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.     

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.     

摩擦摆隔震结构地震反应谱的计算分析

探讨了摩擦摆基底隔震结构的地震反应谱规律。采用上部结构-摩擦摆两质点模型并利用系统振动微分方程，计算绘制了设计参数(质量比、摩擦系数、滑道半径)不同取值下上部结构的绝对加速度、侧向位移和基底水平滑移反应谱。结果表明：摩擦摆系统对刚度较大的上部结构具有良好的隔震效果。摩擦系数对上部结构的加速度反应、层间水平侧移和系统滑移均有较大的影响，质量比的影响次之．而滑道半径仅对系统滑移有较为显著的作用。     

A new area for earthquake resistant engineering: the control of seismic responses of structures

This paper summarizes the origin and idea of the control of civil engineering structures and reviews the state-of-the art of recent advances in structural control both theoretically and technologically. The prospects for structural control and key research objects to remain to be solved are put forward at last. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 375–380, 1993.     

Comparative study of the inelastic response of base isolated buildings

This article presents a numeric comparative study of the inelastic structural response of base isolated buildings. The comparative study includes the following isolation systems: laminated rubber bearings, New Zealand one, pure friction and the frictional pendulum ones. The study is based on obtaining non‐linear response spectra for various design parameters using six earthquake records. Usually the base isolation of a new building seeks to maintain the structure in the linear elastic range. The response of old weak buildings or the response of new ones subjected to extreme earthquakes may not be, necessarily, in the aforementioned ideal elastic range. Consequently, it is important to characterize the response of isolated buildings responding inelastically. A conclusion from this research is that the isolators affect significantly the structural response of weak systems. Rubber isolators seem slightly less sensitive to plastification that may occur in the structure compared to friction isolators. Ductility demands in the structure are affected significantly by friction and neoprene protected systems, in particular sliding ones where larger demands are obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical modeling of MDOF structures with sliding supports using rigid‐plastic link

In this paper, the responses of multi‐degree‐of‐freedom (MDOF) structures on sliding supports subjected to harmonic or random base motions are investigated. Modeling of the friction force under the foundation raft is accomplished by using a fictitious rigid link which has a rigid–perfectly plastic material. This will result in identical equations of motion for the sliding structure, both in the sliding and non‐sliding (stick) phases which greatly simplifies the implementation of the method into a numerical algorithm. In this model the phase transition times are determined with high accuracy. This has two advantages: first, it prevents the so‐called high‐frequency oscillation of the relative velocity at the end of the sliding phase, and second, the time steps can be selected so that each falls exactly within one phase of motion. In this case, the stiffness matrix of the structure remains constant throughout each phase and thus any method for solving the non‐linear differential equations of motion (e.g. Newmark method) can be used without iteration. The proposed method, besides its simplicity, is numerically very efficient and considerably reduces the required analysis time compared with most of the other methods. Copyright © 2001 John Wiley & Sons, Ltd.     

Influence of FPS bearing properties on the seismic performance of base‐isolated structures

The paper analyzes the influence of friction pendulum system (FPS) isolator properties on the seismic performance of base‐isolated building frames. The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the FPS isolator behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. The uncertainty in the seismic input is taken into account by considering a set of natural records with different characteristics scaled to increasing intensity levels. The variation of the statistics of the response parameters relevant to the seismic performance is investigated through the nondimensionalization of the motion equation and an extensive parametric study carried out for different isolator and system properties. The proposed approach allows to explore a wide range of situations while limiting the required nonlinear response history analyses. Two case studies consisting of base‐isolated building frames described as shear‐type systems are finally investigated in order to demonstrate the capabilities of the proposed simplified model in unveiling the essential characteristics of the performance of buildings isolated with FPS bearings. Copyright © 2015 John Wiley & Sons, Ltd.     

摩擦摆隔震双层球面网壳结构的多维地震响应

将摩擦摆(FPS)引入到网壳结构的隔震控制中。文中首先阐明了FPS的工作机理和本构关系,建立了FPS隔震网壳结构的振动方程。通过双层球面网壳结构的数值算例考察了隔震和无控结构在单向和三向地震作用下的振动响应以及FPS的控制效果。研究结果表明,FPS具有良好的隔震和耗能效果,可有效地应用于球面网壳结构的振动控制。     

Development of a tunable friction pendulum system for semi‐active control of building structures under earthquake ground motions

The Friction Pendulum System (FPS) isolator is commonly used as a base isolation system in buildings. In this paper, a new tunable FPS (TFPS) isolator is proposed and developed to act as a semi‐active control system by combining the traditional FPS and semi‐active control concept. Theoretical analysis and physical tests were carried out to investigate the behavior of the proposed TFPS isolator. The experimental and theoretical results were in good agreement, both suggesting that the friction force of the TFPS isolator can be tuned to achieve seismic isolation of the structure. A series of numerical simulations of a base‐isolated structure equipped with the proposed TFPS isolator and subjected to earthquake ground motions were also conducted. In the analyses, the linear quadratic regulator (LQR) method was adopted to control the friction force of the proposed TFPS, and the applicability and effectiveness of the TFPS in controlling the structure's seismic responses were investigated. The simulation results showed that the TFPS can reduce the displacement of the isolation layer without significantly increasing the floor acceleration and inter‐story displacement of the superstructure, confirming that the TFPS can effectively control a base‐isolated structure under earthquake ground motions.     

