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1.
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.  相似文献   

2.
It has been shown that the use of base isolation not only attenuates the response of a primary structural system but also reduces the response of a secondary system mounted on or within the main structure. The isolation system, superstructure and equipment may be made of different materials with significantly different energy dissipation characteristics such that the damping matrix for the combined system is non-classical and can only be approximately expressed by modal damping ratios if the classical mode method is used for analysis. The object of this paper is to evaluate the accuracy of this procedure in approximating the responses of base-isolated structures and internal equipment. The complex mode method can provide exact solutions to problems with non-classical damping and is used here to find the exact response of the isolation-superstructure-equipment system. The entire system is assumed to be linear elastic with viscous damping and the superstructure is assumed to be proportionally damped so that the deformation of the superstructure can be expressed in terms of its classical modes. Recognizing that the ratio of the equipment mass to the structural mass and the ratio of the stiffness of the isolation system to the superstructural stiffness are both small, perturbation methods are used to find the response. This study shows that the response of base-isolated structures can be determined by the classical mode method to some degree of accuracy, but the higher frequency content is distorted. The equipment response derived by the classical mode method is much smaller than the exact solution so that the complex mode method should be applied to find equipment response.  相似文献   

3.
In this paper, a new hybrid control technique, based on a combination of base-isolation and semi-active variable stiffness/damping in a superstructure, is presented. To illustrate the efficiency of the proposed control system, model tests on a mini-electromagnetic shaking table and a numerical simulation were performed. The test and numerical calculation results indicate that this new hybrid control mode with additional damping and smaller additional stiffness can achieve a better control efficiency.  相似文献   

4.
孙臻  刘伟庆 《地震工程学报》2020,42(6):1369-1376
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。  相似文献   

5.
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.  相似文献   

6.
The recorded earthquake response of a base-isolated building—the Foothill Communities Law and Justice Center in Rancho Cucamonga—shaken by the 1985 Redlands earthquake (ML 4–8) is discussed and analysed by employing system identification techniques. The calculated response of one-dimensional and three-dimensional linear structural models is fitted to the recorded motions of the superstructure using the ‘modal minimization method’ for structural identification, in order to determine optimal estimates of the parameters of the dominant modes of the building. Simple one-dimensional analyses are used to identify also the effective values of key parameters (e.g. damping) of the isolation system. Furthermore, the recorded motions obtained from the densely instrumented foundation (i.e. below the isolation bearings) of the structure and from the free-field station located 330 ft
  • 1 1 ft =0.3048 m; 1 mile=1.609 km.
    • from the building show how the presence of the structure affects the incoming seismic waves. It is observed that the transverse component of motion (i.e. the component which is perpendicular to the long dimension of the plan of the building) is affected by the presence of the structure considerably more than the longitudinal component. Factors contributing to this effect are the extreme length of the structure (414 ft) and the rotational motions of the superstructure caused by the spatial variability of ground motion. It is pointed out that, despite the fact that the shift in the effective frequency of the structure induced by the isolation was very small, the elastomeric bearings were very effective in reducing the accelerations transmitted to the structure. This is attributed to the damping capacity of the isolation. Based on the observed response of the building to this small earthquake it can be stated with confidence that the structure performed according to expectations.  相似文献   

    7.
    There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

    8.
    In real‐time hybrid simulations (RTHS) that utilize explicit integration algorithms, the inherent damping in the analytical substructure is generally defined using mass and initial stiffness proportional damping. This type of damping model is known to produce inaccurate results when the structure undergoes significant inelastic deformations. To alleviate the problem, a form of a nonproportional damping model often used in numerical simulations involving implicit integration algorithms can be considered. This type of damping model, however, when used with explicit integration algorithms can require a small time step to achieve the desired accuracy in an RTHS involving a structure with a large number of degrees of freedom. Restrictions on the minimum time step exist in an RTHS that are associated with the computational demand. Integrating the equations of motion for an RTHS with too large of a time step can result in spurious high‐frequency oscillations in the member forces for elements of the structural model that undergo inelastic deformations. The problem is circumvented by introducing the parametrically controllable numerical energy dissipation available in the recently developed unconditionally stable explicit KR‐α method. This paper reviews the formulation of the KR‐α method and presents an efficient implementation for RTHS. Using the method, RTHS of a three‐story 0.6‐scale prototype steel building with nonlinear elastomeric dampers are conducted with a ground motion scaled to the design basis and maximum considered earthquake hazard levels. The results show that controllable numerical energy dissipation can significantly eliminate spurious participation of higher modes and produce exceptional RTHS results. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

