a group of dampers (6% vs. 3.3%).Fig.1 also indicates that the single TMD is as effective as the MSTMD2 control scheme for low frequency disturbances such as wind loads. When the structure is subjected to high frequency excitations, however, the multiple tuning in the MSTMD2 scheme appeals considerably more effective. Optimal mass distribution among dampers tuned to different modesClosed-form solutionFor an N -story shear building structure without TMD or MSTMD, the absolute acceleration in frequency domain can be written as∑==N1i g i i i i x H X )()/()(ωγΦωωω&&&& (3)where H i , Φi , and γi are the transfer function, modal vector and participation factor of the i th mode, respectively. The transfer function can be further expressed intoj21j21H i i 2i i i i i βξββξβ+−+=)( (4)in which i i ωωβ/=, ωi and ξi are the frequency and damping ratio of the i th mode, and 1j −= is an imaginary unit of a complex number. The mean square acceleration at the k th floor can then be expressed into∑∫∑=∞==N 1i 0g i i l l i l ik N1l lk 2kd S H H X E ωωωωωωγγΦΦ)()/()/(][*&& (5) in which S g (ω) is the power spectrum of seismic input. In this study, the widely-used Kanai-Tajimi spectrum is employed2g 2g 22g 22g 2g 0g 4141S S )/()/()/()(ωωξωωωωξω+−+= (6) in which ωg and ξg are the spectral parameters and S 0 is related to the earthquake intensity. For this study, ξg is taken as 0.32.For the proposed MSTMD scheme, the multi-stage dampers tuned to one mode of the structure do not strongly interact with other modes. Therefore, the entire structure-MSTMD system can be approximated into a combination of many two-degree-of-freedom subsystems. Each subsystem consists of a single-degree-of-freedom (SDOF) representation to the structure and a lumped damper, representing the effect of one multi-stage dampers. To further simplify the derivation, every subsystem is approximated into an equivalent SDOF oscillator of frequency ωi and equivalent damping ratio ξei . Then the total responses of the structure can be obtained by the conventional modal superposition method from Eqs. (3) to (6) with ξi replaced by ξei . For each mode, the equivalent damping ratio can be approximately determined by [7]i i ei ξρξ8.04/+= (7)which is originally suggested for SDOF-TMD systems. Here, ρi is the damper-to-structure modal mass ratio of the i th mode. For MSTMD systems it is the ratio of the total mass from the i th multi -stage dampers to the total structural mass.The MSTMD2 control scheme is considered below for the detailed derivation of the optimal mass distribution. When the objective is to minimize the acceleration at the k th floor under a constrained total damper-to-structure mass ratio, the optimal mass distribution can be obtained by solving0X E 12k =∂∂ρ][&&, ρ1+ρ2=ρ (constant) . (8) However, the complete form of Eq.