AN ANALYTICAL HYSTERESIS MODEL FOR ELASTOMERIC SEISMIC ISOLATION BEARINGS

For the purpose of accurately predicting the seismic response of base-isolated structures, an analytical hysteresis model for elastomeric seismic isolation bearings is proposed. An extensive series of experimental tests of four types of seismic isolation bearings—two types of high-damping rubber bearings, one type of lead-rubber bearing and one type of silicon rubber bearing—was carried out with the objective of fully identifying their mechanical characteristics. The proposed model is capable of well-predicting the mechanical properties of each type of elastomeric bearing into the large strain range. Earthquake simulator tests were also conducted after the loading tests of the individual bearings. In order to show the validity of the proposed model, non-linear dynamic analyses were conducted to simulate the earthquake simulator test results. Good agreement between the experimental and analytical results shows that the model can be an effective numerical tool to predict not only the peak response value but also the force–displacement relationship of the isolators and floor response spectra for isolated structures. © 1997 by John Wiley & Sons, Ltd.     

Approximating peak responses in seismically isolated buildings using generalized modal analysis

Although the ability to simulate accurately the detailed behavior of nonlinear isolation bearings and the effects of this nonlinearity on dynamic response of the isolated building is desirable, such detailed analyses are not feasible during initial design stages when bearing properties are being selected. However, it would be very beneficial to be able to estimate accurately key engineering demand parameters at the early stages of design to understand the dynamic response characteristics of the isolated structure and to balance and optimize the bearing and structural characteristics to achieve the performance goals set for the building. Unfortunately, classical modal response spectrum analysis methods do not provide accurate results for problems with large, nonclassical damping, as is characteristic of isolated buildings. To find a method capable of predicting peak building responses even with large nonclassical damping, generalized modal response spectrum analysis is implemented. The responses of several buildings having different heights and isolated by linear viscous as well as triple friction pendulum and single friction pendulum isolation systems are investigated. Generalized modal response spectrum analysis methods were found to give significantly better predictions for all systems compared with classical methods. The behavior of buildings isolated with single friction pendulum systems exhibiting sudden changes in stiffness could not be well predicted by either general or classical modal response spectrum analysis when effective damping was increased. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluating simplified models in predicting global seismic responses of a shake table–test building isolated by triple friction pendulum bearings

This paper evaluates the ability of simplified superstructure models, including two shear frame models and a single-story model, in predicting global responses of a full-scale five-story steel moment-frame buildings isolated by triple friction pendulum bearings subjected to earthquake motions. The investigated responses include displacement of the isolation system, roof drift, story drift, and floor acceleration. Mechanical properties of the simplified superstructure models were derived from the modal information of a verified full 3-D model. The comparison between the analytical responses and experimental responses shows that the simplified models can well predict the displacement of the isolation system. Furthermore, the shear-frame models are adequate for predicting floor acceleration when the specimen is subjected to horizontal ground motions. However, when the specimen is subjected to 3-D motions, the shear-frame models un-conservatively predict floor acceleration. The full 3-D model improves the prediction of story drift compared with the simplified models for both horizontal and 3-D motions.     

隔震与非隔震支座对混凝土箱梁桥地震易损性的影响

为评估隔震和非隔震支座对桥梁地震易损性的影响,以一座3跨连续混凝土箱梁桥为分析对象,首先建立采用铅芯橡胶隔震支座与非隔震型盆式橡胶支座下桥梁的数值模型,求得不同程度地震作用下墩顶与支座的最大位移响应;再定义转角延性比损伤指标,结合支座剪应变,分析桥墩和支座的地震易损性情况;最后通过宽界限法建立全桥地震易损性曲线。研究结果表明,支座是较容易发生损坏的构件,而桥梁系统比桥墩或支座更易发生破坏,同时铅芯橡胶支座的破坏概率明显低于非隔震型盆式支座,可见采用隔震支座能有效减小桥墩墩顶在地震作用下的最大位移,此时桥墩地震易损性优于采用非隔震支座的情况。     