    9.
    A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (Fy/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

    10.
    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 (MCER) 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 MCER-level far-fault motions, whereas minor structural damage is observed under MCER-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.  相似文献   

    11.
    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.  相似文献   

    12.
    殷琳  楼梦麟  康帅 《地震工程学报》2020,42(6):1409-1416,1456
    通过二维数值计算，讨论合理建立阻尼矩阵对高重力坝时域内进行地震反应计算的重要性。首先，以4个不同坝高的混凝土重力坝为计算对象，将三种地震波作为水平输入，解得6种不同的阻尼矩阵形式下坝体的地震反应。然后以频域内解为标准，研究各种阻尼矩阵的合理性。研究结果表明：坝高超过250 m高的重力坝在时域内进行的地震反应计算是长周期系统的动力分析问题，应重视阻尼矩阵的建模方式，不宜采用单频率参数的质量比例阻尼矩阵和刚度比例阻尼矩阵，应采用双频率参数的Rayleigh阻尼矩阵，在确定2个频率参数时除采用坝体基频外还应考虑激振地震波的频谱特性以获得合理的坝体地震反应计算结果。  相似文献   

    13.
    In the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with useful analytical tools to design Rayleigh damping model with good control on the damping ratios throughout inelastic analysis. To that end, a review of the literature dedicated to Rayleigh damping within these last two decades is first presented; then, practical tools to control the modal damping ratios throughout the time history analysis are developed; a simple example is finally used to illustrate the differences resulting from the use of either initial or tangent stiffness‐based Rayleigh damping model. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

    14.
    Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L b , π/L b ], where L b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.  相似文献   

    15.
    Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vortical (geostrophic) and wave (ageostrophic) modes of a three-dimensional (3D) rotating stratified fluid as a function of ε = f/N, where f is the Coriolis parameter and N is the Brunt–Vaisala frequency. Throughout, we employ a random large-scale forcing in a unit aspect ratio domain and set these parameters such that the Froude and Rossby numbers are roughly comparable and much less than unity. Working in regimes characterized by moderate Burger numbers, i.e. Bu = 1/ε2 < 1 or Bu ≥ 1, our results indicate profound change in the character of vortical and wave mode interactions with respect to Bu = 1. Indeed, previous analytical work concerning the qualitatively different nature of these interactions has been in limiting conditions of rotation or stratification domination (i.e. when Bu ? 1 or Bu ? 1, respectively). As with the reference state of ε = 1, for ε < 1 the wave mode energy saturates quite quickly and the ensuing forward cascade continues to act as an efficient means of dissipating ageostrophic energy. Further, these saturated spectra steepen as ε decreases: we see a shift from k ?1 to k ?5/3 scaling for k f < k < k d (where k f and k d are the forcing and dissipation scales, respectively). On the other hand, when ε > 1 the wave mode energy never saturates and comes to dominate the total energy in the system. In fact, in a sense the wave modes behave in an asymmetric manner about ε = 1. With regard to the vortical modes, for ε ≤ 1, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a k ?3 scaling for k f < k < k d and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all k < k f . In contrast, for ε > 1 and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem, though always present, plays an energetically smaller role in the overall dynamics. Combining the vortical and wave modes, the total energy for k > k f and ε ≤ 1 shows a transition as k increases wherein the vortical modes contain a large portion of the energy at large scales, while the wave modes dominate at smaller scales. There is no such transition when ε > 1 and the wave modes dominate the total energy for all k > k f .  相似文献   

