Seismic response of the superstructure and attached equipment in a base-isolated building

Base isolation can be used both to protect the structure and simultaneously to reduce the response of internal equipment. The seismic response of a base-isolated structure has been studied through the shaking table test or numerical calculation before. The object of this paper is to analyse a base-isolated structure by a different analytical approach—perturbation analysis. Recognizing that the horizontal stiffness of an isolation system is much smaller than that of the superstructure, the mathematical expressions of the modal properties of base-isolated structures are derived by the perturbation method in terms of the modal properties of the superstructure and used to study the dynamic response of superstructure and attached equipment in the base-isolated building. This study shows that the first base-isolated mode not only controls the superstructural response but also dominates the response of high-frequency attachment. The contribution of higher modes to the response of base-isolated structures, which is proportional to the horizontal stiffness of isolation system, is very small.     

Seismic response of heavily damped base isolation systems

The development of an efficient energy-dissipating mechanism that works in conjunction with laminated elastomeric bearings in order to reduce the lateral deformation of the isolation system has always been a goal of base isolation research. Theoretically, this deformation will be reduced to the minimum if damping augmentation of the isolation system can reach a critical value. However, augmenting the isolation damping may cause some unwanted side effects. The purpose of this paper is to study the influence of isolation damping on the seismic response of heavily damped base-isolated buildings. The base isolation system is assumed to be linearly viscoelastic and is analysed using the complex mode method. Solutions derived by using perturbation techniques for a two-degree-of-freedom system and the computer simulation for a multiple-degree-of-freedom system reveal that augmenting the isolation damping can reduce efficiently the deformation of the isolation system, but at the price of increasing the high-frequency vibration in the superstructure. When the damping ratio of the isolation system is beyond some level, increasing the isolation damping will enlarge the extreme values of the base and superstructural accelerations. It is also found that approximate solutions derived from the use of classical damping and classical modes of vibration in the seismic analysis of heavily damped base isolation systems can be substantially in error.     

Effects of the improper modeling of viscous damping on the first-mode and higher-mode dominated responses of base-isolated buildings

In many finite element platforms, a classical global damping matrix based on the elastic stiffness of the system (including isolators) is usually developed as part of the solution to the equations of motion of base-isolated buildings. The conducted analytical and numerical investigations illustrate that this approach can lead to the introduction of unintended damping to the first and higher vibration modes and the spurious suppression of the respective structural responses. A similar shortcoming might be observed even when a nonclassical damping model (ie, an assembly of the superstructure and isolation system damping sub-matrices) is used. For example, the use of Rayleigh damping approach to develop the superstructure damping sub-matrix can lead to the undesired addition of damping to the isolated mode arising from the mass-proportional component of the superstructure damping. On the other hand, the improper use of nonclassical stiffness-proportional damping (eg, determining the proportional damping coefficient, β_k , based on the first mode) can result in assigning significant damping to the higher-modes and the unintended mitigation of the higher-mode responses. Results show that a nonclassical stiffness-proportional model in which β_k is determined based on the second modal period of a base-isolated building can reasonably specify the intended damping to the higher modes without imparting undesirable damping to the first mode. The nonclassical stiffness-proportional damping can be introduced to the numerical model through explicit viscous damper elements attached between adjacent floors. In structural analysis software such as SAP2000®, the desired nonclassical damping can be also modeled through specifying damping solely to the superstructure material.     

基于不同参数的基础隔震结构非线性概率密度演化

为了研究不同设计参数条件下基础隔震结构非线性响应的概率密度演化特征,采用两质点模型来模拟基础隔震结构,隔震层与上部结构分别采用Bouc-Wen模型与刚度退化的Bouc-Wen模型来描述其非线性特征,运用概率密度演化理论,进行隔震结构非线性随机地震响应的概率密度演化分析。采用基于物理的随机地震动模型生成人工地震动,提出基础隔震结构非线性随机地震响应的概率密度演化分析的基本步骤。通过改变基础隔震结构的设计参数,同时考虑激励的随机性,研究基础隔震结构非线性随机地震响应的概率密度演化规律。结果表明,基础隔震结构的阻尼比、周期比和屈重比取合理范围,能使隔震结构上部和下部的位移可控。     