适用于村镇房屋的新型摩擦摆隔震性能试验研究

针对村镇房屋隔震设施薄弱的问题,本着低成本、易施工的原则,设计了一种玄武岩纤维混凝土材料的摩擦摆隔震支座。将该新型支座与传统钢制摩擦摆支座进行拟静力试验,研究了该新型支座在相同的竖向荷载作用,不同频率下的干摩擦和润滑摩擦两种工况的支座的滞回性能,得出了该新型支座的基本力学性能,通过利用SAP2000有限元模型对采用该新型支座的隔震结构进行了动力时程分析,并且将该新型支座与传统钢制摩擦摆支座在滞回性能、构造方式和经济性三方面进行对比分析。结果表明:玄武岩纤维混凝土摩擦摆支座的滞回性能略低于钢制摩擦摆支座滞回性能,该支座隔震效果显著且易模性好,便于施工,造价低廉,适用于低层村镇房屋隔震设计与施工。     

Dynamic analysis of sliding structures with unsynchronized support motions

The dynamic analysis of sliding structures is complicated due to the presence of friction. Synchronization of the kinematics of all the isolation bearings is often granted to simplify the task. This, however, may lead to inaccurate prediction of the structural responses under certain circumstances. Stepped structures or continuous bridges with seismic isolation are notable examples where unsynchronized bearing motions are expected. In this paper, a logically simple and numerically efficient procedure is proposed to solve the dynamic problem of sliding systems with unsynchronized support motions. The motion equations for the sliding and non‐sliding modes of the isolated structure are unified into a single equation that is represented as a difference equation in a discrete‐time state‐space form and the base shear forces between the sliding interfaces can be determined through simple matrix algebraic analysis. The responses of the sliding structure can be obtained recursively from the discrete‐time version of the motion equation with constant integration time step even during the transitions between the non‐sliding and sliding phases. Therefore, both accuracy and efficiency in the dynamic analysis of the highly non‐linear system can be enhanced to a large extent. Rigorous assessment of seismic structures with unsynchronized support motions has been carried out for both a stepped structure and a continuous bridge. Effectiveness of friction pendulum bearings for earthquake protection of such structures has been verified. Moreover, evident unsynchronized sliding motions of the friction bearings have been observed, confirming the necessity to deal with each of the bearings independently in the analytical model. Copyright © 2000 John Wiley & Sons, Ltd.     

A new simplified approach for assessing nonlinear seismic response of plan-asymmetric structures considering soil-structure interaction

An innovative approximate method is presented to consider the plan asymmetry, nonlinear structural behaviour and soil-structure interaction (SSI) effects simultaneously. The proposed method so-called Flexible base 2DMPA (F2MPA) is an extension of 2 degrees of freedom modal pushover analysis (2DMPA) approach to consider foundation flexibility in seismic response analysis of plan asymmetric structures which itself were developed based on Uncoupled Modal Response History Analysis method for inelastic fixed-base asymmetric structures. In F2MPA for each mode shape using 2DMPA procedure, the elastic and inelastic properties of 2DOF modal systems corresponding to the fixed-base structure are initially derived. Then in each time step, displacements and inelastic restoring forces of the superstructure are computed from modal equations of the flexibly-supported structure. In each time step, the nonlinear secant stiffness matrix corresponding to the n-th MDOF modal equations of soil-structure system is updated using the corresponding modal 2DOF system of fixed-base structure. To update the transformed modal stiffness matrix of the SSI system, this matrix is partitioned and it is assumed that the non-linear variation of the superstructure can be estimated from the variation of modal stiffness matrix of the fixed-base structure. Accuracy of the proposed method was verified on an 8-story asymmetric-plan building under different seismic excitations. The results obtained from F2MPA method were compared with those obtained by nonlinear response history analysis of the asymmetric soil-structure system as a reference response. It was shown that the proposed approach could predict the results of the nonlinear time history analysis with a good accuracy. The main advantage of F2MPA is that this method is much less time-consuming and useful for the practical aims such as massive analysis of a nonlinear structure under different records with multiple intensity levels.     

Improved dynamic correction method in seismic analysis of both classically and non‐classically damped structures

A step‐by‐step approximate procedure taking into consideration high‐frequency modes, usually neglected in the modal analysis of both classically and non‐classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the mode‐acceleration method and the dynamic correction method, which are very effective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the first step, the number of differential equations of motion are reduced and consequently solved by using the first few undamped mode‐shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of differential equations, formally similar to the original differential equations of motion. The difference between the two groups of differential equations lies in the forcing vector, which is evaluated in such a way as to correct the effects of modal truncation on applied loads. Copyright © 2001 John Wiley & Sons, Ltd.     

