Restoring capability of bilinear hysteretic seismic isolation systems

The restoring capability (or re‐centering capability) is identified by the current design codes as a fundamental feature of seismic isolation systems. In this paper, the restoring capability of bilinear hysteretic or frictional seismic isolation systems is investigated in some detail. Certain energy considerations are examined first in order to provide insight into and reveal governing parameters on individual aspects of the problem. The restoring capability is then investigated through an extensive parametric study of smooth bilinear single‐degree‐of‐freedom hysteretic systems, with parameters covering a range of typical seismic isolation systems, subjected to a large group of recorded earthquakes. The results of the parametric analyses are processed statistically and regression analysis relations are derived that show the dependence of the residual displacement after the earthquake and the cumulative build up of displacements after a series of successive earthquakes on the governing parameters. Based on the analysis results, the features of the bilinear system that ensure sufficient restoring capability are identified. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic response of rotating machines–structure–RFBI systems

The seismic response of a critical rotating machine either rigidly attached to a floor or independently isolated housed within an initially aseismically designed or uncontrolled structure are investigated. A particular isolation system, the Resilient‐Friction Base Isolator (RFBI), is employed. Finite element formulations of a rotor‐disk‐bearing model on a rigid base are developed. The equations of motion for the combined rotating machine–structure–RFBI systems are presented. Parametric studies are performed to investigate the effects of variations in system physical properties including friction coefficient, mass ratio, shaft flexibility, bearing rigidity, bearing damping and speed of rotation on the response of rotating machines for the combined rotating machine–structure–isolator systems. Comparative studies in the peak response of the rotating machine supported on various isolation systems and the corresponding fixed base system are carried out. The study indicates that the Resilient‐Friction Base Isolator can significantly reduce the seismic response of rotating components to potentially damaging ground excitations. Copyright © 2000 John Wiley & Sons, Ltd.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

VFPI: an isolation device for aseismic design

Sliding isolators with curved surface are effective base isolation systems incorporating isolation, energy dissipation and restoring mechanism in one unit. However, practical utility of these systems, such as friction pendulum system (FPS) has limitations due to constant isolator period and restoring force characteristics. A new isolator called the variable frequency pendulum isolator (VFPI) that overcomes these limitations while retaining all the advantages has been described in this paper. VFPI has oscillation frequency decreasing with sliding displacement, and the restoring force has an upper bound so that the force transmitted to the structure is limited. The mathematical formulations for the response of a SDOF structure and energy balance are also described. Parametric studies have been carried out to critically examine the behaviour of structures isolated with VFPI, FPS and PF system. From these investigations, it is concluded that the VFPI combines the advantages of both FPS and PF system, without their undesirable properties. The VFPI performance is also found to be stable during low‐intensity excitations, and fail‐safe during high‐intensity excitations. VFPI is found to exhibit robust performance for a wide range of structure, isolator and ground motion characteristics clearly demonstrating its advantages. Copyright © 2000 John Wiley & Sons, Ltd.     

Non‐linear‐Maxwell‐element‐type hysteretic control force

A simple non‐linear control law is proposed for reducing structural responses against seismic excitations. This law defines control force dynamics by one differential equation involving a non‐linear term that restrains the control force amplitude. If non‐linearity is neglected, the control force becomes the force in a Maxwell element, so it is called the non‐linear‐Maxwell‐element‐type (NMW) control force. The NMW control force vs. deformation relation plots hysteretic curves. The basic performance of an SDOF model with the NMW control force is examined for various conditions by numerical analyses. Furthermore, the control law is extended to fit an MDOF structural model, and an application example is shown. The computational results show that the NMW control force efficiently reduces structural responses. Copyright © 2000 John Wiley & Sons, Ltd.     

考虑耦联影响的二次结构体系减震分析

建立了基础隔震的主次结构体系耦联运动方程,开发了动力分析程序PS—BASE．FOR,对一典型结构的二次结构绝对加速度反应谱与相对位移反应谱计算分析表明,主体结构隔震或同时增大二次结构阻尼,是取得二次结构较好抗震性能的有效途径,增大主体结构的隔震阻尼对二次结构略有不利影响。     

基础隔震房屋模型振动台试验研究

本文结合日本在建的基础隔震实际工程,采用中国有关工厂生产的铅芯橡胶支座的作为基础隔震支座,进行了基础隔震房屋模型和基础固家房屋模型模拟地震动台试验,并引入能量分析方法对两种试验结果进行了分析比较。结果表明,基础隔震模型隔震效果明显,隔震层滞回变能有效吸收地震动入能量,减小模型结构的塑性变形和累积损伤。     