无填充墙基础隔震RC框架在环境激励下的动力特性

对一基础隔震钢筋混凝土框架结构在无填充墙情况下进行了环境激励下的动力测试,重点利用Hilbert-Huang变换与随机减量技术相结合的方法识别了其模态参数,并与随机子空间识别法、有理分式多项式法识别的结果进行了对比。识别结果表明在环境激励下,基础隔震结构的基本周期远小于多遇和罕遇地震工况下设计计算的基本周期;等效黏滞阻尼比很小,近乎于基础固定模型。对隔震层阻尼特性的分析表明,环境激励下可以将基础隔震结构视为经典的比例阻尼系统。进一步以识别的模态参数为基准,采用优化的方法数值反演了环境激励下该结构隔震层的实际水平等效刚度,结果表明其值为多遇地震下计算刚度取值的10.75倍。     

Optimum damping in linear isolation systems

Optimum isolation damping for minimum acceleration response of base-isolated structures subjected to stationary random excitation is investigated. Three linear models are considered to account for the energy dissipation mechanism of the isolation system: a Kelvin element, a linear hysteretic element and a standard solid linear element, commonly used viscoelastic models for isolation systems comprising natural rubber bearings and viscous dampers. The criterion selected for optimality is the minimization of the mean-square floor acceleration response. The effects of the frequency content of the excitation and superstructure properties on the optimum damping and on the mean-square acceleration response are addressed. The study basically shows that the attainable reduction in the floor acceleration largely depends on the energy dissipation mechanism assumed for the isolation system as well as on the frequency content of the ground acceleration process. Special care should be taken in accurately modelling the mechanical behaviour of the energy dissipation devices.     

Roles of soil-structure interaction and damping in base-isolated structures built on numerous soil layers overlying a half-space

This study examines the roles of soil-structure interaction (SSI), higher modes, and damping in a base-isolated structure built on multiple layers of soil overlying a half space. Closed-form solutions for the entire system, including a superstructure, seismic isolator, and numerous soil layers overlying a half-space, were obtained. The formulations obtained in this study simply in terms of well-known frequencies and mechanical impedance ratios can explicitly interpret the dynamic behavior of a base-isolated structure interacting with multiple soil layers overlying a half-space. The key factors influencing the performance of the isolation system are the damping ratio of the isolator and the ratio of the natural frequency of the fixed-base structure to that of the isolated structure by assuming that the superstructure moves as a rigid body. This study reveals that higher damping in the base isolator is unfavorable to higher mode responses that usually dominate the responses of the superstructure and that the damping mechanism plays an important role in transmitting energy in addition to absorbing energy. It is also concluded that it is possible to design a soft soil layer as an isolation system for isolating vibration energy.     

Seismic response of base-isolated structures with vertical-rocking coupling

A base-isolated building is liable to have a small horizontal eccentricity between the centre of mass of the superstructure and the centre of rigidity of the supporting bearings. In seismic analysis, the structure is modelled as a rigid block with tributary masses supported on massless elastomeric rubber bearings placed at a constant elevation below the centre of mass. This simplified system has three degrees of freedom: two translations and one rotation in the vertical plane. The investigation of the dynamic behaviour of a base-isolated building is carried out for both the detuned and the perfectly tuned cases. In the detuned case, the natural frequencies of the system are assumed to be well separated. In the perfectly tuned case, the uncoupled rocking frequency is assumed to be identical to the vertical translational frequency, which may result from an unusual mass distribution and/or an extreme aspect ratio of the superstructure. Perturbation methods are implemented in finding the dynamic characteristics for both cases. However, the dynamic response of the perfectly tuned case is the major concern in this investigation. The Green's functions for the displacement response of the three-degree-of-freedom system are derived for both the undamped and damped conditions. The response spectrum modal superposition method is used in estimating the maximum acceleration response. A simple method, accounting for the effect of closely spaced modes, is proposed for combining modal maxima and results in an approximate solution corresponding to a single-degree-of-freedom system. This approximate solution may be used for the preliminary design of a base-isolated structure. Numerical results for a base-isolated building subjected to the vertical component of the El Centro earthquake of 1940 were carried out for comparison with these analytical results. The proposed modal combination method showed superiority over the conventional Square Root of the Sum of the Squares method in estimating maximum responses. The results also indicated that the approximate single-degree-of-freedom system yields accurate estimations. It is shown that the effect of rocking coupling on the vertical response of base-isolated structures subjected to transient loadings, such as earthquake motions, can generally be neglected as a result of the combined effects of the time lag between the maximum translational and rotational responses and the influence of damping in the isolation system, which for elastomeric bearings can be as high as 8 to 10 per cent of critical.     