(8) is still very complex to evaluate. By dropping the cross terms due to the well-spaced natural frequencies of a regular building structure, Eq.(5) can be simplified into()()∑∑+==++−++++−+=N 1N i i2i 2g 4i 2i 0i 2i 2g 2i 2ik N 1i ei 2i 2g 4i 2i 0i 2i 2g 2i 2ik 2k 114214S 414214S 41X E ξαξααπωαξγΦξαξααπωαξγΦ)(/)(/][&& ∑∑+==+=N 1N i i ik N 1i ei ik 11C C ξξ// (9)in which g i i ωωα/= and N 1 is the number of modes considered. For the case under investigation, N 1 =2. By substituting Eq.(7) into Eq.(9), the equation of (9) becomes∑∑+==++=N 1N i i ik N 1i ii ik 2k 11C 804C X E ξξρ/).//(][&&. (10)Eq.(8) then leads to the following equation for the optimal mass ratio, ρ1,opt :()()22opt 1opt 1k 121opt 1opt 1k 2804C 804C ξρρρρξρρ././,,,,+−−=+ (11) For the example structure and a total damper-to-structure mass ratio ρ=0.06, the root-mean-square (RMS) accelerations at different floors were calculated according to Eq.(5) and its approximation, Eq.(10). Shown in Fig. 2 are the normalized RMS responses][/][,2un N 2N X E X E &&&&vs. mass ratio 1ρ for different ωg values. Here,][2NX E && and ][,2un N X E && are respectively the RMS absolute acceleration at the top floor of thecontrolled and uncontrolled structure. The minimum values on these curves correspond to the optimum values of ρ1, which is ρ1,opt in Eq.(11).When ωg is small, the damper mass is mainly distributed to the 1st mode. As ωg increases, the damper mass is distributed more to the 2nd mode. Despite the difference between the curves calculated by the two methods, the positions of their valleys are almost the same. It should also be noted that in the neighborhood of the valleys, the accelerations are insensitive to the mass distribution. Table 1 gives the optimal mass ratios, ρ1,opt , obtainedby using the two methods. From these results, it can be concluded that the simplified analytical method provides solutions with satisfactory accuracy while it significantly saves computational efforts.0.60.70.80.9100.010.020.030.040.050.06N o r m a l i z e d a c c e l e r a t i o nρ1 Fig. 2 12un N 2N X E X E ρ−][/][,&&&& curves for different ωg valuesWhen dampers in the MSTMD scheme are tuned to more than two modes of the structure, the optimal mass distribution between modes can be achieved in the similarway. However, in light of the relative magnitude of modal responses as shown in Fig.1 and the modal participation factors, tuning to more than three modes may not be efficient.Table 1 Optimal mass distribution for MSTMD2 schemeωg (rad/sec)15.0 22.4 29.2 35.9 1ρ– exact 1ρ – approx.0.052 0.034 0.035 0.038 Numerical solutionAlternatively, the optimal mass distribution of multi-stage dampers can be determined by searching all the valid mass ratios and choosing the one corresponding to the minimum responses. Compared with the approximate analytical solution based on Eqs.