Higher-mode effect on the seismic responses of buildings with viscoelastic dampers

In conventional modal analysis procedures, usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings. The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response, which is called the higher-mode effect. The modal analysis approach, however, may not be directly applied to the dynamic analysis of viscoelastically damped buildings. This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency. Therefore, the structural stiffness and damping contributed from those dampers would be different for each mode. In this study, the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes. Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect. Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response. Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings. The higher-mode effect on base shear is less significant than on story acceleration response. Maximum difference of the seismic response usually occurs at the top story. Also, the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers. For practical application, it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence, is on the conservative side. Supported by: Science Council, Chinese Taipei, grant no. 88-2625-2-002-006     

Inelastic torsion of multistorey buildings under earthquake excitations

The inelastic earthquake response of eccentric, multistorey, frame‐type, reinforced concrete buildings is investigated using three‐ and five‐storey models, subjected to a set of 10, two‐component, semi‐artificial motions, generated to match the design spectrum. Buildings designed according to the EC8 as well as the UBC‐97 code were included in the investigation. It is found that contrary to what the simplified one‐storey, typical, shear‐beam models predict, the so‐called ‘flexible’ side frames exhibit higher ductility demands than the ‘stiff’ side frames. The substantial differences in such demands between the two sides suggest a need for reassessment of the pertinent code provisions. This investigation constitutes one of the first attempts to study the problem of inelastic torsion by means of realistic, multistorey inelastic building models. Additional studies with similar or even more refined idealizations will certainly be required to arrive at definite results and recommendations for possible code revisions. Copyright © 2005 John Wiley & Sons, Ltd.     

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.     

Experimental study on the bidirectional inelastic deformation capacity of U‐shaped steel dampers for seismic isolated buildings

Hysteretic dampers are used to dissipate earthquake‐induced energy in base‐isolated structures by acquiring inelastic deformations, rendering their hysteretic behavior of vital importance. The present paper focuses on investigating the behavior of U‐shaped steel dampers under bidirectional loading; this is significantly different from their corresponding uniaxial behavior. Two main sets of loading tests on full‐scale specimens are conducted in this regard: (i) quasi‐static tests with simple histories and (ii) dynamic tests with realistic loading histories. Based on the results obtained in the quasi‐static tests, an interaction curve that accounts for the reduction of the cyclic deformation capacity is proposed. However, the fidelity of this relation must be assessed under loading conditions similar to those of a seismically isolated structure subjected to an earthquake, which represents the goal of the second set of tests. The results of the dynamic tests validate the proposed interaction curve for estimating the deformation capacity of U‐shaped steel dampers under bidirectional loading. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic performance of buildings retrofitted with nonlinear viscous dampers and adjacent reaction towers

An effective strategy of seismic retrofitting consists of installing nonlinear viscous dampers between the existing building, with insufficient lateral resistance, and some auxiliary towers, specially designed and erected as reaction structures. This allows improving the seismic performance of the existing building without any major alteration to its structural and nonstructural elements, which makes this approach particularly appealing for buildings with heritage value. In this paper, the nonlinear governing equations of the coupled lateral‐torsional seismic motion are derived from first principles for the general case of a multistory building connected at various locations in plan and in elevation to an arbitrary number of multistory towers. This formulation is then used to assess the performance of the proposed retrofitting strategy for a real case study, namely, a 5‐story student hall of residence in the city of Messina, Italy. The results of extensive time‐history analyses highlight the key design considerations associated with the stiffness of the reaction towers and the mechanical parameters of the nonlinear viscous dampers, confirming the validity of this approach.     

