Numerical Modeling of Dynamic Behavior of Annular Tuned Liquid Dampers for Applications in Wind Towers

Abstract: In this study, the performance of annular liquid tanks as a tuned liquid damper (TLD) in mitigating the vibration of wind turbines was investigated using a numerical model. A proposed hybrid wind tower model composed of a concrete shaft and a steel mast with a height of 150 m was simulated using a single‐degree‐of‐freedom system. The structural domain including the tank wall and a rigid mass was modeled using finite element method, while the fluid domain was simulated by finite volume method using CFX software. A parametric study was carried out to investigate the behavior of annular TLD under harmonic loads for different mass and frequency ratios as well as displacement amplitudes. The damping characteristics of the annular TLD model were derived by comparing the numerical results with an equivalent linear model. In addition, the effectiveness of annular TLD was estimated by comparing the numerically calculated damping ratios with those corresponding to the optimum damping ratio values derived for a particular mass ratio based on the concept of tuned mass damper. It was found that that the annular TLD is effective when the amplitude of excitation is small. Moreover, the response of TLD in terms of nonlinear free surface sloshing and the energy dissipated by the system was discussed. Finally, the effectiveness of annular TLD in reducing the structural response of wind turbine towers under random vibrations was evaluated and discussed.     

Optimum design of tuned mass dampers for different earthquake ground motion parameters and models

Tuned mass dampers are frequently used for passive control of vibrations in civil structures subject to seismic and wind actions. Their efficiency depends on selection of their mechanical properties in relation to main system and excitation characteristics. This paper proposes an optimum design strategy of single tuned mass dampers to control vibrations of principal mode of structures excited by earthquake ground motion. The main purpose of the paper is to investigate the influence of the time modulation of earthquake excitation upon the optimal tuned mass dampers design parameters: frequency and damping ratio. The study is based on numerical analyses carried out with different stochastic models for earthquakes: a simple filtered white noise model and two time modulated filtered white noise models. The numerical analyses are carried out to solve an optimization problem with a performance index defined by the reduction of the standard deviation of either the structure displacement or its inertial acceleration as objective function. To complete the work, the influence of the bandwidth excitation over the values of the optimal tuned mass damper parameters is investigated, as well the optimum mass ratio and the structure frequency. The results of the numeral analyses carried out infer that the earthquake excitation characteristics, including its modulation in time domain, highly affect the optimum tuned mass damper design parameters values.     

Earthquake vibration control of structures using hybrid mass liquid damper

A tuned liquid damper (TLD) is a passive vibration control device consisting of a rigid tank filled with water that relies on the sloshing of water inside it to dissipate energy. In a standard TLD configuration the TLD is connected rigidly to the top of the building structure. Earlier research has shown that the TLD is more effective when its base acceleration amplitude is larger, as it dissipates more energy through increased sloshing. This characteristic has been utilized to design this alternate TLD configuration. In this alternate TLD configuration, the TLD is rigidly attached to a secondary mass that is attached to the primary structure through a spring system. This alternate configuration is, thus, defined as a hybrid mass liquid damper (HMLD). For particular values of the secondary spring’s flexibility, the motion of the secondary structure is in phase with that of the primary structure and the TLD base is subjected to a large amplitude acceleration that increases its effectiveness. It should be noted that when the secondary spring is rigid, the alternate and standard TLD configurations are identical for very small values of the secondary mass. It is seen that, for a given structure with HMLD there exists an optimum value of the secondary spring’s stiffness for which the HMLD effectiveness is maximum. An optimally designed HMLD configuration is shown to be more effective as a control device than the standard TLD configuration for both harmonic and broad-band earthquake motions.     

池式调谐质量阻尼器的动力分析

定义了池式调谐质量阻尼器(TMD),运用调谐液体阻尼器(TLD)与TMD相结合的方法综合考虑其总体动力效应;同时推导了结构与TMD、TLD以及池式TMD系统的运动方程.以结构物室内游泳池为例,研究了不同池长设计值的池式TMD在风振与地震激励下对结构的控制性能,对比了相应TMD、TLD的控制效果,并运用相位差分析的方法对池式TMD的设置提出了建议.结果表明:池式TMD经优化设计后可取得与普通TMD相近的控制效果,均远优于TLD;同时,池式TMD较普通TMD更经济且更具实用价值.     