(10) and(11), numerical solutions are more accurate but require significant more computational effort. When the multi-stage dampers are tuned to three vibration modes of a structure, the optimal damper mass ratio between the 1st and the 2nd modes is determined first. Then with this ratio and the total damper-to-structure mass ratio fixed, the optimal mass ratio between all the dampers tuned to the 3rd mode and the structure are searched. This sequential procedure renders the sub-optimal mass distribution among three modes with sufficient accuracy.For the same example structure and ωg = 29.2rad/sec, the numerical method is used to search the optimal mass distribution among various modes. Presented in Fig.3 are the][/][,2un N 2N X E X E &&&& relation with 1ρ for the MSTMD2 system and with 3ρ for three-mode tuned dampers. The total damper-to-structure mass ratio is ρ=0.06.0.650.750.850.9500.010.020.030.040.050.06N o r m a l i z e d a c c e l e r a t i o n31or ρρFig. 3 Control effectiveness for two- and three-mode MSTMDIt can be observed from Fig.3 that, for the given total mass ratio, the optimal two-mode MSTMD (ρ1=0.03) leads to an additional 12% reduction in acceleration over the one-mode tuned dampers (ρ1=0 or 0.06) while the three-mode MSTMD (ρ3=0.01) onlysuppresses another 1% acceleration over the two-mode MSTMD (ρ=0.0). Therefore, the3three-mode MSTMD control scheme is not necessary for ωg= 29.2rad/sec. Based on the extensive numerical simulations, three-mode MSTMD is sufficient for the response control of regular structures even when ωg is greater.Concluding RemarksTo overcome the shortcomings associated with a single damper, a multi-mode MSTMD system has been proposed to simultaneously control the seismic responses of multiple modes of a structure. Such a system is much more robust than the conventional TMD. Itis unlikely that malfunction of one damper will notably degrade the performance of the MSTMD system. Simple equations are derived to determine the optimal mass distribution among several vibration modes and the RMS accelerations of structures under random loading. The results from these equations are in good agreement with those by numerical analyses. In general, two- or three-mode MSTMD scheme is sufficient to control the dynamic responses of a regular structure. Numerical results indicate that the multi-mode and multi-stage tuning can greatly improve the seismic