Experimental investigation of adjacent buildings connected by fluid damper

Dynamic characteristic and harmonic response of adjacent buildings connected by fluid damper were experimentally investigated using model buildings and fluid damper. Two building models were constructed as two three-storey shear buildings of different natural frequencies. Model fluid damper connecting the two buildings was designed as linear viscous damper of which damping coefficient could be adjusted. The two buildings without fluid dampers connected were first tested to obtain their individual dynamic characteristics and responses to harmonic excitation. The tests were then carried out to determine modal damping ratios of the adjacent buildings connected by the fluid damper of different damping coefficients and at different locations. Optimal damper damping coefficient and location for achieving the maximum modal damping ratio were thus found. The measured modal damping ratios and harmonic responses of the building-fluid damper system were finally compared with those from the individual buildings. The comparison showed that the fluid damper of proper parameter could significantly increase the modal damping ratio and tremendously reduce the dynamic response of both buildings. Copyright © 1999 John Wiley & Sons, Ltd.     

Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility

The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil.However,it is often customary to idealize the soil as rigid during the analysis of such structures.In this paper,seismic response time history analyses of base-isolated buildings modelled as linear single degree-of-freedom(SDOF) and multi degree-of-freedom(MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are conducted.The flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots.In the analysis,a large number of parametric studies for different earthquake excitations with three different peak ground acceleration(PGA) levels,different natural periods of the building models,and different shear wave velocities in the soil are considered.For the isolation system,laminated rubber bearings(LRBs) as well as high damping rubber bearings(HDRBs) are used.Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the following conclusions:(1) soil flexibility may considerably influence the stiff superstructure response and may only slightly influence the response of the flexible structures;(2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the system with LRBs;(3) although the peak response is affected by the incorporation of soil flexibility,it appears insensitive to the variation of shear wave velocity in the soil;(4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building,indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions,base isolations and shear wave velocities;(5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories,especially for earthquakes with low and moderate PGA levels;and(6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications,especially at the level of the lower stories.     

Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative

Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.     

Control of the earthquake and wind dynamic response of steel‐framed buildings by using additional braces and/or viscoelastic dampers

The insertion of steel braces equipped with viscoelastic dampers (VEDs) (‘dissipative braces’) is a very effective technique to improve the seismic or wind behaviour of framed buildings. The main purpose of this work is to compare the earthquake and wind dynamic response of steel‐framed buildings with VEDs and achieve optimal properties of dampers and supporting braces. To this end, a numerical investigation is carried out with reference to the steel K‐braced framed structure of a 15‐storey office building, which is designed according to the provisions of Eurocodes 1 and 3, and to four structures derived from the first one by the insertion of additional diagonal braces and/or VEDs. With regard to the VEDs, the following cases are examined: absence of dampers; insertion of dampers supported by the existing K‐braces in each of the structures with or without additional diagonal braces; insertion of dampers supported by additional diagonal braces. Dynamic analyses are carried out in the time domain using a step‐by‐step initial stress‐like iterative procedure. For this purpose, the frame members and the VEDs are idealized, respectively, by a bilinear model, which allows the simulation of the nonlinear behaviour under seismic loads, and a six‐element generalized model, which can be considered as an in‐parallel‐combination of two Maxwell models and one Kelvin model. Artificially generated accelerograms, whose response spectra match those adopted by Eurocode 8 for a medium subsoil class and for different levels of peak ground acceleration, are considered to simulate seismic loads. Along‐wind loads are considered assuming, at each storey, time histories of the wind velocity for a return period T_r=5 years, according to an equivalent spectrum technique. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control. To evaluate the performance of structures installed with viscoelastic dampers, different analytical models have been used to characterize their dynamic force deformation characteristics. The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well. However, accurate analytical procedures are needed to calculate the response of structures with such damper models. This paper presents a modal analysis approach, similar to that used for the analysis of linear systems, for solving the equations of motion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions. The uncoupled modal equations still have fractional derivatives, but can be solved by numerical or analytical procedures. Both numerical and analytical procedures are formulated. These procedures are then used to calculate the dynamic response of a multi-degree of freedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.     

