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.     

Seismic performance evaluation of typical dampers designed by Chinese building code

Adding dampers is a commonly adopted seismic risk mitigation strategy for modern buildings, and the corresponding design procedure of dampers has been well established by the Chinese Building Code. Even though all types of dampers are designed by the same procedure, actual seismic performance of the building may differ from one to the others. In this study, a nine-story benchmark steel building is established, and three different and typical types of dampers are designed according to the Chinese Building Code to realize structural vibration control under strong earthquake excitation. The seismic response of the prototype building equipped with a viscoelastic damper, viscous damper and buckling-restrained brace(BRB) subjected to 10 earthquake records are calculated, and Incremental Dynamic Analysis(IDA) is performed to describe progressive damage of the structure under increasing earthquake intensity. In the perspective of fragility, it shows that the viscoelastic damper has the highest collapse margin ratio(CMR), and the viscous damper provides the best drift control. Both the BRB and viscoelastic dampers can effectively reduce the floor acceleration responses in the mid-rise building.     

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.     

Seismic response control of frame structures using magnetorheological/electrorheological dampers

Semi‐active control of buildings and structures for earthquake hazard mitigation represents a relatively new research area. Two optimal displacement control strategies for semi‐active control of seismic response of frame structures using magnetorheological (MR) dampers or electrorheological (ER) dampers are proposed in this study. The efficacy of these displacement control strategies is compared with the optimal force control strategy. The stiffness of brace system supporting the smart damper is also taken into consideration. An extensive parameter study is carried out to find the optimal parameters of MR or ER fluids, by which the maximum reduction of seismic response may be achieved, and to assess the effects of earthquake intensity and brace stiffness on damper performance. The work on example buildings showed that the installation of the smart dampers with proper parameters and proper control strategy could significantly reduce seismic responses of structures, and the performance of the smart damper is better than that of the common brace or the passive devices. The optimal parameters of the damper and the proper control strategy could be identified through a parameter study. Copyright © 2000 John Wiley & Sons, Ltd.     

Design of yielding metallic and friction dampers for optimal seismic performance

This paper deals with the optimal design of yielding metallic dampers and friction dampers together as they both have similar design characteristics and parameters. Ample tests and analytical studies have confirmed the effectiveness of these energy dissipation devices for seismic response control and protection of building structures. Since these devices are strongly non‐linear with several parameters controlling their behaviour, their current design procedures are usually cumbersome and not optimal. In this paper, a methodology is presented to determine the optimal design parameters for the devices installed at different locations in a building for a desired performance objective. For a yielding metallic damper, the design parameters of interest are the device yield level, device stiffness, and brace stiffness. For a friction device, the parameters are the slip load level and brace stiffness. Since the devices and the structures installed with these devices behave in a highly non‐linearly manner, and thus must be evaluated by a step‐by‐step time history approach, the genetic algorithm is used to obtain the globally optimal solution. This optimal search approach allows an unusual flexibility in the choice of performance objectives. For demonstration purposes, several sets of numerical examples of optimal damper designs with different performance objectives are presented. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimal seismic response control with dampers

The usefulness of energy dissipation devices to reduce seismic response of structures is now well established. For a given installation of such devices in a structure, one can easily compute the level of response reduction achieved. However, the solution of an inverse problem of how many devices one would need to achieve a desired level of response reduction in a structure, or to achieve an expected level of performance from a structural system, is not quite as straightforward and well formulated. In this paper, a method is presented to obtain the amount of viscous and visco‐elastic damping one would need to obtain a desired level of response reduction. The needed supplemental devices are also optimally distributed in the structure to achieve the best performance. To solve the optimal problem, a gradient‐based optimization approach is used. To illustrate the application, numerical results for a 24‐storey building structure are presented where the objective is to achieve the maximum reduction in the performance functions expressed in terms of the inter‐storey drifts, base shear, or floor accelerations. Other forms of performance functions can also be treated similarly. Copyright © 2001 John Wiley & Sons, Ltd.     