Time domain identification of hybrid base isolation systems using free vibration tests

A procedure for the dynamic identification of the physical parameters of coupled base isolation systems is developed in the time domain. The isolation systems considered include high damping rubber bearings (HDRB) and low friction sliding bearings (LFSB). A bi‐linear hysteretic model is used alone or in parallel with a viscous damper to describe the behavior of the HDRB system, while a constant Coulomb friction device is used to model the LFSB system. After deriving the analytical dynamical solution for the coupled system under an imposed initial displacement, this is used in combination with the least‐squares method and an iterative procedure to identify the physical parameters of a given base isolation system belonging to the class described by the models considered. Performance and limitations of the proposed procedure are highlighted by numerical applications. The procedure is then applied to a real base isolation system using data from static and dynamic tests performed on a building at Solarino. The results of the proposed identification procedure have been compared to available laboratory data and the agreement is within ±10%. However, the need for improvement both in models and testing procedures also emerges from the numerical applications and results obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of isolator and ground motion characteristics on the performance of seismic‐isolated bridges

This paper presents the effect of isolator and substructure properties as well as the frequency characteristics and intensity of the ground motion on the performance of seismic‐isolated bridges (SIBs) and examines some critical design clauses in the AASHTO Guide Specification for Seismic Isolation Design. For this purpose, a parametric study, involving more than 800 non‐linear time history analyses of simplified structural models representative of typical SIBs, is conducted. The results from the parametric study are then used to derive important design recommendations and conclusions that may be used by bridge engineers to arrive to a more sound and economical design of SIBs. It is found that the SIB response is a function of the peak ground acceleration to peak ground velocity ratio of the ground motion. Thus, the choice of the seismic ground motion according to the characteristics of the bridge site is crucial for a correct design of the SIB. It is also found that the characteristic strength of the isolator may be chosen based on the intensity and frequency characteristics of the ground motion. Furthermore, the isolator post‐elastic stiffness is found to have a notable effect on the response of SIBs. Copyright © 2005 John Wiley & Sons, Ltd.     

Shaking‐table tests on reinforced concrete frames with different isolation systems

The effectiveness of seismic isolation in protecting structural and non‐structural elements from damage has been assessed in an extensive programme of shaking‐table tests, carried out on four identical 1/3.3‐scale, two‐dimensional, reinforced concrete (R/C) frames. Four different isolation systems were considered, namely: (i) rubber‐based, (ii) steel‐based, (iii) shape memory alloy (SMA)‐based and (iv) hybrid, i.e. based on both SMA and steel components, isolation systems. This paper presents a comprehensive overview of the main results of the experimental tests on base‐isolated models, whose structural response is described through: (i) maximum base displacements; (ii) maximum interstorey drifts; (iii) maximum storey accelerations and (iv) maximum storey shear forces. The evolution of the fundamental frequency of vibration of the R/C frame during the tests is also described. The beneficial effects of using base isolation resulted in no or slight damage, under strong earthquakes, to both structural and non‐structural members, as well as to the internal content of the building. The comparison with the experimental results obtained in shaking‐table tests on similar fixed‐base models emphasizes these positive aspects. Finally, advantages and drawbacks related to the use of each isolation system are discussed in the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal design of an equipment isolation system with nonlinear hysteretic behaviour

Vibration isolation is well recognized as an effective mitigation strategy for acceleration‐sensitive equipment subjected to earthquake. In the present paper, an equipment isolation system with nonlinear hysteretic behaviour is proposed and a methodology for the optimal design is developed. An integrable constitutive model, derived from the mathematical Duhem hysteresis operator, is adopted for the isolation system. The optimization procedure is defined through a dual‐criteria approach that involves a transmissibility criterion combined with an energy performance criterion: the former consists in limiting the absolute acceleration of the isolated equipment below an allowable threshold value; the latter, in maximizing the ratio between the energy dissipation due to hysteresis and the input energy to reduce the isolator displacements. The seismic effectiveness of the nonlinear hysteretic isolation system is numerically investigated under natural accelerograms with different frequency content and increasing levels of excitation. Both ground‐mounted and floor‐mounted equipment items are considered in the analyses; in the second case, the dynamic interaction between the equipment and its supporting structure is taken into account in the design of the isolation system, and its effects on the isolation performance and the structural response are discussed. Comparisons in terms of effectiveness and robustness with a linear isolation system with viscoelastic behaviour are eventually provided. Copyright © 2013 John Wiley & Sons, Ltd.     