    16.
    The damping‐solvent extraction method for the analysis of unbounded visco‐elastic media is evaluated numerically in the frequency domain in order to investigate the influence of the computational parameters—domain size, amount of artificial damping, and mesh density—on the accuracy of results. An analytical estimate of this influence is presented, and specific questions regarding the influence of the parameters on the results are answered using the analytical estimate and numerical results for two classical problems: the rigid strip and rigid disc footings on a visco‐elastic half‐space with constant hysteretic material damping. As the domain size is increased, the results become more accurate only at lower frequencies, but are essentially unaffected at higher frequencies. Choosing the domain size to ensure that the static stiffness is computed accurately leads to an unnecessarily large domain for analysis at higher frequencies. The results improve by increasing artificial damping but at a slower rate as the total (material plus artificial) damping ratio ζt gets closer to 0.866. However, the results do not deteriorate significantly for the larger amounts of artificial damping, suggesting that ζt≈0.6 is appropriate; a larger value is not likely to influence the accuracy of results. Presented results do not support the earlier suggestion that similar accuracy can be achieved by a large bounded domain with small damping or by a small domain with larger damping. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

    17.
    Abstract

    We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983).

    We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude δvy exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber ka are damped over a timescale kuRe 0|δ vy/vA |?2, Re 0 being the Reynolds number corresponding to the Braginskij viscosity coefficient η0 and vA the Alfvén speed. Dissipation is most effective where β = (vs /vA) 2 ≈ 1, vs being the speed of sound.  相似文献   

    18.
    The effects of soil–structure interaction (SSI) while designing the liquid column damper (LCD) for seismic vibration control of structures have been presented in this study. The formulation for the input–output relation of a flexible‐base structure with attached LCD has been presented. The superstructure has been modelled by a single‐degree‐of‐freedom (SDOF) system. The non‐linearity in the orifice damping of the LCD has been replaced by equivalent linear viscous damping by using equivalent linearization technique. The force–deformation relationships and damping characteristics of the foundation have been described by complex valued impedance functions. Through a numerical stochastic study in the frequency domain, the various aspects of SSI on the functioning of the LCD have been illustrated. A simpler approach for studying the LCD performance considering SSI, using an equivalent SDOF model for the soil–structure system available in literature by Wolf (Dynamic Soil–Structure Interaction. International Series in Civil Engineering and Engineering Mechanics. Prentice‐Hall: Englewood Cliffs, NJ, 1985) has also been presented. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

    19.
    The stationary response of base-isolated buildings subjected to earthquake excitation is studied. The frequency content of earthquake input is described by the Clough-Penzien spectral model. The response parameters of interest are (1) the root-mean-square (RMS) displacement σx of the basement relative to the foundation (i.e. shear deformation of the isolation system) and (2) the ratio (σa/σa0) of the RMS value of the absolute acceleration at the roof of the isolated structure over the corresponding value when the isolation system is locked. The variation of these response parameters with the effective frequency f0 of the base-isolated structure is investigated. As input, earthquakes with moment magnitudes M = 7-3 and M = 6-0 are considered. The acceleration spectra corresponding to these two earthquake sizes have pronouncedly different frequency content over the frequency range 0–1-1–0 Hz which is of primary importance for base-isolated structures. An important conclusion that comes from these analyses is that confidence in the effectiveness of a base-isolated system should be based primarily on its capacity to absorb/dissipate energy and less on its influence in shifting the fundamental period of the structure out of the range of dominant earthquake energy.  相似文献   

    20.
    The capability of the numerical discontinuous deformation analysis (DDA) method to perform site response analysis is tested. We begin with modeling one‐dimensional shear wave propagation through a stack of horizontal layers and compare the obtained resonance frequency and amplification with results obtained with SHAKE. We use the algorithmic damping in DDA to condition the damping ratio in DDA by changing the time step size and use the same damping ratio in SHAKE to enable meaningful comparisons. We obtain a good agreement between DDA and SHAKE, even though DDA is used with first order approximation and with simply deformable blocks, proving that the original DDA formulation is suitable for modeling one‐dimensional wave propagation problems. The ability of DDA to simulate wave propagation through structures is tested by comparing the resonance frequency obtained for a multidrum column when modeling it with DDA and testing it in the field using geophysical site response survey. When the numerical control parameters are properly selected, we obtain a reasonable agreement between DDA and the site response experiment in the field. We find that the choice of the contact spring stiffness, or the numerical penalty parameter, is directly related to the obtained resonance frequency in DDA. The best agreement with the field experiment is obtained with a relatively soft contact spring stiffness of k = (1/25)(E × L) where E and L are the Young's modulus and mean diameter of the drums in the tested column. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

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