Simplified design procedure for frame buildings with viscoelastic or elastomeric structural dampers

A simplified design procedure (SDP) for preliminary seismic design of frame buildings with structural dampers is presented. The SDP uses elastic‐static analysis and is applicable to structural dampers made from viscoelastic (VE) or high‐damping elastomeric materials. The behaviour of typical VE materials and high‐damping elastomeric materials is often non‐linear, and the SDP idealizes these materials as linear VE materials. With this idealization, structures with VE or high‐damping elastomeric dampers can be designed and analysed using methods based on linear VE theory. As an example, a retrofit design for a typical non‐ductile reinforced concrete (RC) frame building using high‐damping elastomeric dampers is developed using the SDP. To validate the SDP, results from non‐linear dynamic time history analyses (NDTHA) are presented. Results from NDTHA demonstrate that the SDP estimates the seismic response with sufficient accuracy for design. It is shown that a non‐ductile RC frame building can be retrofit with high‐damping elastomeric dampers to remain essentially elastic under the design basis earthquake (DBE). Copyright © 2005 John Wiley & Sons, Ltd.     

Response prediction,experimental characterization and P‐spectra design of frames with viscoelastic–plastic dampers

Viscoelastic–plastic (VEP) dampers are hybrid passive damping devices that combine the advantages of viscoelastic and hysteretic damping. This paper first formulates a semi‐analytical procedure for predicting the peak response of nonlinear SDOF systems equipped with VEP dampers, which forms the basis for the generation of Performance Spectra that can then be used for direct performance assessment and optimization of VEP damped structures. This procedure is first verified against extensive nonlinear time‐history analyses based on a Kelvin viscoelastic model of the dampers, and then against a more advanced evolutionary model that is calibrated to characterization tests of VEP damper specimens built from commercially available viscoelastic damping devices, and an adjustable friction device. The results show that the proposed procedure is sufficiently accurate for predicting the response of VEP systems without iterative dynamic analysis for preliminary design purposes. A design method based on the Performance Spectra framework is then proposed for systems equipped with passive VEP dampers and is applied to enhance the seismic response of a six‐storey steel moment frame. The numerical simulation results on the damped structure confirm the use of the Performance Spectra as a convenient and accurate platform for the optimization of VEP systems, particularly during the initial design stage. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Investigated is the accuracy in estimating the response of asymmetric one‐storey systems with non‐linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non‐linear VE dampers are replaced by their energy‐equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non‐classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the ‘pseudo‐velocity’ of non‐linear VE dampers, the peak force of the non‐linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude‐ and frequency‐dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one‐storey systems with non‐linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non‐linear supplemental damping systems that satisfy given design criteria for a given design spectrum. Copyright © 2003 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.     

Optimal design of viscoelastic dampers using eigenvalue assignment

In this study a procedure for determining the optimum size and location of viscoelastic dampers is proposed using the eigenvalue assignment technique. Natural frequencies and modal damping ratios, required to realize a given target response, are determined first by the convex model. Then the desired dynamic structural properties are realized by optimally distributing the damping and stiffness coefficients of viscoelastic dampers using non‐linear programming based on the gradient of eigenvalues. This optimization method provides information on the optimal location as well as the magnitude of the damper parameters. The proposed procedure is applied to the retrofit of a 10‐story shear frame, and to a three‐dimensional structure with an asymmetric plan. The analysis results confirm that the responses of model structures retrofitted by the proposed method correspond well with the given target response. Copyright © 2003 John Wiley & Sons, Ltd.     

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     

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.     

Studies on seismic reduction of story‐incresed buildings with friction layer and energy‐dissipated devices

A new type of energy‐dissipated structural system for existing buildings with story‐increased frames is presented and investigated in this paper. In this system the sliding‐friction layer between the lowest increased floor of the outer frame structure and the roof of the original building is applied, and energy‐dissipated dampers are used for the connections between the columns of the outer frame and each floor of the original building. A shaking table test is performed on the model of the system and the simplified structural model of this system is given. The theory of the non‐classical damping approach is introduced to the calculation analyses and compared with test results. The results show that friction and energy‐dissipated devices are very effective in reducing the seismic response and dissipating the input energy of the model structure. Finally, the design scheme and dynamic time‐history analyses of an existing engineering project are investigated to illustrate the application and advantages of the given method. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic design and evaluation of steel moment‐resisting frames with compressed elastomer dampers

