Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

结构附加粘滞阻尼器的抗震设计

本文结合抗震设计规范反应谱,给出了一个附加非线性流体粘滞阻尼器结构的抗震设计方法。研究了非线性阻尼器的力学特性,引入了非线性流体阻尼器的等效线性阻尼比,给出了计算最大加速度时刻附加非线性流体阻尼器结构反应的荷载组合系数,提出了按阻尼力的水平力分量与楼层剪力成正比的原则分配阻尼器阻尼系数的方法。同时给出了基于抗震规范设计反应谱附加非线性阻尼器结构的设计流程,通过一个算例说明了使用该方法设计附加非线性粘滞阻尼器结构的全过程。算例分析表明,这种设计方法适合于手算,便于设计人员掌握,在初步设计阶段可以快速、有效地设计满足给定性能水平的附加非线性流体阻尼器体系。     

Direct displacement-based design for seismic retrofit of existing buildings using nonlinear viscous dampers

This paper presents a direct displacement-based design procedure for seismic retrofit of existing buildings using nonlinear viscous dampers according to equivalent linear systems. Unlike conventional methods, the equivalent linear viscous damping provided by the nonlinear viscous dampers is derived based on the assumption that the average energy dissipated between the linear and the nonlinear viscous dampers is equal. Also, the equivalent period and viscous damping for the equivalent linear systems which are used for representing the behavior of bare frames (the buildings without dampers) are derived from the concept of average storage energy and average dissipated energy, respectively. It is shown from nonlinear time-history analyses that the nonlinear action of the retrofitted structures can be reasonably captured by the presented direct displacement-based procedure.     

非线性黏滞阻尼减震结构基于位移的设计方法

结合我国抗震设计规范,提出非线性黏滞阻尼减震结构基于位移的设计方法.根据减震结构的特点,将其性能划分为使用良好、人身安全和防止倒塌3个水平,并用层间位移角限值予以量化;以简化的方法计算非线性黏滞阻尼器的等效阻尼比.在此基础上将结构转化为等效单自由度体系,利用基于位移的设计方法对非线性黏滞阻尼减震结构进行设计,通过算例,介绍用该方法对框架结构进行非线性黏滞阻尼减震设计的设计过程.实例分析表明,提出的非线性黏滞阻尼减震结构基于位移的设计方法是可行的,并且与时程分析得出的平均结果吻合较好,而且该方法简单实用,便于操作,能够控制减震结构在不同强度水准地震作用下的性能.     

Design formulations for supplemental viscous dampers to highway bridges

Design formulas for supplemental viscous dampers to building structures are readily available in FEMA provisions and MCEER research reports. However, for the design of supplemental viscous dampers corresponding to a desired system damping ratio of highway bridges, there exist, if any, few design guidelines. This is particularly true if the bridge components such as elastomeric bearings, piers and abutment possess different damping ratios, stiffnesses, and lumped masses. In this paper, the design formulas for supplemental viscous dampers to highway bridges have been derived based on the concept of ‘composite damping ratio’. The design formulas can be used to determine the damping coefficients of the dampers corresponding to a desired system damping ratio of the bridge in which different component damping ratios may be assumed for the elastomeric bearings, piers and abutments. The proposed design formulas are numerically validated by comparing the seismic responses of a three‐span bridge equipped with viscous dampers with those of the same bridge without viscous dampers but with an assigned inherent system damping ratio equal to the target system damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

Appropriate viscous damping for nonlinear time‐history analysis of base‐isolated reinforced concrete buildings

There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.     

非线性粘滞阻尼器消能结构设计方法探讨

在建立非线形粘滞阻尼器消能结构性能曲线的基础上，建议了依据减震性能目标确定阻尼器参数的概略设计方法。提出了多自由度非线性粘滞阻尼器消能结构的等效阻尼比计算公式。在此基础上建议了适用于多自由度非线性粘滞阻尼器消能结构地震反应预测的模态叠加法，方法与时程分析结果对比吻合良好。为使各层阻尼器参数更好地满足减震性能要求，提出了将概略设计得到的层阻尼器参数依据减振性能目标进行调整的方法。     

台湾某钢框架大楼采用阻尼器补强结构减震效果评析

阻尼器是一种效果良好的减震装置,将阻尼器安装于结构中能够适时为结构体系提供阻尼力,从而减小地震作用对结构的破坏。黏滞阻尼器对振动的反应比较敏感,在结构受到较小振动时就可以发挥其减震效果,其阻尼力会随着振动周期和使用状态温度的不同而变化。当地震发生时,安装在结构中的阻尼器会消减地震作用,降低传导到主结构体系的地震能量,减小结构相对位移。本文介绍了黏滞阻尼器的工作原理和安装有黏滞阻尼器的结构体系的阻尼比的计算方法,对减震结构的减震效果的评析方法做出探讨,并以一安装有黏滞阻尼器的台湾某既有钢框架结构为例,分析了(1)该结构在遭受地震作用时的地震反应;(2)该结构体系在不同地震作用水平时的阻尼比,包括主体结构阻尼比和黏滞阻尼器阻尼比;(3)结构安装黏滞阻尼器后的减震效果。实例对本文的减震评析方法和减震效果进行了说明和分析,计算及分析结果表明利用黏滞阻尼器加固既有结构能够取得较好的减震效果,本文所提减震效果评析方法是一种实用有效的评析方法,对类似工程的减震评析具有一定的参考价值。     

