Dynamic analysis of space structures with multiple tuned mass dampers

Formulations of the reverberation matrix method (RMM) are presented for the dynamic analysis of space structures with multiple tuned mass dampers (MTMD). The theory of generalized inverse matrices is then employed to obtain the frequency response of structures with and without damping, enabling a uniform treatment at any frequency, including the resonant frequency. For transient responses, the Neumann series expansion technique as suggested in RMM is found to be confined to the prediction of accurate response at an early time. The artificial damping technique is employed here to evaluate the medium and long time response of structures. The free vibration, frequency response, and transient response of structures with MTMD are investigated by the proposed method through several examples. Numerical results indicate that the use of MTMD can effectively alter the distribution of natural frequencies as well as reduce the frequency/transient responses of the structure. The high accuracy, lower computational cost, and uniformity of formulation of RMM are highlighted.     

Coupled shear‐flexural model for dynamic analysis of fixed‐base tall buildings with tuned mass dampers

An equivalent discrete model is developed for time domain dynamic analysis of uniform high‐rise shear wall‐frame buildings with fixed base and carrying any number of tuned mass dampers (TMDs). The equivalent model consists of a flexural cantilever beam and a shear cantilever beam connected in parallel by a finite number of axially rigid members that allow the consideration of intermediate modes of lateral deformation. The proposed model was validated by a building whose lateral resisting system consists of a combination of shear walls and braced frames. The results showed the effectiveness of TMDs to reduce the peak displacements, interstory drift ratio, and accelerations when the building is subjected to a seismic load. The root mean square accelerations due to along‐wind loads also decrease if TMDs are attached to the building.     

Seismic response control of base‐isolated buildings using multiple tuned mass dampers

Seismic response of a base‐isolated building equipped with single tuned mass damper (STMD), multiple tuned mass dampers (MTMDs), and distributed multiple tuned mass dampers (d‐MTMDs) under real earthquake ground motions is investigated. Numerical study is carried out using analytical models of five‐, 10‐, and 15‐storey base‐isolated buildings equipped with the STMD, MTMDs, and d‐MTMDs. The buildings are modeled as shear‐type structure with a lateral degree of freedom at each floor level, and the buildings are isolated using the laminated rubber bearing, lead‐core rubber bearing, friction pendulum system, and resilient‐friction base isolator. The coupled differential equation of motion for the buildings are derived and solved in the incremental form using Newmark's step‐by‐step method of integration. From the numerical study conducted, it is concluded that installing a tuned mass damper at each floor level of a base‐isolated building reduces the structural response in terms of top floor acceleration and bearing displacement. It is found that installing the MTMDs and d‐MTMDs are significantly beneficial in reducing top floor acceleration as compared with the STMD. Further, almost comparable reduction in the bearing displacement could be obtained by installing the STMD, MTMDs at top, and d‐MTMDs in the base‐isolated buildings. The d‐MTMDs are more beneficial as compared with the STMD and MTMDs as otherwise huge controller mass can now be divided and distributed on different floor levels.     

Practical design issues of tuned mass dampers for torsionally coupled buildings under earthquake loadings

In this study, a new design procedure was developed for reducing the dynamic responses of torsionally coupled buildings, particularly existing buildings, under bilateral earthquake excitations, by incorporating the vibration control effectiveness of passive tuned mass dampers (PTMDs) . Some practical design issues such as the optimal location for installation, movement direction and numbers of PTMD are considered in this study. The optimal parameters of the PTMD system are determined by minimizing the mean square displacement response ratio of the controlled degree of freedom between the building with and without PTMDs. In addition, parametric studies of the PTMD planar position and the detuning effect are undertaken to determine their influence on the response control efficacy. The numerical results from two typical multistory torsionally coupled buildings under bidirectional ground accelerations, recorded at the 1979 El Centro earthquake, verify that the proposed optimal PTMDs are more effective and more robust in reducing the building responses. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic response control of asymmetric buildings using tuned mass dampers