Modelling aspects of structures isolated with the frictional pendulum system

Different modelling aspects of structures isolated using the frictional pendulum system and subjected to earthquake ground motions are studied herein. Although the vertical dynamics of these structures is given special emphasis, other effects such as large isolator deformations and bidirectional input motion are also considered. Different structural models of the FPS are developed and tested for single-storey structures and a real four-storey building frame; among them, an ‘exact’ formulation of the FPS force–deformation constitutive relationship is presented. Results show that global building responses can be computed within 20 per cent error in the mean using a simplified model that ignores the vertical motion of the building; however, structural member deformations and forces need to be computed using a model that considers such motion. This is of particular importance when there exist correlation between the horizontal and vertical components of ground motion. Further, a physical model of the FPS is introduced and used to determine the response of a real four-storey frame, including uplift and downward impact. Results from this analysis show that local column responses may vary substantially depending on the stiffness of the isolation storey and the presence of a mass at the isolation level. Such mass is capable of filtering the large increase in column shear that results from the impact of the structure after uplift. Uplift occurs at several instants of the response of the structure considered, leading to an increase in column base shear as large as 3 times the shear obtained by ignoring the vertical dynamics of the building. © 1998 John Wiley & Sons, Ltd.     

Shaking table tests of a reinforced concrete bridge pier with a low-cost sliding pendulum system

After the occurrence of various destructive earthquakes in Japan, extensive efforts have been made to improve the seismic performance of bridges. Although improvements to the ductile capacities of reinforced concrete (RC) bridge piers have been developed over the past few decades, seismic resilience has not been adequately ensured. Simple ductile structures are not robust and exhibit a certain level of damage under extremely strong earthquakes, leading to large residual displacements and higher repair costs, which incur in societies with less-effective disaster response and recovery measures. To ensure the seismic resilience of bridges, it is necessary to continue developing the seismic design methodology of RC bridges by exploring new concepts while avoiding the use of expensive materials. Therefore, to maximize the postevent operability, a novel RC bridge pier with a low-cost sliding pendulum system is proposed. The seismic force is reduced as the upper component moves along a concave sliding surface atop the lower component of the RC bridge pier. No replaceable seismic devices are included to lengthen the natural period; only conventional concrete and steel are used to achieve low-cost design solutions. The seismic performance was evaluated through unidirectional shaking table tests. The experimental results demonstrated a reduction in the shear force transmitted to the substructure, and the residual displacement decreased by establishing an adequate radius of the sliding surface. Finally, a nonlinear dynamic analysis was performed to estimate the seismic response of the proposed RC bridge pier.     

大震下被动与智能隔震结构动力可靠度的对比

对被动及智能隔震结构在“大震”条件下的动力可靠度进行探讨。将被动及智能隔震体系均取作弹塑性模型,并用退化Bouc-W en滞变模型描述上部结构的恢复力,用非退化Bouc-W en模型描述隔震层的恢复力。采用虚拟激励法计算结构的随机响应,根据我国抗震规范中“大震不倒”的设防目标,采用各层最大层间位移峰值响应和累积滞变耗能构造双参数的随机疲劳累积损伤指数,作为功能状态指标。假定各层失效相关,用串联系统计算体系动力可靠度。通过数值算例,对比了被动隔震、智能隔震与非隔震体系的条件失效概率,从动力可靠度角度显示了智能隔震体系的减震优势。     

新型滑移隔震结构模型的振动台试验研究

利用实体软钢棒作为消能限位装置,将一种摩擦性能优良的二硫化钼材料作为隔震支座的滑移材料,提出并制作了一种可以应用于框架结构既能隔震又可以消能的新型摩擦滑移隔震装置。探讨了其设计方法和应用方法,并对安装了该新型摩擦滑移隔震装置的一相似比为1:5的5层框架结构模型进行了振动台试验,测试了框架结构在单向地震波作用下的地震反应规律,分析了摩擦滑移隔震结构的加速度反应、层间剪力反应、隔震层滑移量及隔震层剪力的变化规律。结果表明:一般情况下当设防烈度为8度,Ⅱ类场地时,该隔震结构的加速度响应可降低50%左右,层间剪力响应可降低50%左右,减震效果比较明显。另外,只要确定合理的构造方案和实施方案,这种新型摩擦滑移隔震装置就能满足框架结构的隔震减震要求,可应用于实际工程结构中。     