performance of tuned mass dampers in suppressing the structural responses under high frequency disturbances. AcknowledgementsFinancial supports from the UM Research Board and the Intelligent Systems Center at UMR to complete this study are acknowledged.References1. Chowdhury, A. H., and Iwuchukwu, M. D. (1987). “The past and future of seismiceffectiveness of tuned mass dampers”, Proc. 2nd Int. Symposium Struct. Control (Leipholz, H. H. E. ed), Martinus Nijhoff Publishers,105-127.2. Clark, A. J. (1988). “Multiple passive tuned mass dampers for reducing earthquakeinduced building motion”, Proc. 9th World Conf. Earthquake Engrg., Tokyo-Kyoto, Japan, V, 779-784.3. Xu, K., and Igusa, T. (1994). “Vibration control using multiple tuned mass dampers”,J. Sound Vib. 175(4), 491-503.4. Kareem, A. and Kline, S. (1995). “Performance of multiple mass dampers underrandom loading”, J. Struct. Engrg., 121(2), 348-361.5. Chen, G. (1996). “Multi-stage tuned mass damper”, Proc. 11th World Conf.Earthquake Engrg., Acapulco, Mexico, Paper No. 1326.6. Chen, G. and Soong, T.T. (1996). “Exact solutions to a class of structure-equipmentsystems”, J. Engrg. Mech., ASCE, 122(11), 1093-1100.7. Luft, R. W. (1979). “Optimal tuned mass dampers for buildings”, J. Struct. Division,ASCE,105, ST12, 2766-2772.8. Warburton, G. B., and Ayorinde, E. Q. (1980). “Optimum absorber parameters forsimple systems”, Earthquake Engrg. Struct. Dyn., 8, 219-236.。
单摆式TMD简介及其减振性能分析
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图1
台北 101 大楼调谐质量阻尼器配置示意图 Schematic drawing of the Taipei 101 Tower’ s Tuned Mass Damper
Fig． 1
同济大学施卫星、 严峻等进行了一个单摆式 TMD 安装在风力发电塔上的减振试验［2］， 并得出
Structural Engineers Vol． 28 ， No． 6
（ 3）
以上在忽略主结构阻尼的情况下导出了单摆 式 TMD 最优参数的表达式。然而， 主结构的阻尼 忽略主结 往往具有显著的消耗振动能量的作用， 对于 构的阻尼显然具有明显的不合理性。 因此， 主结构阻尼 ζ p ≠ 0 的形式， 有阻尼系统最优参数 的解并不可以用无阻尼系统最优参数求解的方法 求出， 准确的数值解不具有无阻尼结构最优参数 的表达式的形式， 而只能根据式 （ 3 ） 用数值搜索 的方法找出最小峰值的反应。 对于确定 结 构 阻 尼 比 ζ p ， 找出最优的参数 γ ，f ，ζ s 是一种数值迭代的过程。 把振动响应 | u p | / H 看成是关于 g 的函数， 对于第一组特定 的 γ 和 f 的值， 代入不同的 ζ s 的值： （ ζ s1 ， ζ s2 ， ζ s3 ， …， ζ s4 ， ζ si ） 。 找出函数各自的最大值： | up | | u | | up | ， p … H max1 H max2 H
［3 ］
1
引
言
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2． 1
单摆式 TMD
单摆式 TMD 的工作原理
目前， 有关单摆式 TMD 装置减振性能的研究 还比较少， 应用也很有限， 其中最具代表性的是台 北 101 大楼。单摆式 TMD 主要由单摆和阻尼器 组成。其工作原理： 将单摆的自振频率调整接近 于主结构的控制频率， 当外力 （ 风力、 地震力 ） 作 用于主结构上使之产生振动时， 单摆产生与主结 构始终反向的摆动， 产生反向作用力作用于主结 从而控制结构的振动， 作用在主结构上的能 构上， 量通过单摆式 TMD 的阻尼器消散， 从而控制结构 。 对于外力作用的振动反应
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Radio telescope
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High-speed photo : spreading circular waves on water. 高速相片：在水面散開的圓形波。
Examples of fluid mechanics: 流體力學的範例： Flow speed vs river width Plane flight 流速對河寬 飛機飛行