The aim of the present study is to investigate the efficiency of the torsional tuned mass dampers (T‐TMDs) in response control of asymmetric buildings under bidirectional earthquake ground excitations. The efficiency of the T‐TMDs is compared with bidirectional tuned mass dampers (BTMDs). The T‐TMDs are oriented to the rotation of the structures about vertical axis with a single torsional mass attached to spring–dashpot elements, whereas the BTMD connects a single mass to two orthogonal sets of spring–dashpot elements oriented to principal axes of the building. The buildings are idealized three‐dimensional models with two translational and one torsional degrees of freedom for each floor. Three different configurations (cruciform‐shaped, L‐shaped, and T‐shaped) of multistory buildings are considered. The 5‐, 15‐, and 20‐story buildings with and without the tuned mass damper schemes are subjected to bidirectional earthquake ground excitation. In order to evaluate the effectiveness of the T‐TMDs and BTMD, the rotation, displacement, acceleration, and base shear force responses are computed. Parametric studies are conducted for all the configurations installed with the T‐TMDs and BTMD by varying their mass ratio, damping ratio, and ground motions. It is concluded that the T‐TMDs are more effective in mitigating the torsional response of asymmetric buildings as compared with the BTMD.     

地震作用下某高层结构MTMD减震控制研究

通过数值模拟研究了地震作用下高层结构多个调谐质量阻尼器(MTMD)减震控制。根据实际工程,利用国际通用软件ETABS建立了结构三维有限元模型,进行了动力特性的分析,得到了结构的前几阶频率;根据不同场地类型,选取了4条典型的地震波;研究了调谐质量阻尼器(TMD)的参数选取和有限元的模拟;运用时程分析方法,分别研究了不同地震作用下高层结构有无控制下的反应。研究结果表明,MTMD对高层结构的减震控制效果明显,场地类型对减震控制效果有一定的影响。所获得的结果为高层结构减震控制设计提供参考和依据。     

Suppression of bridge flutter using tuned mass dampers based on robust performance design

This study addresses design methodologies of TMDs for control of bridge flutter, considering the uncertainty of aerodynamic data in order to enhance the robustness of tuned mass dampers (TMDs) against frequency drift caused by wind-bridge interaction. To evaluate the robust performance of a TMD system, the concept of minimum flutter velocity is introduced in the presence of perturbed unsteady aerodynamic forces. Two types of multiple tuned mass dampers (MTMD) are considered, i.e. the frequencies of each TMD are regularly or irregularly spaced. An optimization procedure for an irregular MTMD (IMTMD), which has an unequal frequency interval and different damping ratio of each individual TMD, is proposed based on genetic algorithms. The proposed TMDs are then applied to a cable stayed bridge and a suspension bridge to prove the validity of the methods. From the numerical results, the proposed IMTMD shows remarkable control efficiency compared with conventional single TMD (STMD) and MTMD.     

Robust optimum design of tuned mass dampers for high‐rise buildings under moderate earthquakes

In the present study the optimum design of tuned‐mass‐damper (TMD) devices used for the vibration control of high‐rise buildings subject to moderate earthquakes is developed. For these structures a large acceleration demand can produce damage in equipment and contents: therefore, the performance of TMD will be based on the capacity of reducing this structural response. In order to maximize the performance and the efficiency of the TMD strategy, the ratio between the absolute accelerations of the protected and of the unprotected systems is assumed as objective function in the optimum design. The method is carried out in a stochastic way and a stationary‐filtered stochastic process is assumed to model the seismic action. Since the main disadvantage of using a single TMD is the mistuning related to errors in the evaluation of the natural frequency of the main structure, an uncertainty is introduced for this structural parameter, which is modelled as a random variable. Uncertainties in other structural mechanical properties and in TMD are neglected. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimum design of multiple positioned tuned mass dampers for structures constrained with axial force capacity

The stories of structure may have different and limited axial force capacity. In order to passively control the translational movement of structures, a tuned mass damper (TMD) positioned on a story may cause to exceed axial force capacity of a story. The optimum performance is achieved when all additional masses are positioned on the top story. Whereas, the top stories of structure may be constructed with lower axial force capacity than the lower stories. In that case, the maximum allowed TMD mass for upper stories may be low. In that situation, several TMDs may be positioned on several stories. In the current study, the optimum tuning of TMDs positioned on multiple stories of structure is investigated. By using small masses, it is also possible to obtain effective passive control with dampers that have small damping coefficients comparing with a single TMD on the top of the structure. The design variables of the optimization problem such as the period and damping ratio of TMD are tuned according to a metaheuristic algorithm called flower pollination algorithm. The TMD is optimized for near‐fault excitations by using impulsive motions during the optimization process. The proposal was applied to four case studies. According to the results, the multiple positioned TMDs may be a practical and effective option comparing with the use of a single heavy TMDs on the top of a structure.     