基础隔震结构随机地震响应分析的复模态法

本文对多自由度基础隔震结构的随机地震响应问题进行了系统研究，首先建立了运动方程，然后用第一振型将上部结构展开，针对所得方程为非经典阻尼、非对称质量和非对称刚度情况，用复模态法解耦，获得了以第一振型表示的结构地震响应的解析解，对单自由度体系，此解即为结构响应的精确解，从而建立了两自由度体系在任意非经典阻尼与非对称质量和刚度情况下随机地震响应解析解分析的一般方法。本文方法也可用于带TMD减震结构、无损伤“加层减震”加固结构的随机地震响应分析与优化设计。     

Seismic response evaluation of base-isolated reinforced concrete buildings under bidirectional excitation

This paper reports on an investigation of the seismic response of base-isolated reinforced concrete buildings, which considers various isolation system parameters under bidirectional near-fault and far-fault motions. Three-dimensional models of 4-, 8-, and 12-story base-isolated buildings with nonlinear effects in the isolation system and the superstructure are investigated, and nonlinear response history analysis is carried out. The bounding values of isolation system properties that incorporate the aging effect of isolators are also taken into account, as is the current state of practice in the design and analysis of base-isolated buildings. The response indicators of the buildings are studied for near-fault and far-fault motions weight-scaled to represent the design earthquake (DE) level and the risk-targeted maximum considered earthquake (MCE_R) level. Results of the nonlinear response history analyses indicate no structural damage under DE-level motions for near-fault and far-fault motions and for MCE_R-level far-fault motions, whereas minor structural damage is observed under MCE_R-level near-fault motions. Results of the base-isolated buildings are compared with their fixed-base counterparts. Significant reduction of the superstructure response of the 12-story base-isolated building compared to the fixed-base condition indicates that base isolation can be effectively used in taller buildings to enhance performance. Additionally, the applicability of a rigid superstructure to predict the isolator displacement demand is also investigated. It is found that the isolator displacements can be estimated accurately using a rigid body model for the superstructure for the buildings considered.     

Seismic response of base-isolated buildings including soil–structure interaction

This study investigates the effect of soil–structure interaction (SSI) on the response of base-isolated buildings. The equations of motion are formulated in the frequency domain, assuming frequency-independent soil stiffness and damping constants. An equivalent fixed-base system is developed that accounts for soil compliance and damping characteristics of the base-isolated building. Closed-form expressions are derived, followed by a thorough parametric study involving the pertinent system parameters. For preliminary design, the methodology can serve as a means to assess effective use of base isolation on building structures accounting for SSI. This study concludes that the effects of SSI are more pronounced on the modal properties of the system, especially for the case of squat and stiff base-isolated structures.     

Seismic response of segmental buildings

This paper proposes an aseismic design concept in which the superstructure of a base-isolated building is divided into several segments. Each segment may comprise a few storeys and is interconnected by additional vibrational isolation systems. The dynamic characteristics of the segmental buildings are investigated. The optimum parameters of the vibration isolation systems are determined by minimizing the mean square acceleration response. The seismic response of a typical segmental building subjected to the N—S component of the 1940 El Centro earthquake input is evaluated and compared with the responses of the corresponding fixed-base and conventional base-isolated buildings. The comparisons show that, when the superstructure is segmented, while the acceleration response in the superstructure remains as small as that in the conventional base-isolated building, the displacement across the base isolation system at foundation level is substantially reduced.     

结构随机地震响应分析的复模态法

本文对多自由度基础平动结构随机地震响应问题进行了系统研究。针对用第1振型近似代表上部结构所得方程为非经典阻尼和非对称结构情况。用复模态法解耦。获得了以第1振型表示的结构地震响应的解析解。对单自由度体系。此解即为结构响应的精确解。本文方法也可用于带TMD减震结构等的随机地震响应分析与优化设计。     

脉冲型地震动作用下隔震结构动力响应的影响参数研究

通过对隔震结构进行非线性动力响应分析,分别研究地震动参数和支座参数对结构地震响应的影响。首先,建立铅芯橡胶支座基础隔震结构的非线性运动方程;然后,以人工合成脉冲型地震动作为输入,运用MATLAB进行编程并求解结构在脉冲型地震动作用下的地震响应;最后,分别研究速度脉冲周期、支座屈服力、屈服后与屈服前的刚度比对隔震支座最大位移和上部结构层间位移的影响。研究结果表明,脉冲周期对结构地震响应影响很大,在进行隔震设计时应使结构自振周期远离脉冲周期;支座刚度比对结构地震响应影响较大,在进行支座选型时应重点关注;支座屈服力对支座位移的影响显著,屈服力越大,支座位移越小。     

Approximate soil–structure interaction analysis by a perturbation approach: The case of soft soils

An approximate solution of the classical eigenvalue problem governing the vibrations of a relatively stiff structure on a soft elastic soil is derived through the application of a perturbation analysis. The full solution is obtained as the sum of the solution for an unconstrained elastic structure and small perturbing terms related to the ratio of the stiffness of the soil to that of the superstructure. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented earlier for the case of stiff soils. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure.     

