Re‐shaping hysteretic behaviour—spectral analysis and design equations for semi‐active structures

Semi‐active dampers offer significant capability to reduce dynamic wind and seismic structural response. A novel resetable device with independent valve control laws that enables semi‐active re‐shaping of the overall structural hysteretic behaviour has been recently developed, and a one‐fifth scale prototype experimentally validated. This research statistically analyses three methods of re‐shaping structural hysteretic dynamics in a performance‐based seismic design context. Displacement, structural force, and total base‐shear response reduction factor spectra are obtained for suites of ground motions from the SAC project. Results indicate that the reduction factors are suite invariant. Resisting all motion adds damping in all four quadrants and showed 40–60% reductions in the structural force and displacement at the cost of a 20–60% increase in total base‐shear. Resisting only motion away from equilibrium adds damping in quadrants 1 and 3, and provides reductions of 20–40%, with a 20–50% increase in total base‐shear. However, only resisting motion towards equilibrium adds damping in quadrants 2 and 4 only, for which the structural responses and total base‐shear are reduced 20–40%. The spectral analysis results are used to create empirical reduction factor equations suitable for use in performance based design methods, creating an avenue for designing these devices into structural applications. Overall, the reductions in both response and base‐shear indicate the potential appeal of this semi‐active hysteresis sculpting approach for seismic retrofit applications—largely due to the reduction of the structural force and overturning demands on the foundation system. Copyright © 2006 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.     

Hybrid seismic protection of cable‐stayed bridges

This paper proposes a hybrid control strategy combining passive and semi‐active control systems for seismic protection of cable‐stayed bridges. The efficacy of this control strategy is verified by examining the ASCE first‐generation benchmark problem for a seismically excited cable‐stayed bridge, which employs a three‐dimensional linearized evaluation bridge model as a testbed structure. Herein, conventional lead–rubber bearings are introduced as base isolation devices, and semi‐active dampers (e.g., variable orifice damper, controllable fluid damper, etc.) are considered as supplemental damping devices. For the semi‐active dampers, a clipped‐optimal control algorithm, shown to perform well in previous studies involving controllable dampers, is considered. Because the semi‐active damper is a controllable energy‐dissipation device that cannot add mechanical energy to the structural system, the proposed hybrid control strategy is fail‐safe in that the bounded‐input, bounded‐output stability of the controlled structure is guaranteed. Numerical simulation results show that the performance of the proposed hybrid control strategy is quite effective in protecting seismically excited cable‐stayed bridges. Copyright © 2004 John Wiley & Sons, Ltd.     

Predictive control of seismic structures with semi‐active friction dampers

In this paper a predictive control method especially suitable for the control of semi‐active friction dampers is proposed. By keeping the adjustable slip force of a semi‐active friction damper slightly lower than the critical friction force, the method allows the damper to remain in its slip state throughout an earthquake of arbitrary intensity, so the energy dissipation capacity of the damper can be improved. The proposed method is formulated in a discrete‐time domain and cast in the form of direct output feedback for easy control implementation. The control algorithm is able to produce a continuous and smooth slip force for a friction damper and thus avoid exerting the high‐frequency structural response that usually exists in structures with conventional friction dampers. Using a numerical study, the control performance of a multiple degrees of freedom (DOF) structural system equipped with passive friction dampers and semi‐active dampers controlled by the proposed method are compared. The numerical case shows that by merely using a single semi‐active friction damper and a few sensors, the proposed method is able to achieve better acceleration reduction than the case using multiple passive dampers. Copyright © 2004 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.     

Semi‐explicit rate‐dependent modeling of damage‐avoidance steel connections using HF2V damping devices

A rate‐dependent modeling technique is developed for moment resisting steel connections that utilize non‐linear viscous dampers. First, a model of the Maxwell‐type is developed that considers the non‐linear viscous damper and connection flexibility for translational motion. This model is compared with experimental results at several input motion frequencies to validate the results. The model is then extended to represent an exterior steel beam‐to‐column connection using damage‐avoidance design and non‐linear viscous dampers. By including terms to represent structural member and connection flexibility, using appropriate geometric transformations the model can be formulated to give the overall lateral load‐drift structural performance. Validation analysis shows good agreement between experimental observations and the model predictions. 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.     

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.     

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.     