Design,test and analysis of a light‐weight dissipative bracing system for seismic protection of structures

The paper deals with the proposal and the experimental validation of a novel dissipative bracing system for the seismic protection of structures; compared with other similar systems, it is characterized by smaller size and weight, which makes it easier to move and to install, as well as particularly suitable to be inserted in light‐framed structures (e.g. steel structures of industrial plants). The proposed system consists of an articulated quadrilateral with steel dissipaters inserted, to be connected by tendons to frame joints; the prototypes have been designed and realized for the seismic protection of a two‐storey, large‐scale, steel frame, specially designed for shaking‐table tests. The paper, after an illustration of the system, and of its design and behaviour, presents the shaking‐table tests carried out. The experimental results have fully validated the proposed system, showing its good performance in controlling the seismic response of framed structures. A numerical non‐linear model, set up and validated on the basis of the physical tests, has been used to help interpreting the experimental results, but also to perform parametrical studies for investigating the influence of the design parameters on the performance of the control system. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal yield level of bilinear seismic isolation devices

The yield level of an insulator is one of the important parameters which are related to responses and absorbing energy under seismic input energy in isolated structures. The purpose of this paper is to determine the optimal ratios of yield force of the isolator (Q_y) to the total weight of the structures (W). To obtain the optimal ratio, 1044 two-degree-of-freedom isolated bridge models, which have bilinear isolators, were selected. These 2-DOF isolated bridge models with superstructure isolation can consider pier flexibility and various parameters of the isolator. Two formulas for determining the optimal yield ratio are proposed and compared with the previous researches. RAE (the ratio of absorbed energy by the isolator to the total input energy) is related directly to structural responses, and Optimal Yield Ratio (OYR), defined as a yield ratio at maximum RAE, can be obtained from the relationship between RAE and Q_y/W. Here, we found that RAE is a reliable factor to evaluate OYR, and it is proportional to earthquake amplitudes under the same kinds of earthquake loadings. Using the proposed formulas, OYR is determined and the optimal yield force of the isolator can be obtained easily and reliably at a seismic isolation design stage. Copyright © 1999 John Wiley & Sons, Ltd.     

An enhanced base isolation system equipped with optimal tuned mass damper inerter (TMDI)

In seismic base isolation, most of the earthquake‐induced displacement demand is concentrated at the isolation level, thereby the base‐isolation system undergoes large displacements. In an attempt to reduce such displacement demand, this paper proposes an enhanced base‐isolation system incorporating the inerter, a 2‐terminal flywheel device whose generated force is proportional to the relative acceleration between its terminals. The inerter acts as an additional, apparent mass that can be even 200 times higher than its physical mass. When the inerter is installed in series with spring and damper elements, a lower‐mass and more effective alternative to the traditional tuned mass damper (TMD) is obtained, ie, the TMD inerter (TMDI), wherein the device inertance plays the role of the TMD mass. By attaching a TMDI to the isolation floor, it is demonstrated that the displacement demand of base‐isolated structures can be significantly reduced. Due to the stochastic nature of earthquake ground motions, optimal parameters of the TMDI are found based on a probabilistic framework. Different optimization procedures are scrutinized. The effectiveness of the optimal TMDI parameters is assessed via time history analyses of base‐isolated multistory buildings under several earthquake excitations; a sensitivity analysis is also performed. The enhanced base‐isolation system equipped with optimal TMDI attains an excellent level of vibration reduction as compared to the conventional base‐isolation scheme, in terms not only of displacement demand of the base‐isolation system but also of response of the isolated superstructure (eg, base shear and interstory drifts); moreover, the proposed vibration control strategy does not imply excessive stroke of the TMDI.     