Optimal design theories of tuned mass dampers with nonlinear viscous damping

Optimal design theory for linear tuned mass dampers(TMD) has been thoroughly investigated,but is still under development for nonlinear TMDs.In this paper,optimization procedures in the time domain are proposed for design of a TMD with nonlinear viscous damping.A dynamic analysis of a structure implemented with a nonlinear TMD is conducted fi rst.Optimum design parameters for the nonlinear TMD are searched using an optimization method to minimize the performance index.The feasibility of the proposed optimiza...     

Nonstationary stochastic response of structural systems equipped with nonlinear viscous dampers under seismic excitation

Nonlinear viscous dampers are supplemental devices widely used for enhancing the performance of structural systems exposed to seismic hazard. A rigorous evaluation of the effect of these damping devices on the seismic performance of a structural system should be based on a probabilistic approach and take into account the evolutionary characteristics of the earthquake input and of the corresponding system response. In this paper, an approximate analytical technique is proposed for studying the nonstationary stochastic response characteristics of hysteretic single degree of freedom systems equipped with viscous dampers subjected to a fully nonstationary random process representing the seismic input. In this regard, a stochastic averaging/linearization technique is utilized to cast the original nonlinear stochastic differential equation of motion into a simple first‐order nonlinear ordinary differential equation for the nonstationary system response variance. In comparison with standard linearization schemes, the herein proposed technique has the significant advantage that it allows to handle realistic seismic excitations with time‐varying frequency content. Further, it allows deriving a formula for determining the nonlinear system response evolutionary power spectrum. By this way, ‘moving resonance’ effects, related to both the evolutionary seismic excitation and the nonlinear system behavior, can be observed and quantified. Several applications involving various system and input properties are included. Furthermore, various response parameters of interest for the seismic performance assessment are considered as well. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed technique. Copyright © 2014 John Wiley & Sons, Ltd.     

Spectral and fragility evaluations of retrofitted structures through strength reduction and enhanced damping

A retrofit procedure for existing buildings called the "weakening and damping technique" (WED) is presented in this paper. Weakening of structures can limit the maximum response accelerations during severe ground motions, but leads to an increase in the displacements or inter-story drifts. Added damping by using viscous dampers, on the other hand, reduces the inter-story drifts and has no significant effect on total accelerations, when structures behave inelastically. The weakening and damping technique addresses the two main causes for both structural and nonstructural damage in structures. The weakening retrofit is particularly suitable for structures that have overstressed components and weak brittle components. In this paper, the advantages of the WeD are verified by nonlinear dynamic analysis and simplified spectral approach that has been modified to fit structures with additional damping devices. A hospital structure located in the San Femando Valley in California is selected as a case study. The results from both analyses show that the retrofit solution is feasible to reduce both structural acceleration and displacement. A sensitivity analysis is also carried out to evaluate the effectiveness of the retrofitting method using different combinations of performance thresholds in accelerations and displacements through fragility analysis.     

Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation

The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop ‘spurious’ damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the ‘spurious’ damping forces. This is the damping model recommended for nonlinear RHA. Replacing the stiffness‐proportional part of Rayleigh damping by the tangent stiffness matrix is shown to improve response results. However, this model is not recommended because it lacks a physical basis and has conceptual implications that are troubling: hysteresis in damping force–velocity relationship and negative damping at large displacements. Furthermore, the model conflicts with the constant‐damping model that has been the basis for fundamental concepts and accumulated experience about the inelastic response of structures. With a distributed plasticity model, the structural response is not sensitive to the damping model; even the Rayleigh damping model leads to acceptable results. This perspective on damping provides yet another reason to employ the superior distributed plasticity models in nonlinear RHA. OpenSees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Although this model leads to a full populated damping matrix, the additional computational demands are demonstrated to be minimal. Copyright © 2015 John Wiley & Sons, Ltd.     

考虑支撑变形时安装非线性粘滞消能器结构的抗震设计方法

通过理论分析和大量数值模拟,揭示了线性和非线性粘滞消能器两端的相对水平位移幅值与所在层的层间位移幅值之间的关系,总结提出了考虑支撑变形时安装非线性粘滞消能器结构的实用抗震设计步骤。上述研究结果拓展了现行《建筑抗震设计规范》中有关粘滞消能器部分的设计规定。     

设置黏滞阻尼器的钢结构实用减震设计方法

黏滞阻尼器作为一种有效的消能减震装置,已在钢结构建筑中得到了大量应用.然而由于钢结构的延性和阻尼特征,实用的钢结构附加黏滞阻尼器设计方法仍需深度探讨.文中提出一种基于黏滞阻尼器延性需求的减震设计方法.首先,根据钢结构需求量化层间位移角性能目标及目标附加阻尼比,计算黏滞阻尼器延性需求,并确定黏滞阻尼器布置数量、进行控制效...     