Parameter identification of torsionally coupled shear buildings from earthquake response records

This paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state‐space model of the structure using the cross‐correlations among the measured responses. The dynamic characteristics of the structure are determined from the state‐space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight‐storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records. Copyright © 2008 John Wiley & Sons, Ltd.     

Free and steady state vibration of non-linear structures using a finite element–non-linear eigenvalue technique

The problem of free vibration of non-linear structures is considered initially. It is shown that this problem can be represented as a non-linear eigenvalue problem. Variational principles for non-linear eigenvalue problems are defined. These variational principles are implemented with finite element models to define numerical approximations for the free vibration problem. The solution of these approximate equations provides a set of non-linear modal vectors and natural frequencies which vary with the amplitude of the solution. The non-linear eigenvalue parameters can be used in modal expansion approximations for the non-linear transient or steady state response of structural systems. To demonstrate the proposed techniques the free vibration and steady state vibration characteristics of a geometrically non-linear circular plate are determined.     

A mechanical model for elastomeric seismic isolation bearings including the influence of axial load

For the purpose of predicting the large‐displacement response of seismically isolated buildings, an analytical model for elastomeric isolation bearings is proposed. The model comprises shear and axial springs and a series of axial springs at the top and bottom boundaries. The properties of elastomeric bearings vary with the imposed vertical load. At large shear deformations, elastomeric bearings exhibit stiffening behavior under low axial stress and buckling under high axial stress. These properties depend on the interaction between the shear and axial forces. The proposed model includes interaction between shear and axial forces, nonlinear hysteresis, and dependence on axial stress. To confirm the validity of the model, analyses are performed for actual static loading tests of lead–rubber isolation bearings. The results of analyses using the new model show very good agreement with the experimental results. Seismic response analyses with the new model are also conducted to demonstrate the behavior of isolated buildings under severe earthquake excitations. The results obtained from the analyses with the new model differ in some cases from those given by existing models. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic characterization of a long span bridge: A finite element based approach

Aging bridges coupled with increasing traffic loads are producing a severe toll on the nation's infrastructure. This has made it necessary to take a closer look at the health of existing bridges and develop automated damage identification methods if possible. Recent works in the field of structural dynamics have shown that damage detection techniques utilizing parameters like mode shapes, modal frequencies and damping ratios can be used to identify damage in structural systems. It is, however, important to be able to establish a baseline model for the structure first, and then a model updating technique can be utilized to evaluate the condition of the structure from time to time. It is with this goal in mind that the authors have decided to establish the process for obtaining a baseline model for a long span bridge. Based on the actual design drawings of a bridge, finite element (FE) models of the bridge in question are developed using SDRC-IDEAS. Three models of the bridge are simulated using Normal Mode Dynamics solver in SDRC-IDEAS to obtain the modal parameters of interest, in this case the modal frequencies and the mode shapes. A modal assurance criteria (MAC) is utilized to compare the different simulated mode shapes and, finally, the modal frequencies that have been obtained from the FE analysis are compared to frequencies that have been obtained from some preliminary field tests.     

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.     

Investigation of the seismic response of high‐rise buildings supported on tension‐resistant elastomeric isolation bearings

In many applications of seismic isolation, such as in high‐rise construction, lightweight construction, and structures with large height‐to‐width aspect ratios, significant tension forces can develop in bearings, raising concerns about the possible rupture of elastomeric bearings and the uplift of sliding bearings. In this paper, a novel tension‐resistant lead plug rubber bearing (TLRB) with improved tension‐resisting capabilities is developed and experimentally and numerically assessed. This TLRB consists of a common lead plug rubber bearing (LRB) and several helical springs. After describing the theory underlying the behavior of the TLRB, the mechanical properties of reduced‐scale prototype bearings are investigated through extensive horizontal and vertical loading tests. The test results indicate that TLRBs can improve the shear stiffness and tension resistance capacity even under significant tensile loads. A series of shaking table tests on scaled models of high‐rise buildings with different aspect ratios were conducted to investigate the dynamic performance of the TLRB and the seismic responses of base‐isolated high‐rise buildings. Three different cases were considered in the shaking table tests: a fixed base condition and the use of TLRB and LRB isolation systems. The results of the shaking table test show that (a) base‐isolated systems are effective in reducing the structural responses of high‐rise buildings; (b) an isolated structure's aspect ratio is an important factor influencing its dynamic response; (c) TLRBs can endure large tensile stresses and avoid rupture on rubber bearings under strong earthquakes; and (d) the experimental and numerical results of the responses of the models show good agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Optimization of the stochastic response of a bridge isolation system with hysteretic dampers

A bridge structure with a seismic isolation system consisting of rubber bearings and hysteretic dissipators is considered. The non-linear equations of motion are derived for the first mode vibration and the stochastic response to a white noise or a filtered white noise ground acceleration is determined by using the method of equivalent linearization. The sensitivity of the stochastic response to principal pàrameters for the bridge is investigated. Results of optimum design of the isolation system are presented.     