This paper evaluates the hysteretic behavior of an innovative compressed elastomer structural damper and its applicability to seismic‐resistant design of steel moment‐resisting frames (MRFs). The damper is constructed by precompressing a high‐damping elastomeric material into steel tubes. This innovative construction results in viscous‐like damping under small strains and friction‐like damping under large strains. A rate‐dependent hysteretic model for the compressed elastomer damper, formed from a parallel combination of a modified Bouc–Wen model and a non‐linear dashpot is presented. The model is calibrated using test data obtained under sinusoidal loading at different amplitudes and frequencies. This model is incorporated in the OpenSees [17] computer program for use in seismic response analyses of steel MRF buildings with compressed elastomer dampers. A simplified design procedure was used to design seven different systems of steel MRFs combined with compressed elastomer dampers in which the properties of the MRFs and dampers were varied. The combined systems are designed to achieve performance, which is similar to or better than the performance of conventional steel MRFs designed according to current seismic codes. Based on the results of nonlinear seismic response analyses, under both the design basis earthquake and the maximum considered earthquake, target properties for a new generation of compressed elastomer dampers are defined. Copyright © 2011 John Wiley & Sons, Ltd.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Earthquake response

Investigated are earthquake responses of one‐way symmetric‐plan, one‐storey systems with non‐linear fluid viscous dampers (FVDs) attached in series to a linear brace (i.e. Chevron or inverted V‐shape braces).Thus, the non‐linear damper is viscous when the brace is considered rigid or viscoelastic (VE) when the brace is flexible. The energy dissipation capacity of a non‐linear FVD is characterized by an amplitude‐dependent damping ratio for an energy‐equivalent linear FVD, which is determined assuming the damper undergoes harmonic motion. Although this formulation is shown to be advantageous for single‐degree‐of‐freedom (SDF) systems, it is difficult to extend its application to multi‐degree‐of‐freedom (MDF) systems for two reasons: (1) the assumption that dampers undergo harmonic motion in parameterizing the non‐linear damper is not valid for its earthquake‐induced motion of an MDF system; and (2) ensuring simultaneous convergence of all unknown amplitudes of dampers is difficult in an iterative solution of the non‐linear system. To date, these limitations have precluded the parametric study of the dynamics of MDF systems with non‐linear viscous or VE dampers. However, they are overcome in this investigation using concepts of modal analysis because the system is weakly non‐linear due to supplemental damping. It is found that structural response is only weakly affected by damper non‐linearity and is increased by a small amount due to bracing flexibility. Thus, the effectiveness of supplemental damping in reducing structural responses and its dependence on the planwise distribution of non‐linear VE dampers were found to be similar to that of linear FVDs documented elsewhere. As expected, non‐linear viscous and VE dampers achieve essentially the same reduction in response but with much smaller damper force compared to linear dampers. Finally, the findings in this investigation indicate that the earthquake response of the asymmetric systems with non‐linear viscous or VE dampers can be estimated with sufficient accuracy for design applications by analysing the same asymmetric systems with all non‐linear dampers replaced by energy‐equivalent linear viscous dampers. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

巨子型有控结构体系中黏滞阻尼器参数研究

巨子型有控结构体系(Mega-sub Controlled Structure System,即MSCSS)是一种新型的超高层建筑结构体系.本文针对MSCSS的构造特点,提出一种安装黏滞阻尼器的新的布置方案,通过研究该布置方案中取不同黏滞阻尼器参数时巨子型有控结构体系在罕遇地震作用下的动力响应,提出了与该结构体系动力特...     

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.     

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.     

Modeling of a large‐scale magneto‐rheological damper for seismic hazard mitigation. Part I: Passive mode

Magneto‐rheological (MR) dampers are a promising device for seismic hazard mitigation because their damping characteristics can be varied adaptively using an appropriate control law. During the last few decades researchers have investigated the behavior of MR dampers and semi‐active control laws associated with these types of dampers for earthquake hazard mitigation. A majority of this research has involved small‐scale MR dampers. To investigate the dynamic behavior of a large‐scale MR damper, characterization tests were conducted at the Lehigh Network for Earthquake Engineering Simulation equipment site on large‐scale MR dampers. A new MR damper model, called the Maxwell Nonlinear Slider (MNS) model, is developed based on the characterization tests and is reported in this paper. The MNS model can independently describe the pre‐yield and post‐yield behavior of an MR damper, which makes it easy to identify the model parameters. The MNS model utilizes Hershel–Bulkley visco‐plasticity to describe the post‐yield non‐Newtonian fluid behavior, that is, shear thinning and thickening behavior, of the MR fluid that occurs in the dampers. The predicted response of a large‐scale damper from the MNS model along with that from existing Bouc–Wen and hyperbolic tangent models, are compared with measured response from various experiments. The comparisons show that the MNS model achieves better accuracy than the existing models in predicting damper response under cyclic loading. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental study on multiple tuned mass dampers to reduce seismic responses of a three‐storey building structure