附加黏弹性阻尼与金属阻尼耗能的自复位墙结构抗震性能对比分析

相对传统结构,自复位墙结构在地震作用下具有更大的变形能力且几乎无残余位移,但其耗能能力较弱,需采用附加阻尼来增加整体耗能.目前,金属阻尼器已广泛用于自复位墙结构,其可显著减小结构大震下的地震响应,但小震下的位移和加速度减震效果不佳.因此,将小变形下即可耗能的黏弹性阻尼器应用于自复位墙结构中.设计一幢10层自复位墙结构,分别采用黏弹性阻尼器和 U 型金属阻尼器作为附加耗能构件,通过弹塑性时程分析对比采用两种耗能机制的结构地震响应.结果表明,黏弹性阻尼器可显著减小自复位墙结构在小震下的位移和加速度响应;U 型金属阻尼器在中震下开始耗能,在大震和巨震下,其减震效果会超越黏弹性阻尼器.因此,为进一步优化自复位墙结构在不同水准地震作用下的抗震性能,建议结合阻尼器的特点进行合理设计.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Limit states and failure mechanisms of viscous dampers and the implications for large earthquakes

Fluid viscous dampers are used to control story drifts and member forces in structures during earthquake events. These elements provide satisfactory performance at the design‐level or maximum considered earthquake. However, buildings using fluid viscous dampers have not been subjected to very large earthquakes with intensities greater than the design and maximum considered events. Furthermore, an extensive database of viscous damper performance during large seismic events does not exist. To address these issues, a comprehensive analytical and experimental investigation was conducted to determine the performance of damped structures subjected to large earthquakes. A critical component of this research was the development and verification of a detailed viscous damper mathematical model that incorporates limit states. The development of this model and the laboratory and simulation results conclude good correlation with the new model and the damper limit states and provide superior results compared with the typical damper model when considering near collapse evaluation of structures. Copyright © 2010 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.     

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.     

Effects of brace stiffness on performance of structures with supplemental Maxwell model‐based brace–damper systems

Shear‐type buildings with Maxwell model‐based brace–damper systems are studied in this paper with a primary emphasis on the effects of brace stiffness. A single‐story building with a viscous damper installed on top of a Chevron‐brace is first investigated. Closed‐form solutions are derived for the simple structure, relating the brace stiffness and damper coefficient to the targeted reduction in response displacement or acceleration. For a given brace stiffness, the solution is minimized to give a set of formulae that will allow the optimal damper coefficient to be determined, assuring the desired performance. The model is subsequently extended to multistory buildings with viscous dampers installed on top of Chevron‐braces. For a targeted reduction in the mean square of the interstory drift, floor acceleration or base shear force, the minimum brace stiffness and optimal damper coefficients are obtained through an iterative procedure. The response reduction, which signifies the improved performance, is achieved by a combination of brace stiffness and viscous damper coefficients, unlike conventional approaches where damper coefficients are typically optimized independent of brace stiffnesses. Characteristics of multi‐degree‐of‐freedom systems are studied using a 2‐story and a 10‐story buildings where the effects of brace stiffness on the overall performance of the building can be quantified. Copyright © 2010 John Wiley & Sons, Ltd.     

Simultaneous topology and sizing optimization of viscous dampers in seismic retrofitting of 3D irregular frame structures

A new methodology for performance‐based optimal seismic retrofitting using a limited number of size groups of viscous dampers is presented. The damping coefficient of each size group of dampers is taken as a continuous variable and is determined by the optimization algorithm. Furthermore, for each potential location, a damper of a single size group is optimally assigned, if any. Hence, the formulation presents a large step forward towards practical optimal design of dampers. The key for achieving an efficient optimization scheme is the incorporation of material interpolation techniques that were successfully applied in other structural optimization problems of discrete nature. This results in a very effective optimization methodology that is expected to be very efficient for large‐scale structures. The proposed approach is demonstrated on several example problems of 3D irregular frame structures. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliability of U‐shaped steel dampers used in base‐isolated structures subjected to biaxial excitation