Dancers from the Bandaloop Project perform on vertical surfaces, executing graceful slow-motion jumps. 帶個圈計劃的舞者在垂直的面上表演，執行幽雅的慢動作跳躍。 What determines the duration of these jumps? 甚麼東西决定這些跳躍的持續時間？
Determine the spring constant & the maximum speed & acceleration of the block. 找出彈簧系數，與水泥塊的最高速率和加速度。
电气工程高层建筑论文中英文资料外文翻译文献
电气工程高层建筑论文中英文资料外文翻
译文献
本文的主要目标是翻译一些电气工程和高层建筑方面的外文文献。
这些文献分别为：
1. "Application of lateral tuned mass damper to high-rise structure under random wind excitations"，这篇文章主要介绍了侧向调谐质量阻尼器（lateral tuned mass damper）在高层建筑中的应用。
该文通过计算分析和试验研究，得出了调谐阻尼器的结构参数和其对建筑物抗震能力的影响。
2. "Reliability Analysis of Power Supply System in High-rise Building"，这篇文章主要介绍了高层建筑电力供应系统的可靠性分析。
该文分别从电力系统的结构、功能和基本原理入手，阐述了电力系统的可靠性分析方法，并根据有关标准和规范，对高层建筑电力系统的可靠性进行了分析。
3. "Dynamic Analysis on Earthquake Resistance of High-rise Buildings Based on Pushover Method"，该文介绍了基于 Pushover 方
法对高层建筑的抗震性能进行动力学分析。
该方法通过对结构的位移、剪力和弯矩等特性进行预测，可以更加准确地评估高层建筑的抗震性能。
以上三篇文献分别介绍了高层建筑中的电气工程和抗震技术方面的研究成果，对于高层建筑的设计和建造具有一定的参考价值。
调谐质量阻尼器(TMD)在高层抗震中的应用
调谐质量阻尼器（TMD）在高层抗震中的应用摘要：随着经济的发展，高层建筑大量涌现，TMD系统被广泛应用。
越来越多的学者对TMD系统进行研究和改进。
本文介绍了TMD系统的基本工作原理，总结了其各种新形式，分析了它的研究现状，并指出了两个新的研究方向等。
关键词：TMD系统高层建筑抗震原理发展应用The use of the tuned mass damper in the seismic resistanceof the high-rise buildingAbstract：With the economic development, the high-rise buildings spring up, then, the tuned mass dampers are extensively used. More and more scholars research and improve the tuned mass damper. This thesis introduces the operating principle of the tuned mass damper，summarizes many new forms of the tuned mass damper, analyzes its research status and even points out two new research directions.Keyword: the tuned mass damper the high-rise building seismic resistance principle development use1.引言随着社会经济的快速发展，城市人口密度不断增长，城市建筑用地日益紧张，高层建筑成为城市化发展的必然趋势[1-3]。
高层及超高层建筑的不断涌现，加上建筑物的高度和高宽比的增加以及轻质高强材料的应用，导致结构刚度和阻尼不断下降。
基于TMD技术的高层建筑结构振动控制研究
基于TMD技术的高层建筑结构振动控制研究俞晓;林小国;胡伟利;张梅【摘要】传统的建筑结构抗震设计方法是利用结构本身物理特性来保证结构具有一定的强度、刚度和延性。
在强震地区或结构所受的动力荷载超过某种程度后，这种抗震手段很难达到预期的效果。
TMD技术是确保地震过程中建筑结构安全性的另一种有效方法之一。
本文根据振动控制理论，推导运动方程，建立仿真模型，设计TMD系统各参数。
最后，以25层建筑结构为实例，计算结果表明本文方法减震效果明显。
%Traditional anti-seismic method in the realm of building structures used to the physical characteristics of the structure itself to ensure that the structure has a certain strength, stiffness and ductility. This method is usually difficult to achieve the desired effect when the structure is exposed to the power loads or in the violent earthquake areas. TMD technology is another effective way to ensure the security of the building in the process of earthquake. In the paper, the system motion equations are derived and the simulation models are established, as well, the parameters of the TMD are obtained based to the theory of vibration control. Finally, the 25-story building is used as a example as well as the calculated results show that the anti-seismic effect is very effective.