Effect of dominant ground frequency and soil on multiple tuned mass dampers

Using the proposed model of earthquake ground motions, the parametric study is performed to examine the effects of the DGF and SC on the performance of the MTMD with identical stiffness and damping coefficient but unequal mass. Examination on the optimum parameters of the MTMD is conducted through minimization of the minimum values of the maximum displacement dynamic magnification factors of the structure with the MTMD. The optimum parameters of the MTMD include the optimum frequency spacing measuring the robustness, average damping ratio and tuning frequency ratio. Minimizing the minimum values of the maximum displacement dynamic magnification factors, non‐dimensionalized by the maximum displacement dynamic magnification factors of the structure without the MTMD, is used to measure the effectiveness of the MTMD. Likewise, an evaluation is made on the stroke displacement of the MTMD through assessing the maximum displacement dynamic magnification factors of each TMD in the MTMD. The results indicate that DGF and SC, in particular, the former, have significant effects on the optimum parameters, effectiveness and stroke displacement of the MTMD. Nonetheless, the MTMD may be used to reduce the seismic response of the structure with controlled natural frequency less than DGF. Copyright © 2009 John Wiley & Sons, Ltd.     

浅液矩形TLD对地震作用下高层振动的控制

在研究TLD减振耗能机理的基础上，分别分析了TLD的主要设计参数，即频率比、深度比及质量比对控制效果的影响，由此给出了对TLD进行有效设计的主要步骤，说明了只要对TLD各参数合理调整，就可以很好地控制结构在地震作用下的响应。     

基于振动台试验的滑移隔震-限位混凝土矩形贮液结构减震研究

混凝土矩形贮液结构由于其独特的优势,在土木工程领域具有广泛的应用,但是历次地震中都不乏该类结构的破坏案例,减小其在地震作用下的破坏概率迫在眉睫。为研究滑移隔震在混凝土矩形贮液结构减震方面的有效性,运用振动台缩尺试验对比研究了非隔震、铅芯橡胶隔震、滑移隔震-限位混凝土矩形贮液结构的动力响应,探讨滑移隔震对贮液结构的减震优势,研究限位装置对结构滑移位移的控制效果,并验证基于ALE法数值模型的合理性。结果表明,滑移隔震对结构动力响应和液体晃动波高都具有很好的控制效果,其减震效果明显优于铅芯橡胶隔震,进行合理的限位装置设计能够克服滑移隔震混凝土矩形贮液结构位移超限和震后残余位移较大的缺陷。滑移隔震-限位减震系统能够在震后保持完好,且造价低廉,因此其在混凝土矩形贮液结构减震方面具有非常优越的应用前景。     

改进遗传算法的结构调谐质量阻尼器风振控制的优化设计

为获得带调谐质量阻尼器(TMD)的建筑结构在随机风荷载作用下基于舒适度及动力可靠度的TMD装置的最优参数,在获得与舒适度相关的结构一阶模态加速度风振响应的解析解的基础上,根据随机过程极值理论,获得受控结构平均最大风振位移的解析解;然后,定义结构在设置TM,和不设置TMD的平均最大风振位移之比作为减振效果指标,并以之为优...     

Optimizing parameters of tuned mass damper subjected to critical earthquake

Tuned mass damper (TMD) has been proposed as one of the vibration control methods for rehabilitation of buildings. Because the parameters of TMD can significantly affect the seismic performance of structures, many researches focused on finding the optimum parameters. Because earthquakes are random phenomena and future earthquakes in comparison with past earthquakes may be more destructive, the optimum design of TMD subjected to selected earthquakes can be nonconservative. Hence, the main contribution of this paper is to present the optimal design of TMD for the seismic vibration control of a structure subjected to a critical earthquake that produces the most severe response of a structure. In order to achieve this purpose, the parameters of TMD are optimized through minimizing the maximum displacement of the roof. First, three optimization methods are used to obtain the optimal parameters of TMD for a 10‐story shear building subjected to the critical earthquakes. Finally, the responses of the controlled and uncontrolled buildings such as the roof displacement, strokes, transfer function, and different forms of energy are compared. Results show that the optimum designs of TMD not only effectively reduce the roof displacement but also improve the seismic performance of the building.     

Energy‐based predictive algorithm for semi‐active tuned mass dampers

There are various control strategies proposed and implemented for the protection of structures against different types of dynamic excitations. Currently, semi‐active control devices are very popular due to their adaptability and low power requirement. In this paper, a novel energy‐based predictive (EBP) algorithm is proposed, and its effectiveness is studied when applied to semi‐active tuned mass damper (SATMD). The mechanical energy of the primary structure is taken as the key parameter to be used by the algorithm to predict a suitable value of the manipulated variable, the damping of the tuned mass damper (TMD). The choice of the damping is made such that the damping used at a time interval leads to the least possible mechanical energy of the primary structure. The efficacy of the proposed control algorithm is studied by employing the EBP algorithm on single‐story and multistory structures equipped with the SATMD. The performance of the proposed algorithm when applied to the SATMD is also compared with that with the passive TMD for similar parameters. The results of the study show that the implementation of the EBP algorithm leads to significantly reduced dynamic response as compared with the passive TMD. Furthermore, numerical studies are conducted to gain insight into the effect of various parameters such as the mass ratio, the TMD damping ratio, and the flexibility of the structure.     