A reliable performance of anti‐seismic devices when the upper‐structure is subjected to strong biaxial seismic excitation is of vital importance to ensure the latter doesn't reach critical behavior. U‐shaped steel dampers are hysteretic devices used to dissipate the earthquake‐induced energy of base‐isolated structures. In the framework of performance‐based design, which is gaining more and more recognition, it is of particular importance to assess the performance of base‐isolated structures with such dampers under different intensity levels of bidirectional ground motion. To achieve this goal, an analytical model able to simulate the bidirectional displacement response of an isolation system is adopted. Incremental dynamic analysis (IDA) is used to obtain the relation between the earthquake‐induced bidirectional damage of U‐shaped steel dampers and different intensity levels of the considered records. The performance of the dampers is categorized into 5 levels delimited by 4 limit states for which fragility curves are derived. The results obtained using the bidirectional approach are quantitatively compared to those given by employing an in‐plane model (widely used in current design practices in Japan) with the purpose of assessing whether the latter provides unconservative estimates of the performance of the dampers. The main conclusion is that, for large seismic intensities, the safety margin against fracture of the dampers is significantly overestimated when an in‐plane model is adopted. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal design of passive energy dissipation systems based on H∞ and H2 performances

Passive energy dissipation devices (EDDs), such as viscous dampers, viscoelastic dampers, etc., have been used to effectively reduce the dynamic response of civil infrastructures, such as buildings and bridges, subject to earthquakes and strong winds. The design of these passive energy dissipation devices (EDDs) involves the determination of the optimal locations and the corresponding capacities. In this paper, we present two optimal design methodologies for passive EDDs based on active control theories, including H_∞ and H₂ performances, respectively. The optimal design methodologies presented are capable of determining the optimal locations and the corresponding capacities of EDDs. Emphasis is placed on the application of linear matrix inequality (LMI) for the effective design of passive EDDs using the popular MATLAB toolboxes. One important advantage of the proposed approaches is that the computation of the structural response is not needed in the design process. The proposed optimal design methodologies have been applied to: (i) a 10‐storey building and a 24‐storey building both subject to earthquake excitations, and (ii) a 76‐storey wind‐excited benchmark building, to demonstrate the advantages of the proposed design methodologies over the conventional equal capacity design. Copyright © 2002 John Wiley & Sons, Ltd.     

Shaking table test of the effects of multi‐unit particle dampers attached to an MDOF system under earthquake excitation

This paper presents the results of an experimental and analytical/computational study of the performance of multi‐unit particle dampers with an MDOF system. A series of shaking table tests of a three‐storey steel frame with the particle damper system were carried out to evaluate the performance of the system and to verify the analysis method. An analytical solution based on the discrete element method is also presented. A comparison between the experimental and computational results shows that reasonably accurate estimates of the response of a primary system under earthquake excitations can be obtained. These results also indicate that the excitation characterization influences the performance of the particle damper system, for example, particle dampers have good performance in reducing the seismic response of structures and particle movements of plug flow pattern can yield good vibration attenuation effects. It is shown that by using properly designed multi‐unit particle dampers, a lightly damped primary system can achieve a reasonable reduction in its response, with a small weight penalty. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

粘弹性阻尼器连接的相邻结构非线性随机地震反应分析

本文用随机等价线性化方法探讨了相邻结构之间用粘弹性阻尼器连接后的非线性随机地震反应，分析发现：在小震作用下，粘弹性阻尼器对相邻结构可以同时达到较好的控制效果；但是在强烈地震作用下，安装粘弹性阻尼器有可能会在减少一个结构的地震反应的同时，增大另外一个结构的地震反应。     

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.