Designing optimal tuned mass dampers for nonlinear frames by distributed genetic algorithms

In this paper, the capabilities of tuned mass dampers (TMDs) for the mitigation of response of nonlinear frame structures subjected to earthquakes have been studied. To determine the optimal parameters of a TMD, including its mass, stiffness and damping, we developed an optimization algorithm based on the minimization of a performance index, defined as a function of the response of the nonlinear structure to be controlled. Distributed genetic algorithm has been used to solve the optimization problem. For illustration, the method has been applied to the design of a linear TMD for an eight‐story nonlinear shear building with bilinear hysteretic material behavior subjected to earthquake. The results have shown that the method has been successful in determining the TMD parameters to reduce the structure response. The simplicity and desirable convergence behavior of the method have also been two important results of the method. Two performance indices have been defined: (a) the minimization of the maximum drift and (b) the accumulated hysteretic energy. It has also been shown that the efficiency of the TMD has been influenced by the mass ratio of the TMD, the maximum TMD stroke length and the TMD design earthquake. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimum design of pendulum‐type tuned mass dampers

The equations of motion are derived for a translational single degree of freedom system equipped with a ‘pendulum‐type’ tuned mass damper (TMD) under dynamic force and base acceleration excitations. The complex frequency response functions are obtained. Following response minimization procedures, the optimum parameters of the TMD under random white noise excitations are determined. The effect of the TMD in reducing the response is expressed in terms of an equivalent viscous damping. The optimum design parameters and the corresponding efficiency of the TMD under both wind and earthquake dynamic loads are presented in design charts. The effect of the structure inherent and aerodynamic damping on the optimum parameters is studied and simplified charts to account for such effect are provided. Moreover, a design chart for the over‐optimum‐damped TMDs is presented. The translational‐type TMD is treated as a special case of the pendulum‐type. Copyright © 2005 John Wiley & Sons, Ltd.     

Coupled‐two‐beam discrete model for dynamic analysis of tall buildings with tuned mass dampers including soil–structure interaction

An equivalent coupled‐two‐beam discrete model is developed for time‐domain dynamic analysis of high‐rise buildings with flexible base and carrying any number of tuned mass dampers (TMDs). The equivalent model consists of a flexural cantilever beam and a shear cantilever beam connected in parallel by a finite number of axially rigid members that allows the consideration of intermediate modes of lateral deformation. The equivalent model is applied to a shear wall–frame building located in the Valley of Mexico, where the effects of soil–structure interaction (SSI) are important. The effects of SSI and TMDs on the dynamic properties of the shear wall–frame building are shown considering four types of soil (hard rock, dense soil, stiff soil, and soft soil) and two passive damping systems: a single TMD on its top (1‐TMD) and five uniformly distributed TMDs (5‐TMD). The results showed a great effectiveness of the TMDs to reduce the lateral seismic response and along‐wind response of the shear wall–frame building for all types of soils. Generally speaking, the dynamic response increases as the flexibility of the foundation increases.     

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.     

土木工程结构振动控制的最佳多重调谐质量阻尼器模型

刚度和阻尼系数保持常量但质量不同的频率线性分布的FD-MTMD能够提供更好的有效性和鲁棒性且最易制作。但是，FD-MTMD存在近零最优平均阻尼比。鉴此，本文提出了刚度和阻尼系数保持常量但质量线性分布的MD-MTMD新模型策略。数值结果表明，MD-MTMD不存在近零最优平均阻尼比，MD-MTMD和FD-MTMD能够近似地达到相同的鲁棒性和有效性。而且，总的来说，MD-MTMD的冲程小于FD-MTMD的冲程。因此。MD-MTMD是土木工程结构振动控制的最佳MTMD模型策略。     

Diagrid structural systems for tall buildings: characteristics and methodology for preliminary design

Diagrid structural systems are emerging as structurally efficient as well as architecturally significant assemblies for tall buildings. This paper presents a simple methodology for determining preliminary member sizes. The methodology is applied to a set of building heights ranging from 20 to 60 stories, and parameters for the optimal values of the grid geometry are generated for representative design loadings. These values are shown to be useful for architects and engineers as guidelines for preliminary design. Associated architectural and constructability issues of diagrid structures are also discussed here. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of hysteretic damping on the seismic performance of tuned mass dampers