Tuned mass dampers for response control of torsional buildings

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

双向地震波输入时振动方向对拱坝地震响应的影响

拱坝-地基三维地震响应分析中大多只分析入射地震波在拱坝-地基系统坐标系方向输入时的地震响应,而事实上,垂直入射的剪切波其振动方向是不确定的,地震波动的合理输入对拱坝-地基系统的地震响应分析起着决定性的作用.本文研究了拱坝-地基系统在双向地震波输入时不同振动方向对拱坝-地基系统地震响应的影响.计算结果表明:在双向地震波输入情形时,拱坝位移及应力响应最大值均不是发生在传统方法的横河向或者顺河向,而是与输入地震波相关,所以在研究拱坝-地基三维地震响应时有必要考虑入射地震波振动方向的影响.     

设置斜撑粘弹性阻尼器框架结构空间协同工作分析方法的控制研究

粘弹性阻尼器（ved）是抗震被动控制中一种十分有效的耗能减震装置。本文根据粘弹性阻尼材料的应力－应变关系，推导了粘弹性阻尼器和人字型支撑的组合层间单元刚度矩阵及单元控制力向量；并基于框架结构的空间特性，建立了设置斜撑Ved框架结构在考虑空间协同分析的基础上地震反应时程分析的控制方法；最后，应用本文的方法，对设置Ved斜支撑后钢筋混凝土框架结构进行了结构地震反应时程分析，并根据计算结果对其减震效果进行了分析讨论。     

双向地震作用下液化水平和倾斜场地-桩基-桥梁结构地震反应的差异研究

根据已经完成的液化侧向扩展场地-群桩基础-上部结构体系大型振动台试验,在有限元软件OpenSees中建立了可液化倾斜场地振动台试验的有限元模型。通过与试验结果对比,验证了数值模型的可靠性。基于此,建立了典型水平和倾斜液化场地-桩基-桥梁结构体系的数值模型,讨论了双向地震作用下水平和倾斜场地体系地震响应的差异,结果表明:相比水平场地,倾斜场地超孔隙水压力在峰值阶段波动幅度更大,土体的侧向位移增加明显,尤其是在饱和砂土中部位置;倾斜场地中桩基础的破坏程度更大,可液化层中部桩基曲率最大可增大约13倍,桩身水平位移显著增加;而水平场地桥墩曲率比倾斜场地桥墩曲率大,建议在液化场地桩基设计中应考虑场地倾斜带来的影响。      

MR阻尼器对桅杆结构风振响应的智能半主动控制

本文基于修正的拉格朗日坐标描述法，推导了空间四节点纤绳单元的大位移刚度矩阵的具体表达式。在将桅杆结构离散为空间四节点纤绳单元和梁单元的计算模型的基础上，建立了桅杆结构非线性风振响应分析的有限元方法。根据瞬时最优主动控制的原则，提出了MR阻尼器对桅杆结构风振反应智能半主动控制基于阻尼器位移的“开关—耗能”半主动控制策略。算例结果表明MR阻尼器能有效地减小桅杆结构的风振反应。     

两结构高效阻尼控制体系试验研究

本文通过模拟地震动振动台试验，研究了两个相邻结构模型的地震响应，结构模型采用一种高效阻尼装置(High Efficient Damper for Multi—Structure System即HEDMS)连接。非线性时程分析与振动台试验结果都证明了该阻尼装置能高效发挥软钢阻尼器的耗能能力，从而显著减轻两结构模型的地震响应。同时，研究还指出了进行阻尼装置设计时应该注意的一些问题。     

双向耦合地震作用下滑移隔震结构振动控制及其优化研究

目前,滑移隔震结构的分析通常只考虑水平地震动而不考虑竖向地震动的影响,有关多向地震动及其相关性的研究也很少。水平与竖向地面运动具有相关性,从而影响控制效果,因此对双向耦合地震作用下滑移隔震结构模型的理论进行研究,建立动力分析模型并得出运动微分方程。以6层滑移隔震结构为例,对其进行地震反应分析。研究表明,在考虑竖向地震作用的情况下,滑移隔震结构也具有良好的控制作用,但是竖向地震作用的存在使结构的地震反应有不同程度的增加,其增量随着竖向地震作用的增加而增加。因此,在高烈度地区的滑移隔震结构应该考虑竖向地震作用对结构的影响。建立滑移隔震装置的参数优化设计模型,采用IHGA程序对结构的重要参数进行优化设计。结果表明,滑移隔震结构在各种工况下的各项地震反应均得到更好的控制。     