基于动力可靠度的隔震结构参数模糊优化

分别选取Bouc—Wen和退化Bouc—Wen模型描述隔震层及上部结构滞变回复力，采用虚拟激励法进行隔震结构随机响应分析。用各层最大层间位移响应和累计疲劳损伤指数建立双参数的功能状态方程，用一次二阶矩理论计算隔震结构失效概率。选用一个隔震框架作为数值算例，探讨了低频过滤器、隔震阻尼比和隔震刚度对隔震结构各子系统条件失效概率的影响。建立了隔震结构参数多目标优化模型，用失效概率确定单因素评判的隶属度，并采用最大隶属度法对隔震参数进行模糊优化。     

平扭耦联隔震体系隔震支座阻尼分布影响分析

为了研究铅芯橡胶隔震支座的阻尼分布对平扭耦联隔震体系隔震效果的影响,本文对一个三层两跨钢框架,通过调整上部结构负重块位置及下部铅芯橡胶隔震支座的分布位置,进行不同偏心工况下平扭耦联隔震体系地震模拟振动台试验,获得了不同偏心工况、不同阻尼分布情况下结构位移和加速度的时程曲线。试验和分析表明:隔震层阻尼中心与上部结构的质心位置接近,或者增大隔震层的阻尼半径,可显著地降低上部结构的扭转反应。     

磁流变智能基础隔震系统研究

本文将磁流变(MR)阻尼器与普通橡胶隔震支座相结合,组成智能基础隔震系统应用到结构控制中。在详细介绍了系统的各部分与整体运行情况后,采用LQR经典线性最优控制算法对结构进行了振动台试验研究。试验结果表明,由MR阻尼器提供可调阻尼力的智能隔震控制系统,能有效克服被动隔震最优控制频带窄的缺点,对较宽频域范围地震激励能进行有效的振动控制。其相对一般被动隔震装置,能同时减小上部结构加速度和隔震层位移.     

Analytical solution of seismic response of base-isolated structure with supplemental inerter

Closed-form solutions are derived for the modal characteristics and seismic response of a base-isolated structure equipped with additional inerters. By simplifying the structure-isolator-inerter system in terms of the two-degree-of-freedom (2DOF) model, the modal frequencies, mode shapes, damping ratios, and participation factors of the system are derived. Consequently, analytical seismic response solutions are formulated by the modal superposition method. Utilizing these analytical solutions, an extensive parametric study has been carried out to investigate the effect of supplement inerters on both the modal characteristics and seismic response of the structure-isolator-inerter system. There is a critical inertance leading to the zero second modal participation factor (ie, the disappearance of the second modal response). The associated critical inertance ratio is derived in closed form as well. Moreover, it is observed that the reduction of deformation of isolators by increasing the inertance may be offset by the increase in relative displacements of the superstructure. To circumvent this adverse effect, an optimal range of inertance is identified whereby both the deformation of isolators and the relative displacement of the superstructure are mitigated concurrently.     

Damping‐adjusted combination rule for the response spectrum analysis of base‐isolated buildings

The classical response spectrum method continues to be the most popular approach for designing base‐isolated buildings, therefore avoiding computationally expensive nonlinear time‐history analyses. In this framework, a new method for the seismic analysis and design of building structures with base isolation system (BIS) is formulated and numerically validated, which enables one to overcome the main shortcomings of existing techniques based on the response spectrum method. The main advantages are the following: first, reduced computational effort with respect to an exact complex‐valued modal analysis, which is obtained through a transformation of coordinates in two stages, both involving real‐valued eigenproblems; second, effective representation of the damping, which is pursued by consistently defining different viscous damping ratios for the modes of vibration of the coupled BIS‐superstructure dynamic system; and third, ease of use, because a convenient reinterpretation of the combination coefficients leads to a novel damping‐adjusted combination rule, in which just a single response spectrum is required for the reference value of the viscous damping ratio. The proposed approach is specifically intended for design situations where (i) the dynamic behaviour of seismic isolators can be linearised and (ii) effects of nonproportional damping, as measured by modal coupling indexes, are negligible in the BIS‐superstructure assembly. Copyright © 2012 John Wiley & Sons, Ltd.