The optimum design of a base isolation system with frictional elements

A linear multistorey structure with a seismic base isolation system consisting of rubber bearings and frictional elements is considered. The non-linear equations of motion are derived for the first mode vibration and the stochastic response to a white noise ground acceleration is determined. Based on this response, suitable objective functions are defined and the optimum design of the isolation system is performed. It is shown that a small amount offriction increases the effectiveness of the system compared with the same system but without frictional elements.     

Multiple‐slider surfaces bearing for seismic retrofitting of frame structures with soft first stories

A new isolation interface is proposed in this study to retrofit existing buildings with inadequate soft stories as well as new structures to be constructed with soft first story intended for architectural or functional purposes. The seismic interface is an assembly of bearings set in parallel on the top of the first story columns: the multiple‐slider bearings and rubber bearings. The multiple‐slider bearing is a simple sliding device consisting of one horizontal and two inclined plane sliding surfaces based on polytetrafluoroethylene and highly polished stainless steel interface at both ends set in series. A numerical example of a five‐story reinforced concrete shear frame with soft first story is considered and analyzed to demonstrate the efficiency of the proposed isolation system in reducing the ductility demand and damage in the structure while maintaining the superstructure above the bearings to behave nearly in the elastic range with controlled bearing displacement. Comparative study with the conventional system as well as various isolation systems such as rubber bearing interface and resilient sliding isolation is carried out. Moreover, an optimum design procedure for the multiple‐slider bearing is proposed through the trade‐off between the maximum bearing displacement and the first story ductility demand ratio. The results of extensive numerical analysis verify the effectiveness of the multiple‐slider bearing in minimizing the damage from earthquake and protecting the soft first story from excessively large ductility demand. Copyright © 2012 John Wiley & Sons, Ltd.     

System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: normal modes

Based on the Hilbert–Huang spectral analysis, a method is proposed to identify multi‐degree‐of‐freedom (MDOF) linear systems using measured free vibration time histories. For MDOF systems, the normal modes have been assumed to exist. In this method, the measured response data, which are polluted by noises, are first decomposed into modal responses using the empirical mode decomposition (EMD) approach with intermittency criteria. Then, the Hilbert transform is applied to each modal response to obtain the instantaneous amplitude and phase angle time histories. A linear least‐square fit procedure is proposed to identify the natural frequency and damping ratio from the instantaneous amplitude and phase angle for each modal response. Based on a single measurement of the free vibration time history at one appropriate location, natural frequencies and damping ratios can be identified. When the responses at all degrees of freedom are measured, the mode shapes and the physical mass, damping and stiffness matrices of the structure can be determined. The applications of the proposed method are illustrated using three linear systems with different dynamic characteristics. Numerical simulation results demonstrate that the proposed system identification method yields quite accurate results, and it offers a new and effective tool for the system identification of linear structures in which normal modes exist. Copyright © 2003 John Wiley & Sons, Ltd.     

新型组合隔震支座设计与性能研究

在已有研究基础上,为提高摩擦型组合隔震支座变形能力、改进各摩擦组件位移协调性,建立实体化和参数化计算模型,对新型三段两级摩擦组合隔震支座进行构造及内力分析研究,使用ABAQUS软件对摩擦阻尼器和组合隔震支座进行实体有限元模拟。针对设置常规隔震支座和新型组合隔震支座的某隔震结构案例进行建模及非线性时程地震响应分析,推导组合隔震支座出力和构造参数的关系。研究结果表明,文章所采用的摩擦阻尼器参数化建模方法是准确的,新型组合支座可明显降低支座拉应力,减小隔震层位移,提高结构抗倾覆能力。文章提出的针对摩擦阻尼器的简化单元可大幅提高有限元模型的计算效率。