竖向地震动对滑动摩擦隔震桥梁结构地震反应的影响

利用接触摩擦单元建立了滑动摩擦隔震桥梁支座在竖向地震动作用下的有限元模型,通过算例讨论了竖向地震动对不同支座摩擦系数和不同刚度(墩径)滑动摩擦隔震桥梁地震反应的影响,初步探讨了竖向地震动的激励方向对分析结果的影响,分析结果表明,竖向地震动对滑动摩擦隔震桥梁结构的地震反应有较大的影响,在竖向地震动较为明显地区的滑动摩擦隔震桥梁结构设计时,应予以考虑。     

结构内设备的摩擦摆隔震响应分析

基于系统耦和振动微分方程，分析了结构内摩擦摆隔震设备的响应规律和隔震效果。计算结果表明，经过合理设计的摩擦摆系统能够显著控制设备的地震绝对加速度响应从而有效提高设备的抗震可靠度。     

支座滑道半径对摩擦摆基础隔震结构地震反应的影响

对摩擦摆基础隔震结构进行了地震反应分析,研究了支座滑道半径对支座位移、楼层加速度和楼层剪力的影响,表明当支座的摩擦系数较小时,随着支座滑道半径的增大,隔震结构的自振周期增大,摩擦摆支座位移逐渐增大,结构的加速度反应和楼层剪力减小当支座的摩擦系数较大时,改变支座的滑道半径,调整基础隔震结构周期对支座位移、结构加速度反应和...     

Independent component regression for predicting the responses of biaxial base‐isolated buildings

This paper presents a regression model to predict the base displacement responses of biaxial base‐isolated buildings using independent component analysis. The model proposed utilizes multiple ground motion intensity measures from North American and Japanese earthquakes as inputs, and transforms them into an independent component space using independent component regression (ICR). Unlike other latent variable methods, such as principal component regression, ICR does not readily allow for dimensionality reduction of the components that do not contribute significantly to the explained variance of the original data set. Hence, a whitening‐step to transform the correlated variables into uncorrelated ones is introduced prior to performing ICR. Prediction results are presented and compared with the simulation results for two building models with increasing degree of complexity. The results show that the model based on ICR results in good estimates for the base displacement responses, and the standard errors remain relatively small and constant across a range of isolation periods. Copyright © 2009 John Wiley & Sons, Ltd.     

Experimental and computational verification of reasonable design formulae for base‐isolated structures

It is clear that base isolation is a sensible strategic design in attenuating the responses of a structural system induced by ground motions. The design of seismically isolated structures is mainly governed by the Uniform Building Code (UBC) published by the International Conference of Building Officials. The UBC code emphasizes a simple, statically equivalent design method that displacements of an isolated structure are concentrated at the isolation level. Therefore, the superstructure nearly moves as a rigid body and the design forces of elements above isolators are based on the behaviour of isolators at the design displacement. However, in the UBC code, the distribution of inertial (or lateral) forces over the height of the superstructure above isolation has been found to be too conservative for most isolated structures. In view of this, two simple and reasonable design formulae for the lateral force distribution on isolated structures have been proposed in this paper. Results obtained from a full‐scale isolated structure tested on the shaking table and numerical analyses of two additional examples verify the suitability of design formulae. It is illustrated that the proposed formulae can predict well the lateral force distribution on isolated structures during earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic response analysis of bridges isolated with friction pendulum bearings

A systematic method is developed for the dynamic analysis of the structures with sliding isolation which is a highly non-linear dynamic problem. According to the proposed method, a unified motion equation can be adapted for both stick and slip modes of the system. Unlike the traditional methods by which the integration interval has to be chopped into infinitesimal pieces during the transition of sliding and non-sliding modes, the integration interval remains constant throughout the whole process of the dynamic analysis by the proposed method so that accuracy and efficiency in the analysis of the non-linear system can be enhanced to a large extent. Moreover, the proposed method is general enough to be adapted for the analysis of the structures with multiple sliding isolators undergoing independent motion conditions simultaneously. The superiority of the proposed method for the analysis of sliding supported structures is verified by a three-span continuous bridge subjected to harmonic motions and real earthquakes. In addition, the side effect of excessive displacement of the superstructure induced by the sliding isolation is eliminated by replacing one of the roller supports on the abutments with hinge support. Therefore, both reductions in the forces of the substructure and the displacements of the superstructure can be achieved simultaneously. © 1998 John Wiley & Sons, Ltd.     

摩擦隔震结构中不同摩擦力模型在地震作用下结构响应分析

本文选用两种摩擦力模型来分析隔震结构的地震响应，运用newmark方法推导了隔震结构采用库仑摩擦力模型在地震作用下结构响应的计算公式。并编程计算了实例，进行了综合分析，得出质量比、摩擦系数对隔震效果的影响；并给出在其他结构参数相对稳定的条件下，滑移面摩擦系数的取值范围。