TLD减小钢桥塔涡激振动的原理及应用研究

讨论了TLD（Tuned Liquid Damper）的减振机理，并用解析形式给出了TLD对结构控制的减振力，求出了TLD与结构相互作用时结构的位移响应，推导了结构安装TLD后结构的等效阻尼比，给出了结构的减振效率，验证了TLD减振效果非常好，可以保证桥塔建设过程中的施工安全。     

Application of spherical tuned liquid damper in vibration control of wind turbine due to earthquake excitations

A spherical tuned liquid damper (TLD) is proposed as a cost‐effective method to reduce the earthquake‐induced vibration of wind turbines. A 1/20‐scale test model was designed to investigate its performance of controlling the structural vibration. A series of free and forced vibration experiments with different water depths in hemispherical containers were performed on the shaking table. Three measured ground acceleration‐time histories, including El Centro NS, El Centro EW and Tianjin EW, were selected to verify the effectiveness of spherical TLD in suppressing the earthquake‐induced vibration. The experimental results showed that the spherical TLD could effectively improve the damping capacity of the test model. The standard deviation of the dynamic response could be effectively reduced when the excitation frequency was approximately equal to its fundamental frequency. The liquid sloshing motion in containers was characterized by a highly nonlinear and complex nature. The effectiveness of spherical TLDs does not increase linearly as the mass of water in containers and is influenced greatly by the frequency components of earthquake excitations. For El Centro EW excitation, the standard deviations of the dynamic responses could be reduced more than 40% when the liquid mass was about 2% of the generalized mass. Copyright © 2015 John Wiley & Sons, Ltd.     

用TLD减小电视塔动力反应的振动台试验研究

本文介绍了用环形调频液体阻尼器（ＴＬＤ）减小电视塔动力反应的模型结构振动台试验研究。结果表明，ＴＬＤ能有效地减小第一振型的位移共振反应；在地震激励下，ＴＬＤ减小峰值反应的效果不十分显著；但地震停止后，ＴＬＤ使模型结构的自由振动迅速衰减。     

半主动电涡流单摆式调谐质量阻尼器减震性能研究

为了提高传统的调谐质量阻尼器（TMD）对建筑结构的减震效果,提出了一种可实时调整频率和阻尼的半主动电涡流单摆式调谐质量阻尼器(SAEC-PTMD)。由Hilbert-Huang变换(HHT)识别结构的瞬时频率,通过基于HHT的控制算法实时调节SAEC-PTMD的摆长进行频率的调节。研究并拟合了电涡流有效阻尼系数与磁导间距之间的关系,通过基于线性二次型高斯(LQG)的控制算法实时调节磁导间距,以实时调节阻尼系数。为了验证SAEC-PTMD对建筑结构的减震效果,对一单自由度结构模型在地震激励下的震动响应进行数值模拟。数值模拟中,采用一经优化设计的被动TMD (PTMD)作为对比,并考虑由主结构的累积损伤引起自身频率下降而造成PTMD的失调效应。以主结构的加速度和位移时程峰值、整体均方根值及其加速度和位移反应谱作为评价指标,评估了SAEC-PTMD在结构发生损伤前后对PTMD的改良效果。数值模拟结果表明,在结构发生损伤前后,SAEC-PTMD均比经优化设计的PTMD具有更好的减震效果。     

悬吊结构体系优化设计及减震性能研究

对悬吊摆隔震系统组成的悬吊结构体系进行研究,建立了该体系的两自由度分析模型。根据拉格朗日方程建立了系统的运动方程,并给出了地震作用下上下部子结构位移响应均方值理论表达式。通过引入性能指数,综合考虑上下部子结构位移响应,定义了悬吊结构体系性能目标函数。以性能目标函数最小为优化目标,推导了悬吊结构体系最优设计参数理论解,并通过不同性能指数下体系参数分析验证了理论解的正确性。最后,以某两层剪切型框架结构作为工程算例,对结构体系的减震性能进行数值分析。结果表明:最优参数均随性能指数的增大而增大,最优阻尼比与质量比呈正相关关系,最优频率比与质量比呈负相关关系; 增大性能指数,上部子结构位移响应峰值减震率增大,而下部子结构位移响应峰值减震率减小; 只要性能指数取值合理,悬吊隔震体系能同时有效控制上部子结构与下部子结构地震位移响应; 性能指数为1时,结构体系上下部子结构位移响应峰值减震率分别可达67.45%和25.16%以上。     