In this study, several mass dampers were designed and fabricated to suppress the seismic responses of a ¼‐scale three‐storey building structure. The dynamic properties of the dampers and structure were identified from free and forced vibration tests. The building structure with or without the dampers was, respectively, tested on a shake table under the white noise excitation, the scaled 1940 El Centro earthquake and the scaled 1952 Taft earthquake. The dampers were placed on the building floors using the sequential procedure developed by the authors in previous studies. Experimental results indicated that the multiple damper system is substantially superior to a single tuned mass damper in mitigating the floor accelerations even though the multiple dampers are sub‐optimal in terms of tuning frequency, damping and placement. These results validated the sequential procedure for placement of the multiple dampers. The structure was also analysed numerically based on the shake table excitation and the identified structure and damper parameters for all test cases. Numerical and experimental results are in good agreement, validating the dynamic properties identified. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimal placement of dampers for passive response control

The effectiveness of viscous and viscoelastic dampers for seismic response reduction of structures is quite well known in the earthquake engineering community. This paper deals with the optimal utilization of these dampers in a structure to achieve a desired performance under earthquake‐induced ground excitations. Frequency‐dependent and ‐independent viscous dampers and viscoelastic dampers have been considered as the devices of choice. To determine the optimal size and location of these dampers in the structure, a genetic algorithm is used. The desired performance is defined in terms of several different forms of performance functions. The use of the genetic approach is not limited to any particular form of performance function as long as it can be calculated numerically. For illustration, numerical examples for different building structures are presented showing the distribution and size of different dampers required to achieve a desired level of reduction in the response or a performance index. Copyright © 2002 John Wiley & Sons, Ltd.     

Viscoelastic coupling dampers (VCDs) for enhanced wind and seismic performance of high‐rise buildings

As high‐rise buildings are built taller and more slender, their dynamic behavior becomes an increasingly critical design consideration. Wind‐induced vibrations cause an increase in the lateral wind design loads, but more importantly, they can be perceived by building occupants, creating levels of discomfort ranging from minor annoyance to severe motion sickness. The current techniques to address wind vibration perception include stiffening the lateral load‐resisting system, adding mass to the building, reducing the number of stories, or incorporating a vibration absorber at the top of the building; each solution has significant economic consequences for builders. Significant distributed damage is also expected in tall buildings under severe seismic loading, as a result of the ductile seismic design philosophy that is widely used for such structures. In this paper, the viscoelastic coupling damper (VCD) that was developed at the University of Toronto to increase the level of inherent damping of tall coupled shear wall buildings to control wind‐induced and earthquake‐induced dynamic vibrations is introduced. Damping is provided by incorporating VCDs in lieu of coupling beams in common structural configurations and therefore does not occupy any valuable architectural space, while mitigating building tenant vibration perception problems and reducing both the wind and earthquake responses of the structure. This paper provides an overview of this newly proposed system, its development, and its performance benefits as well as the overall seismic and wind design philosophy that it encompasses. Two tall building case studies incorporating VCDs are presented to demonstrate how the system results in more efficient designs. In the examples that are presented, the focus is on the wind and moderate earthquake responses that often govern the design of such tall slender structures while reference is made to other studies where the response of the system under severe seismic loading conditions is examined in more detail and where results from tests conducted on the viscoelastic material and the VCDs in full‐scale are presented. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic response of linear and non‐linear asymmetric systems with non‐linear fluid viscous dampers

This investigation is concerned with the seismic response of one‐story, one‐way asymmetric linear and non‐linear systems with non‐linear fluid viscous dampers. The seismic responses are computed for a suite of 20 ground motions developed for the SAC studies and the median values examined. Reviewed first is the behaviour of single‐degree‐of‐freedom systems to harmonic and earthquake loading. The presented results for harmonic loading are used to explain a few peculiar trends—such as reduction in deformation and increase in damper force of short‐period systems with increasing damper non‐linearity—for earthquake loading. Subsequently, the seismic responses of linear and non‐linear asymmetric‐plan systems with non‐linear dampers are compared with those having equivalent linear dampers. The presented results are used to investigate the effects of damper non‐linearity and its influence on the effects of plan asymmetry. Finally, the design implications of the presented results are discussed. Copyright © 2005 John Wiley & Sons, Ltd.