A tuned mass damper (TMD) as a convenient passive device in average to tall buildings has limitations specifically against broad band seismic excitations. According to evidences from the literature, this drawback can be dominated by using nonlinear stiffness in TMDs; however, past studies did not explore this issue, and observations are not sufficient to reach a conclusion about seismic performance of nonlinear TMDs. This paper considers seismic performance of a nonlinear TMD developed by adding a martensitic shape memory alloy spring with significant stable features to conventional TMDs. To this end, single degree of freedom structures (from short to large periods) equipped with the nonlinear TMD are investigated subjected to set of ground motions, and through numerical analyses, effects of hysteretic damping and energy absorption capacity of the nonlinear TMD are examined. In addition, features of the proposed TMD configuration and effects of the excitation properties have been scrutinized through graphing frequency response curves by the arc length continuation method. Results indicate that the proposed configuration can make the nonlinear TMD robust against variations of the loading properties. Moreover, due to significant hysteretic damping of the shape memory alloy, spring seismic performance of the nonlinear TMD is better than conventional TMDs.     

结构被动和主动多重调谐质量阻尼器控制策略的发展

广泛评述了被动多重调谐质量阻尼器(MTMD)的研究现状，提出了结构主动多重调谐质量阻尼器(AMTMD)和多重主被动调谐质量阻尼器(MAPTMD)的新控制策略，介绍了从AMTMD和MAPTMD的研究进展，并指出了进一步研究的发展方向。     

Integrated damping systems for tall buildings: tuned mass damper/double skin facade damping interaction system

As today's tall buildings become ever taller and more slender, wind‐induced vibration is a serious design issue. This paper presents integrated damping systems for tall buildings. An emphasis is placed on investigating the potential of double skin facades (DSF) as an integrated damping system for tall buildings. In the first scheme, the connectors between the inner and outer skins of the DSF system are designed to have low axial stiffness with a damping mechanism. Through this design, vibration of the primary building structure can be substantially reduced. However, excessive movements of the DSF outer skin masses are a design limitation. In the second scheme, the tuned mass damper (TMD) and DSF damping (DSFD) interaction system is studied to mitigate the design limitation of the first scheme and to resolve other TMD‐related design issues. TMDs are usually very large and located near the top of tall buildings for their effective performance. As a result, very valuable occupiable space near the top of tall buildings is sacrificed to contain large TMDs. In addition, installing TMD systems means adding additional masses to tall buildings. Through the TMD/DSFD interaction system, these issues can also be substantially addressed. Compared with the conventional TMD system, the TMD/DSFD interaction system requires a significantly reduced TMD mass ratio to achieve the same target damping ratio. Compared with the first scheme only with the DSFD mechanism, movements of the DSF outer skins can be better controlled in the TMD/DSFD interaction system. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Seismic analysis for tall and irregular temple buildings: A case study of strong nonlinear viscoelastic dampers

Viscoelastic (VE) dampers, composed of VE layers sandwiched between relative rigid steel plates, have been widely used as dissipation devices to improve performance of structures under dynamic loads. Corresponding analytical and experimental investigations have been carried out by many scholars. However, most of VE dampers studied before are typically traditional dampers applied in regular structures. This paper introduces a new type of VE damper with strong nonlinearity used in the complex and irregular structure of Nanjing Dabaoen Temple. The new VE dampers show obvious nonlinear behavior, improved capacity of dissipation, and larger additional stiffness compared to the traditional ones. Nanjing Dabaoen Temple is a high‐rise steel structure by use of 112 new VE dampers. To investigate dissipation characteristics and control effect of the VE dampers in the complex structure, we established a suitable finite element model using SAP2000 software in which the VE dampers were simulated by Maxwell and Wen models connected in parallel, and then nonlinear time history analysis is executed using seven ground motions of moderate earthquakes and three of major earthquakes. Analytical results indicate that control effect of the VE dampers on structural displacement is preferable to that on structural acceleration and shear force due to dampers' additional stiffness. In addition, owing to incremental deformation of VE dampers under major earthquakes, damping effect of the VE dampers on all structural responses under major earthquakes is more obvious than that under moderate earthquakes. Analytical methods and conclusions in this paper will provide significant reference for analysis, design, and application of complex high‐rise structures added with VE dampers.