Understanding and predicting effects of supplemental viscous damping on seismic response of asymmetric one‐storey systems

Supplemental damping could mitigate the earthquake‐induced damage in buildings with asymmetric plan, known to be more vulnerable to damage than comparable symmetric‐plan buildings. This investigation aims to improve the understanding of how and why planwise distribution of fluid viscous dampers (FVDs) influences the response of linearly elastic, one‐storey, asymmetric‐plan systems. Starting with vibration mode shapes, we predict this influence on the modal damping ratios, and in turn on the individual modal responses and the total response. These predictions are confirmed by the computed responses, which demonstrated that the reduction in earthquake response of the system achieved by supplemental damping is strongly influenced by its planwise distribution, which is characterized by four parameters. Identified are asymmetric distributions of supplemental damping that are more effective in reducing the response compared to symmetric distribution. The percentage reduction achieved by a judiciously selected asymmetric distribution can be twice or even larger compared to symmetric distribution. Copyright © 2001 John Wiley & Sons, Ltd.     

基于楼层剪力的等效阻尼比计算方法研究

针对现有附加有效阻尼比计算方法存在的问题,本文从能量的角度揭示了阻尼比对结构影响的机理.从结构设计的角度,提出一种在时程分析下基于楼层剪力的消能减震结构等效阻尼比计算方法.对布置黏滞阻尼器和软钢阻尼器的消能减震模型,采用本文提出的等效阻尼比计算方法,建立等效结构进行结构响应对比.结果表明,由该计算方法得到的等效阻尼比能...     

Damping identification of a full‐scale passively controlled five‐story steel building structure

A series of large‐scale dynamic tests was conducted on a passively controlled five‐story steel building on the E‐Defense shaking table facility in Japan to accumulate knowledge of realistic seismic behavior of passively controlled structures. The specimen was tested by repeatedly inserting and replacing each of four damper types, that is, the buckling restrained braces, viscous dampers, oil dampers, and viscoelastic dampers. Finally, the bare steel moment frame was tested after removing all dampers. A variety of excitations was applied to the specimen, including white noise, various levels of seismic motion, and shaker excitation. System identification was implemented to extract dynamic properties of the specimen from the recorded floor acceleration data. Damping characteristics of the specimen were identified. In addition, simplified estimations of the supplemental damping ratios provided by added dampers were presented to provide insight into understanding the damping characteristics of the specimen. It is shown that damping ratios for the specimen equipped with velocity‐dependent dampers decreased obviously with the increasing order of modes, exhibiting frequency dependency. Damping ratios for the specimen equipped with oil and viscoelastic dampers remained constant regardless of vibration amplitudes, whereas those for the specimen equipped with viscous dampers increased obviously with an increase in vibration amplitudes because of the viscosity nonlinearity of the dampers. In very small‐amplitude vibrations, viscous and oil dampers provided much lower supplemental damping than the standard, whereas viscoelastic dampers could be very efficient. Copyright © 2012 John Wiley & Sons, Ltd.     

A seismic retrofit method by connecting viscous dampers for microelectronics factories

The implementation of viscous dampers to microelectronics factories has been previously proved not to affect the micro‐vibration of the factories in operation so that the vibration‐sensitive manufacturing process will not be interfered. Therefore, a seismic retrofit strategy which employs the viscous dampers installed in between the exterior and interior structures of the ‘fab’ structure is proposed in the study. The design formulas corresponding to the proposed retrofit method are derived using the non‐proportional damping theory. Based on the study, it is found that the added damping ratio to the fab structure depends greatly on the frequency ratio of the two structures in addition to the damping coefficients of the added dampers. Outside the bandwidth of the frequency ratio in which the added damping ratio is very sensitive to the variation of the frequency ratio, the added damping ratio can be well captured using the classical damping theory. Copyright © 2007 John Wiley & Sons, Ltd.     

附加或不附加粘滞阻尼墙的RC框架试验与分析

本文阐述了附加或不附加粘滞阻尼墙的2个相同的RC框架模型振动台试验和理论分析的情况.这2个钢筋混凝土框架模型为3层1跨两开间,几何相似关系大致为1：2.将阻尼墙附加到一个RC框架模型当中,先后对附加或不附加阻尼墙的2个相同的RC框架模型进行振动台试验.试验结果表明,阻尼墙有效减小了框架模型的地震反应.对耗能框架模型和普通框架模型进行了弹性和弹塑性时程分析,计算结果和试验结果吻合良好.改变阻尼墙的参数进行分析,结果表明选取合适的阻尼墙参数,才能达到最好的耗能减振效果;适当减小层间位移较小处的阻尼墙参数,对减振效果影响很小而又能节省投资.