Structural vibration control using modified tuned liquid dampers

A tuned liquid damper (TLD) is a passive damper consisting of a solid tank filled with water that uses the water sloshing inside it to dissipate energy. The standard TLD configuration is where a TLD is connected rigidly to the top of the building. It has been popular as a control device for wind excitation. Earlier research has shown that the TLD behaviour is amplitude dependent, i.e. it is more effective when excitation amplitude is increased and more energy is dissipated due to sloshing. A modified TLD configuration is proposed here, where the TLD rests on an elevated platform that is connected to the top of the building through a rigid rod with a flexible rotational spring at its bottom. For particular values of the rotational spring flexibility, the rotational acceleration of the rod is in phase with the structure top acceleration and the TLD base is subjected to a large amplitude acceleration that increases its effectiveness. It should be noted that when the rotational spring is rigid, the modified and standard TLD configurations are identical. It is seen that, for aiven structure with modified TLD configuration, there exists an optimum value of the rotational spring stiffness for which the effectiveness of the modified TLD is maximum. Thus, it is seen that an optimally designed modified TLD configuration may be more effective as a structural control device than a standard TLD configuration, for both harmonic and broad-band earthquake motions.     

设置阻尼负刚度系统的高层隔震结构地震响应分析

基于预压弹簧的变形受力特点设计了一种附带阻尼的负刚度系统，该系统通过预压弹簧的斜向变形出力可实现负刚度性能，并采用黏滞阻尼器提供阻尼性能。根据上述思想设计组装了负刚度模型装置并进行静力试验研究，基于试验结果提出了考虑弹簧刚度、弹簧长度、弹簧预压缩量的负刚度系统的力学模型，并进一步建立了负刚度隔震系统的动力分析模型，提出了负刚度装置的最优参数选取方法，指出了最优负刚度配比的选取由隔震支座的阻尼比决定。将所提出的负刚度系统应用于某高层隔震结构中并进行了动力分析，结果表明，附加负刚度系统不仅能够减小高层建筑在地震作用下上部结构的加速度响应、层间变形，而且可有效控制隔震层的位移响应，实现了在罕遇地震作用下同时降低上部结构的加速度响应和隔震层位移响应的目标。     

TLCMD的工程设置方法

结构物的储水装置可被设计成调谐液柱/质量阻尼器(TLCMD);液体的动力效应会影响调频阻尼系统的控制效果。结合调谐液柱阻尼器(TLCD)与调谐质量阻尼器(TMD)共同作用的原理综合考虑了TLCMD的总体控制效果,并提出运用最优动力方法对TLCMD进行设置。算例分析表明:运用最优动力方法设置的TLCMD的控制效果明显优于普通方法,并为适应结构物内部使用空间要求提供了更为宽松的条件。     

Dual criterion equivalent linearization approach for yielding structures under earthquake excitation

In order to estimate both maximum displacement and maximum inertia force of bilinear hysteretic system subjected to earthquake motions, an equivalent linearization approach with new effective parameters is presented. Effective mass and effective damping ratio as pair of effective parameters instead of the effective period and effective damping ratio in existing equivalent linear systems are introduced. Two error measures for displacement and inertia force are defined. Error distributions over a two‐dimensional parameter space of effective parameters are analysed, and the parameters are determined through a statistical approach with a dual optimization criterion for displacement and inertia force errors applicable to structural design. Single‐degree‐of‐freedom systems with bilinear hysteretic model; natural periods from 0.1 to 3.0 s; linear damping ratios from 3 to 50%; ductility ratios from 1.5 to 6; and post‐yield slope ratios 0, 0.05, 0.1 are considered. Analytical expressions for the effective parameters, and the ratio of the maximum inertia force to the maximum restoring force as functions of response ductility, elastic damping ratio and natural period of inelastic system are proposed for different site conditions and post‐yield slope ratios. Evaluation of proposed equations is performed, which reveals that the linear parameters lead to permissible error ranges. Copyright © 2010 John Wiley & Sons, Ltd.     

高层建筑结构的风振阻尼控制分析与设计方法

本文首先分析了阻尼比对结构风振反应的控制效果,重点讨论了阻尼比对风振脉动增大系数的减小效果和具体计算方法,给出了便于工程实际应用的阻尼比为10%～30%的风振脉动增大系数随基本风压和结构基本周期变化的计算图表。结果表明,结构阻尼比增大,风振脉动增大系数明显减小。其次,分析了结构耗能减振系统的附加阻尼特性,给出了调频质量阻尼器(TMD)、调频液体阻尼器(TLD)和速度线性相关型耗能器附加给结构阻尼比的实用计算公式。最后给出了100层钢结构分别设置TMD和线性粘滞阻尼器的风振控制分析和设计实例。实例结果表明,两种被动阻尼控制系统对结构最大位移和最大加速度控制效果相同,可以达到40%～55%,同时说明了本文提出的方法可以方便地用于大型结构的风振阻尼控制分析和设计。