【期刊名称】《宁波工程学院学报》【年(卷),期】2012(024)003【总页数】3页(P66-68)【关键词】TMD;高层建筑;振动控制【作者】俞晓;林小国;胡伟利;张梅【作者单位】宁波工程学院,浙江宁波315016;宁波工程学院,浙江宁波315016;杭州市萧山区钱塘江灌区管理处,浙江杭州311200;江苏河海工程·建设监理有限公司,江苏南京201198【正文语种】中文【中图分类】TU311.3;TP273.1引言建筑结构被动控制技术之一的调谐质量阻尼器（Tuned Mass Damper，TMD），因其构造简单，易于安装，维护方便，经济实用且无需外部能量供给，对结构功能影响小等优点，并且采用调谐质量阻尼器（TMD）对建筑物进行抗震[1-3]是一种有效手段，已大量应用于实际工程领域。
某大跨度人行悬索桥舒适度分析
某大跨度人行悬索桥舒适度分析摘要：本文以某实际工程为例，采用德国EN03规范对某大跨度人行悬索桥进行舒适度分析。
针对该悬索桥，研究表明：侧向舒适度在中跨1/2处最差；竖向舒适度在中跨1/4处最差，边跨1/2处也较差。
但当在中跨1/2和中跨1/4处分别设置TMD后，可以起到良好的减振效果，提高行人行走的舒适性。
此外，该悬索桥由于敷设供热和供水管道，结构恒载变化，导致振动情况相对复杂，可为类似人行桥梁设计提供参考。
关键词：人行悬索桥；舒适度；振动控制；调谐质量阻尼器0 引言悬索桥由于结构轻型美观、构造简单、建筑高度小和跨越能力强等特点多用于人行桥。
但人行悬索桥多采用柔性悬索桥，其结构刚度小，阻尼低，自振频率小，往往不能满足结构基频的要求。
人行走的步频与人行桥基频相近时，容易引起人行桥的振动和人行走的不舒适性，通常采用频率控制法和限制动力响应法来控制人行桥振动。
我国现行《城市人行天桥与城市人行地道技术规范》（CJJ/69-1995）采用频率控制法，要求人行天桥结构竖向基频不得小于3Hz[1]。
但大跨度人行悬索桥结构基频一般较小，通常不能达到控制结构振动的目的，因而需要进行舒适度分析。
当舒适度较差时，可采用调谐质量阻尼器（TMD）进行振动控制，以提高人行桥舒适度。
对人行桥舒适度分析已有较多的研究，但桥梁结构恒载一般不变，结构基频固定。
本文人行悬索桥主梁采用钢桁架结构，上层行人通行，下层敷设热力和给水管道，是管道、人行共用桥梁。
由于供水、供热情况不同，会导致结构恒载变化，从而导致结构基频基频变化，结构振动情况相对复杂，本文因此对该大跨度悬索桥进行舒适度分析。
1 工程概况及动力特性分析1.1 工程概况本文工程背景为某一管道、人行共用钢桁架悬索桥，全桥长188.56m，主桥跨径布置为（34.28+120+34.28）m。
钢桁梁宽3.5m，高2.5m，采用Q345qD钢。
主缆线型采用二次抛物线，计算矢跨比1/7，矢高17.14m，主缆及吊索中心距均为2.5m，单根主缆采用1根Φ95mm Z型密闭钢丝绳。
大跨人行过街天桥利用调谐质量阻尼器的减振设计
大跨人行过街天桥利用调谐质量阻尼器的减振设计摘要：大跨人行过街天桥在行人激励下可能产生过大的竖向振动，从而引起行人的恐慌，并在一定程度上减小桥梁的使用寿命。
本文针对此问题开展研究，以一实际大跨人行过街天桥为例，采用有限元软件，对桥的动力反应进行分析，并提出了调谐质量阻尼器减振方案。
计算结构表明，采用调谐质量阻尼器后，天桥的动力反应能够得到有效降低。
关键词：人行天桥，动力反应，人行荷载，调谐质量阻尼器1. 引言随着城市高速发展和人居环境的不断改善，许多城市的主干道修建了人行过街天桥，以保证交通通畅和过往行人的安全。
这些人行天桥通常跨度比较大（超过40米），结构形式为单跨简支梁，自振频率为2~3 Hz。
而统计结果表明，人步行的频率大约为2Hz左右，因此，当人在天桥上行走时，容易出现共振现象。
这种振动会不仅会在桥梁内部产生损伤从而缩短天桥的使用寿命，而且，振动超过人体的舒适度标准后，还会引起行人的恐慌，影响天桥的正常使用[1-2]。
为避免共振，常规的设计方法是通过改变刚度等方法来调整天桥的自振频率，使其尽量远离行人的步行频率。
但是对于大跨天桥结构，较大幅度的调整其频率是不太经济的。
而结构振动控制方法为解决这个问题提供了一条有效途径[3]。
调频质量阻尼器（Tuned Mass Damper，简称TMD）是一种典型的减振控制装置，在建筑结构的抗震和抗风领域有着广泛的应用。
由于单个TMD的自振频率与结构的受控频率不一致时，TMD的控制效果将会大大降低，为了改善TMD 控制系统的有效性，许多学者对多重调谐质量阻尼器（Multiple Tuned Tuned Dampers，简称MTMD）的减振特性进行研究[4-5]。
本文以沈阳某大跨天桥为算例，对TMD减小人行天桥竖向振动的问题进行研究。
2. 调谐质量阻尼器简介调频质量阻尼器（Tuned Mass Damper，简称TMD）是一种经典的吸振装置，早期被用来减小机器所引起的振动，即人们常称的动力吸振器，70年代以后开始用于建筑结构的动力反应控制。
TLD_结构体系转化为TMD_结构体系的减振计算方法_柳国环
第28卷第5期 V ol.28 No.5 工 程 力 学 2011年 5 月 May 2011 ENGINEERING MECHANICS31———————————————收稿日期：2008-09-25；修改日期：2011-01-05基金项目：国家自然科学基金重点项目(50638010)；高等学校学科创新引智计划项目(B08014)；教育部创新团队项目(IRT0518) 作者简介：*柳国环(1980―)，男，天津人，博士，从事工程结构抗震、抗风研究(E-mail: carecivil@)；李宏男(1957―)，男，沈阳人，教授，博士，博导，院长，从事工程结构抗震、抗风、健康监测与诊断研究(E-mail: hnli@); 文章编号：1000-4750(2011)05-0031-04TLD-结构体系转化为TMD-结构体系的减振计算方法*柳国环，李宏男，国 巍(大连理工大学土木水利学院，辽宁，大连 116024)摘 要：提出了调谐液体阻尼器(Tuned Liquid Damper ，TLD)转化为调谐质量阻尼器(Tuned Mass Damper ，TMD)对结构减振控制的计算方法，采用该方法可方便地采用能够容易数值模拟的TMD 实现TLD 对结构的减振控制分析。