砌体结构工程抗震软件的结构隔震功能及算例分析

在砌体结构抗震软件开发过程中，为完善软件功能，添加了结构减震设计验算程序。作为首次应用性软件开发，暂只包含橡胶热隔震的设计与验算功能。本文主要介绍了软件应用时，橡胶垫隔震支座的设计过程，并通过对一个模拟的8层砌体建筑进行隔震设计与对比分析，给出了隔震设计后隔震效果的有关结论。     

Response of structures supported on SCF isolation systems

Aseismic base isolation is an effective method used to protect structures and their contents against earthquakes. An isolated structure may be designed to remain elastic throughout major ground motions as a result of the efficiency of the isolation systems. In this paper, the equations of motion of two‐dimensional elastic structures supported on a new base isolation system called the Sliding Concave Foundation (SCF) are presented and a procedure for their solution is suggested. The responses of a number of structures subjected to different earthquake records are evaluated and the results are compared with those of the same structures supported on two other famous isolation systems and also a fixed base condition. The results indicate the effectiveness of the SCF in protecting the supported structures even during very strong and/or long period earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

Estimating the seismic displacement of friction pendulum isolators based on non‐linear response history analysis

A procedure for developing equations that estimate the isolator displacement due to strong ground motion is applied to buildings isolated with the friction pendulum system. The resulting design equations, based on rigorous non‐linear analysis, offer an alternative to the iterative equivalent‐linear methods used by current U.S. building codes. The governing equations of the system are reduced to a form such that the median normalized displacement of the system due to an ensemble of ground motions is found to depend on only the isolation period—a function of the curvature of the isolator—and the friction force at incipient slip normalized by peak ground velocity. The normalization is effective in minimizing the dispersion of the normalized displacement for an ensemble of ground motions, implying that the median normalized displacement is a reliable estimate of response. The design equations reflect the significant (20 to 38%) increase in displacement when the excitation includes two lateral components of ground motion instead of just one component. Equivalent‐linear methods are shown to underestimate by up to 30% the exact median displacement determined by non‐linear response history analysis for one component of ground motion, and building codes include at most a 4.4% increase for a second component. Copyright © 2003 John Wiley & Sons, Ltd.     

基础隔震单层偏心结构扭转地震反应分析

采用微分型滞回恢复力模型模拟隔震支座的恢复力特性，对基础隔震单层偏心结构的扭转地震反应进行分析，研究隔震系统偏心距和上部结构偏心距对结构扭转反应的影响。结果表明，采用隔震技术可以显著降低隔震结构的扭转地震反应。     

Earthquake response of elastic SDF systems with non‐linear fluid viscous dampers

The steady‐forced and earthquake responses of SDF systems with a non‐linear fluid viscous damper (FVD) are investigated. The energy dissipation capacity of the FVD is characterized by the supplemental damping ratio ζsd and its non‐linearity by a parameter designated α. It is found that the structural response is most effectively investigated in terms of ζ_sd and α because (1) these two parameters are dimensionless and independent, and (2) the structural response varies linearly with the excitation intensity. Damper non‐linearity has essentially no influence on the peak response of systems in the velocity‐sensitive spectral region, but differences up to 14% were observed in the other spectral regions. The structural deformation is reduced by up to 25% when ζ_sd= 5%; and by up to 60% when ζ_sd= 30%. Non‐linear FVDs are advantageous because they achieve essentially the same reduction in system responses but with a significantly reduced damper force. For practical applications, a procedure is presented to estimate the design values of structural deformation and forces for a system with non‐linear FVD directly from the design spectrum. It is demonstrated that the earthquake‐induced force in a non‐linear FVD can be estimated from the damper force in a corresponding system with linear FVD, its peak deformation, and peak relative velocity; however, the relative velocity should not be approximated by the pseudo‐velocity as this approximation introduces a large error in the damper force. Finally, a procedure is presented to determine the non‐linear damper properties necessary to limit the structural deformation to some design value or the structural capacity for a given design spectrum. Copyright © 2002 John Wiley & Sons, Ltd.     

Evolutionary aseismic design and retrofit of structures with passive energy dissipation

A new computational framework is developed for the design and retrofit of building structures by considering aseismic design as a complex adaptive process. For the initial phase of the development within this framework, genetic algorithms are employed for the discrete optimization of passively damped structural systems. The passive elements may include metallic plate dampers, viscous fluid dampers and viscoelastic solid dampers. The primary objective is to determine robust designs, including both the non‐linearity of the structural system and the uncertainty of the seismic environment. Within the present paper, this computational design approach is applied to a series of model problems, involving sizing and placement of passive dampers for energy dissipation. In order to facilitate our investigations and provide a baseline for further study, we introduce several simplifications for these initial examples. In particular, we employ deterministic lumped parameter structural models, memoryless fitness function definitions and hypothetical seismic environments. Despite these restrictions, some interesting results are obtained from the simulations and we are able to gain an understanding of the potential for the proposed evolutionary aseismic design methodology. Copyright © 2005 John Wiley & Sons, Ltd.