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.     

磁流变耗能器及其性能

磁流变换（ＭＲ）是一种智能材料,它能够在强磁场的作用下从牛顿流体变化为粘塑流体,用磁流变液制作的耗能装置简单,体积小,能耗小,可连续可逆变化,是实现半主动控制的理想控制元件,本文介绍了磁流变液的材料特征,建立了磁流变耗能器的恢复力简化模型,根据磁流变液耗器的特点,提出了制作磁流变耗器时参数设计的基本要求;最后,利用等效线性化方法,提出了磁流变耗能器总阻尼系数的计算方法,并且比较了其中的粘性阻尼系数     

Semi‐active control of sliding isolated bridges using MR dampers: an experimental and numerical study

Sliding base‐isolation systems used in bridges reduce pier drifts, but at the expense of increased bearing displacements under near‐source pulse‐type earthquakes. It is common practice to incorporate supplemental passive non‐linear dampers into the isolation system to counter increased bearing displacements. Non‐linear passive dampers can certainly reduce bearing displacements, but only with increased isolation level forces and pier drifts. The semi‐active controllable non‐linear dampers, which can vary damping in real time, can reduce bearing displacements without further increase in forces and pier drifts; and hence deserve investigation. In this study performance of such a ‘smart’ sliding isolation system, used in a 1:20 scaled bridge model, employing semi‐active controllable magneto‐rheological (MR) dampers is investigated, analytically and experimentally, under several near‐fault earthquakes. A non‐linear analytical model, which incorporates the non‐linearities of sliding bearings and the MR damper, is developed. A Lyapunov control algorithm for control of the MR damper is developed and implemented in shake table tests. Analytical and shake table test results are compared. It is shown that the smart MR damper reduces bearing displacements further than the passive low‐ and high‐damping cases, while maintaining isolation level forces less than the passive high‐damping case. Copyright © 2005 John Wiley & Sons, Ltd.     

Concept and performance testing of a high‐capacity oil damper comprising multiple damper units

There has been a significant increase in the size of building structures in recent years. Huge structures such as high‐rise buildings and large‐domed stadiums require high‐performance structural control, including the use of high‐capacity dampers, especially in an earthquake‐prone country like Japan. The objective of the present study was the enhancement of both human and structural safety in such structures through the development of a rate‐dependent type of damper with a high damping capacity. Among the various available types of rate‐dependent dampers, the authors focused on the oil damper owing to its stable performance against long‐duration vibrations. The target maximum damping force was 6000 kN, which is higher than that of any existing oil damper utilized in building structures. The authors developed a novel concept for achieving this high capacity while maintaining the size of the damper within acceptable dimensions from an architectural point of view. The concept involves the use of multiple damper units that produce mechanically parallel damping forces spatially arranged in series. As a prototype, a 1500‐kN oil damper was fabricated by combining three 500‐kN dampers. The 1500‐kN prototype damper was conceived as a full‐scale prototype of a damper that is more slender than comparable commercially available dampers in Japan, and as a scaled model of the proposed 6000‐kN damper. Sinusoidal loading tests were conducted on the prototype damper using a frequency range of 0.1–1.5 Hz and a velocity range of 0.4–300 mm/s. The results confirmed that the damper produced the design damping forces. The results of earthquake loading tests also revealed that the damper exerted a stable damping force against a large earthquake and maintained its performance after the earthquake. The damper is particularly effective against earthquakes with long‐period components that could increase the temperature of a damper. This is afforded by its high heat capacity compared to conventional dampers. Considering that the proposed 6000‐kN damper will generate a damping force that is about 2–3 times that of the strongest conventional oil damper, existing manufacturer test machines would be inadequate for evaluating its full performance characteristics. To address this issue, the authors also propose a test method for evaluating the overall damping force. The method is premised on the fact that the characteristic feature of the proposed damper is its combination of multiple damper units. The overall performance is thus evaluated using the test results for the individual damper units while the other dampers are bypassed. This method was verified by the results of the abovementioned sinusoidal loading tests, with the error for the 1500‐kN prototype damper found to be less than 5%. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of semi‐active tuned mass dampers to base‐excited systems