TLD-结构体系转化为TMD-结构体系的理论推导过程简洁、物理概念清晰，并通过实例分析了一幢250m 的高层建筑结构，进而说明该文方法的可行性与合理性，可便于结构工程师直接利用商业有限元程序对TLD-结构体系进行数值仿真。
关键词：TLD ；TMD ；减振控制；数值模拟；高层建筑 中图分类号：TU311.3 文献标识码：AAN EQUIVALENT CALCULATION METHOD FOR ANALYSIS OF STRUCTURAL VIBRATION CONTROL OF TRANSFORMINGTLD-STRUCTURE TO TMD -STRUCTURE SYSTEM*LIU Guo-huan , LI Hong-nan , GUO Wei(School of Civil & Hydraulic Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China)Abstract: An equivalent calculation method for structural vibration control of a transforming TLD-structure to TMD-structure system is presented and proposed due to the easy implementation of TMD by numerical simulation. The derivation process of the transformation is reasonable and has explicit physical meaning. The analysis of a high-rise building structure 250m in height shows that the proposed method is feasible, accurate and can be directly used in the numerical analysis of the TLD-structure system by adopting commercial finite element software.Key words: tuned liquid damper; tuned mass damper; vibration control; numerical simulation; high-risebuilding随着社会进步和经济发展，大跨、超高层和高耸结构日渐增多。
Turned Mass Damper
C := [p0 ( m 1 2k1k2 ) p0 c p0 k2
p0 c ]
u1, max u1, stat
4 1
2 2 2
4
2 2 2 2 2
2
2
2 2
2
1
m2 m1
0
0.10 0.32
u1, max u1, stat
1
All lines meet in the points S and T
S
T
u1 ( 0) u1 ( ) u1, stat u1, stat
→
2 2 1 2 2 2 2 2 2 1 1 1
S T
1 2 2 2 2
Optimal ratio of eigenfrequencies:
1 1
→ Optimal spring constant
k2
Minimize
u1, S u1,T
3 u1, stat 3 8 1
2
2 2
static deformation: eigenfrequencies: ratio of frequencies:
u1, stat
p0 k1
k1 m1
1
2
k2 m2
2 1
1
c2 2 m2 2
Damping ratio of Lehr: mass ratio:
solution:
u1 C1 cos t C2 sin t
调谐质块阻尼器
谢谢观看
工作原理
风对高层建筑的影响有多大？一般说，在正常的风压状态下，距地面高度为10米处，如风速为5米/秒，那么 在90米的高空，风速可达到15米/秒。若高达300-400米，风力将更加强大，即风速达到30米/秒以上时，摩天大 楼会产生晃动。纽约世贸中心在春季刮风时，通常摇晃偏离中心6-12英寸(15-30厘米)，在强飓风作用下，位移 可达3英尺(1英尺约等于30厘米)，设计按最大风力下的最大偏离为4英尺。
为了减少强风对建筑物的影响，防止高空强风及台风吹拂造成的摇晃，高层建筑通常会安装调谐质块阻尼器 （tuned mass damper，又称调质阻尼器）。调谐质块阻尼器通电后，一旦建筑物因强风产生的摇晃可以通过传 感器传至风阻尼器，此时风阻尼器的驱动装置会控制配重物的动作进而降低建筑物的摇晃程度。如果强风从北面 刮来，钢球就好比一个巨大的‘钟摆’摆向北面，使风阻尼器会产生一种与风向相反的‘力量’，从而‘消化’ 建筑物的摇晃程度 构造
03 起源
目录
02 目的 04 工作原理
调谐质块阻尼器(tuned mass damper)主要是安放在建筑物的较高层位置，是钟摆形式运作。Damper是一个 大约数百吨重的混凝土块，四边用弹簧连接，当有外力传于建筑物，建筑物的摆动会将能量传到damper，令 damper同时摆动。经过计算的damper会产生相反的摆动，这相反的摆动刚好与建筑物的摆动不同，所以可令建筑 物本身的摆动减少，不少摩天大楼都应用这系统建筑技术。
Den Hartog(Ormondroyd and Den Hartog，1928)最早研究了主系统中没有阻尼时的无阻尼和有阻尼动力 吸振器理论，他们提出了吸振器的基本原理及确定适当参数的过程。主系统的阻尼包含在Bishop和 Welboun(1952)提出的动力吸振器的分析中。紧接在上述工作之后，Falcon等(1967)设计了一个优化过程以获得 主系统的最小峰值响应和最大有效阻尼。