Effects of structural walls on the elastic–plastic earthquake responses of frame–wall buildings

Effects of structural walls on the elastic–plastic earthquake response of short- to medium-height reinforced concrete buildings were investigated. The analytical model consists of independent lumped mass systems representing walls and frames connected at each floor. The wall structure undergoes flexural as well as shear deformation and fails in shear at relatively small story drifts, the frames deforming only in shear. As a measure of structural damage, the ductility factor responses of frame structures were calculated for different combinations of base shear coefficients for the frames and walls. In buildings with relatively weak frames, the installation of structural walls did not improve the large plastic response of the frames up to the point where the walls were unfailed in shear and the ductility factors of the frame structure were suddenly reduced to a very small number. For relatively strong frames, however, the response displacements decreased gradually as the number of walls increased, whether or not the walls failed. Empirical formulas for the required base shear coefficients of the walls and frames which gave a target ductility factor response also were derived for two particular groups of accelerograms. These equations should be of practical use in designing frame-wall type buildings and in retrofitting damaged buildings. Copyright © 1999 John Wiley & Sons, Ltd.     

Extended consecutive modal pushover procedure for estimating seismic responses of one-way asymmetric plan tall buildings considering soil-structure interaction

Performance based design becomes an effective method for estimating seismic demands of buildings. In asymmetric plan tall building the effects of higher modes and torsion are crucial. The consecutive modal pushover (CMP) procedure is one of the procedures that consider these effects. Also in previous studies the influence of soil-structure interaction (SSI) in pushover analysis is ignored. In this paper the CMP procedure is modified for one-way asymmetric plan mid and high-rise buildings considering SSI. The extended CMP (ECMP) procedure is proposed in order to overcome some limitations of the CMP procedure. In this regard, 10, 15 and 20 story buildings with asymmetric plan are studied considering SSI assuming three different soil conditions. Using nonlinear response history analysis under a set of bidirectional ground motion; the exact responses of these buildings are calculated. Then the ECMP procedure is evaluated by comparing the results of this procedure with nonlinear time history results as an exact solution as well as the modal pushover analysis procedure and FEMA 356 load patterns. The results demonstrate the accuracy of the ECMP procedure.     

Performance of base‐isolated reinforced concrete buildings under bidirectional seismic excitation considering pounding with retaining walls including friction effects

Seismic pounding of base‐isolated buildings has been mostly studied in the past assuming unidirectional excitation. Therefore, in this study, the effects of seismic pounding on the response of base‐isolated reinforced concrete buildings under bidirectional excitation are investigated. For this purpose, a three‐dimensional finite element model of a code‐compliant four‐story building is considered, where a newly developed contact element that accounts for friction and is capable of simulating pounding with retaining walls at the base, is used. Nonlinear behavior of the superstructure as well as the isolation system is considered. The performance of the building is evaluated separately for far‐fault non‐pulse‐like ground motions and near‐fault pulse‐like ground motions, which are weighted scaled to represent two levels of shaking viz. the design earthquake (DE) level and the risk‐targeted maximum considered earthquake (MCE_R) level. Nonlinear time‐history analyses are carried out considering lower bound as well as upper bound properties of isolators. The influence of separation distance between the building and the retaining walls at the base is also investigated. It is found that if pounding is avoided, the performance of the building is satisfactory in terms of limiting structural and nonstructural damage, under DE‐level motions and MCE_R‐level far‐fault motions, whereas unacceptably large demands are imposed by MCE_R‐level near‐fault motions. In the case of seismic pounding, MCE_R‐level near‐fault motions are found to be detrimental, where the effect of pounding is mostly concentrated at the first story. In addition, it is determined that considering unidirectional excitation instead of bidirectional excitation for MCE_R‐level near‐fault motions provides highly unconservative estimates of superstructure demands. Copyright © 2014 John Wiley & Sons, Ltd.