A continuously variable semi‐active damper is used in a tuned mass damper (TMD) to reduce the level of vibration of a single‐degree‐of‐freedom system subjected to harmonic base excitations. The ground hook dampers as have been used in the auto‐industry are being studied here. Using these dampers a new class of tuned mass dampers, named as ground hook tuned mass dampers (GHTMD) is being introduced. In order to generalize the design properties of the GHTMDs, they are defined in terms of non‐dimensional parameters. The optimum design parameters of GHTMDs for lightly damped systems are obtained based on the minimization of the steady‐state displacement response of the main mass. These parameters are computed for different mass ratios and main system damping ratios. Frequency responses of the resulting systems are compared to that of equivalent TMDs using passive dampers. In addition, other characteristics of this system as compared to the passive TMDs are discussed. A design guide to obtain the optimum parameters of GHTMD using the developed diagrams in this paper based on non‐dimensional values is presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic loading test and simulation analysis of full‐scale semi‐active hydraulic damper for structural control

A semi‐active hydraulic damper (SHD) for a semi‐active damper system, which is useful for practical structural control especially for large earthquakes, has been developed. Its maximum damping force is set to 1 or 2 MN, and it is controlled by only 70 W of electric power. An SHD with a maximum damping force of 1 MN was applied to an actual building in 1998. This paper first presents the results of a dynamic loading test to confirm the control performance of the SHD. Next, an analytical model of SHDs (SHD model) is constructed with the same concept for two kinds of SHDs based on the test results. Through simulation analyses of the test results using the proposed SHD model, the dynamic characteristics of the SHD can be well represented within practical conditions. Simulation analyses are also carried out using a simple structure model with the SHD model. It is shown that this SHD model can be used to precisely evaluate the control effect of the semi‐active damper system and is useful in practical SHD design under the applied conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

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...     

Critical damping of structures with elastically supported visco‐elastic dampers

This paper presents a new formulation for critical damping of structures with elastically supported visco‐elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco‐elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third‐order differential equation and the conventional method for defining the critical damping for second‐order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi‐infinite) for second‐order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd.     

Phasors-techniques design of inertial passive dampers for tower buildings. Stability and performance evaluations

This work introduces a geometric formalism, based on the use of phasors in the Argand-Gauss plane for the design and sizing of inertial dampers to be applied to multimodal structural oscillators. Their damping effect depends on the fact that the response of the secondary oscillator (the damper) delays the response of the primary mass to be controlled by 90°, so that the elastic force transmitted by the damper becomes a viscous force on the controlled oscillator. When such condition occurs we say that the damper is ‘tuned’ to the main oscillator; the damping induced by the damper is modest and serves only to limit the displacement of main oscillator.Our geometrical approach provides a method whose language is close to that of structural mechanics, thus paving the way to the professional for: (i) sizing the damper parameters; and (ii) evaluating the stability to the damped system and its performance limits. The aim of the development is explore the use of dampers to control the initial response modes of buildings under horizontal seismic and aerodynamic loads. Having introduced the concept of a monomass oscillator equivalent to a given mode of vibration, we develop a multimodal multidamper model which we then use to perform numerical evaluations. Several control strategies (involving changes in number and position of the dampers) are considered in relation to variation in bandwidth and intensity of the external forcing action. We discuss the advantages and limitations of this passive approach to structural control.     

Modeling of a large‐scale magneto‐rheological damper for seismic hazard mitigation. Part II: Semi‐active mode

A magneto‐rheological (MR) damper is a semi‐active device where the damper force capacity is controlled by varying the input current into the damper. In this paper, the dynamics of MR dampers associated with variable current input is studied. Electromagnetic theory is used to model the dynamics of an MR damper including the eddy current effect and the nonlinear hysteretic behavior of damper material magnetization. A nonlinear differential equation that relates the input current to the damper with a constant equivalent current is proposed. The nonlinear differential equation is combined with the Maxwell Nonlinear Slider (MNS) model to create the variable current MNS model to predict the damper force under variable input current and random damper displacement loading. The model is evaluated by comparing the predicted response of a large‐scale MR damper to the measured damper response from experiments. The experiments include a real‐time hybrid simulation of a 3‐story building structure with a large‐scale MR damper subjected to the design earthquake. The exceptional agreement observed between the predicted and experimental results illustrate the robustness and the accuracy of the variable current MNS model. Copyright © 2012 John Wiley & Sons, Ltd.