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。     

摩擦单摆支座等效摩擦系数数值仿真及试验研究

对摩擦单摆支座的主要参数等效摩擦系数进行了数值仿真及试验研究,为桥梁结构的减隔震设计提供了参考。数值仿真包括等效摩擦系数与滑动面和转动面的摩擦系数、竖向承载力及加载频率三者关系的研究,对比分析了模拟结果与试验结果。结果表明:当滑动面与转动面的摩擦系数为不同取值时,支座等效摩擦系数的模拟值略大于理论值,初步验证了支座等效摩擦系数理论公式的正确性;通过模拟结果与试验结果的对比分析,进一步验证了该理论公式的合理性。     

层间滑移隔震结构地震作用有限元分析

将二硫化钼作为摩擦材料设计出一种带限位器的滑移隔震支座。根据多层框架结构变形的特点,给出适用于滑移框架隔震结构的计算模型,推导出层间滑移隔震结构的运动方程。运用SAP2000有限元软件建立一层间滑移框架隔震结构的有限元模型,对比分析El Centro地震波下摩擦系数和隔震层位置不同时隔震结构的地震反应。结果表明,上部结构的动力反应随摩擦系数的增加而不断增大,滑移隔震结构的减震效果逐渐减弱,但隔震层的滑移量却在不断减小;摩擦系数的选取应综合考虑减震效果和隔震层滑移量两个因素。随着隔震层的增高,结构的加速度反应和层间位移反应整体上呈增大趋势,隔震效果不断减弱,且隔震层的加速度值下部层比上部层要大得多,一层隔震和三层隔震时的变形主要集中于隔震层,而五层隔震时结构层间位移并未出现突变,说明隔震层设置在较高位置处对结构体系的影响较小。     

村镇建筑砌体结构滑移隔震性能研究1

村镇建筑多以砖混结构为主,抗震性能相对较弱,砂垫层摩擦滑移隔震技术由于诸多优点较适合广大农村建筑.本文介绍了砂垫层基础滑移隔震的设计原则和分析模型,以常见的两层砖混结构为例,采用Abaqus有限元软件分析不同摩擦系数、不同加速度峰值下隔震层的滑移,并在此基础上确定隔震层在多遇和罕遇地震作用下的摩擦系数及滑移量建议限值;通过验算不同砂浆的抗震受剪承载力,得出不同摩擦力作用下满足抗震受剪承载力的最低砂浆标准,所得结论对农村滑移隔震建筑的选材具有一定参考意义.     

单轴平扭耦联基础隔震结构动力简化分析

为了建立单轴平扭耦联基础隔震结构的动力简化分析方法,探讨了影响结构扭转反应的参数取值规律,首先基于层单元模型,通过假定上部结构楼层回转半径、偏心距、弹力半径相等,推导了单轴平扭耦联基础隔震结构线性化的动力计算方程;其次,运用该简化分析方程,通过一算例进行了动力响应的参数分析。结果表明:调整隔震层刚心使其与上部结构质心位置接近,可显著降低偏心隔震结构扭转反应;增大隔震层刚度半径及阻尼半径可有效减少或抑制结构扭转反应;所建简化分析方程能有效模拟偏心隔震结构动力响应。     

Characterizing friction in sliding isolation bearings

The force–displacement behavior of the Friction Pendulum? (FP) bearing is a function of the coefficient of sliding friction, axial load on the bearing and effective radius of the sliding surface. The coefficient of friction varies during the course of an earthquake with sliding velocity, axial pressure and temperature at the sliding surface. The velocity and axial pressure on the bearing depend on the response of the superstructure to the earthquake shaking. The temperature at an instant in time during earthquake shaking is a function of the histories of the coefficient of friction, sliding velocity and axial pressure, and the travel path of the slider on the sliding surface. A unified framework accommodating the complex interdependence of the coefficient of friction, sliding velocity, axial pressure and temperature is presented for implementation in nonlinear response‐history analysis. Expressions to define the relationship between the coefficient of friction and sliding velocity, axial pressure, and temperature are proposed, based on available experimental data. Response‐history analyses are performed on FP bearings with a range of geometrical and liner mechanical properties and static axial pressure. Friction is described using five different models that consider the dependence of the coefficient of friction on axial pressure, sliding velocity and temperature. Frictional heating is the most important factor that influences the maximum displacement of the isolation system and floor spectral demands if the static axial pressure is high. Isolation system displacements are not significantly affected by considerations of the influence of axial pressure and velocity on the coefficient of friction. Copyright © 2014 John Wiley & Sons, Ltd.     

Spherical sliding isolation bearings with adaptive behavior: Theory

The principles of operation and force–displacement relationships of three novel spherical sliding isolation bearings are developed in this paper. These bearings are completely passive devices, yet exhibit adaptive stiffness and adaptive damping. That is, the stiffness and damping change to predictable values at calculable and controllable displacement amplitudes. The primary benefit of adaptive behavior is that a given isolation system can be separately optimized for multiple performance objectives and/or multiple levels of ground shaking. With the devices presented here, this is accomplished using technology that is inherently no more complex than what is currently used by the civil engineering profession. The internal construction consists of various concave surfaces and behavior is dictated by the different combinations of surfaces upon which sliding can occur over the course of motion. As the surfaces upon which sliding occurs change, the stiffness and effective friction change accordingly. A methodology is presented for determining which surfaces are active at any given time based on the effective radius of curvature, coefficient of friction and displacement capacity of each sliding surface. The force–displacement relationships and relevant parameters of interest are subsequently derived based on the first principles. Copyright © 2007 John Wiley & Sons, Ltd.     

Control of structures with friction controllable sliding isolation bearings

A friction controllable sliding isolation system was developed and experimentally and analytically investigated by Feng et al. (Feng, Q., Shinozuka, M. & Fujii, S. A. friction controllable sliding isolation system. J. Eng. Mech., ASCE, 1993, 119(6), in press), the control algorithm having been developed based on a key assumption that the structural motion is always in the sliding phase. However, this assumption may not be valid in cases where the sticking phase of the structural motion dominates. In this paper a new control algorithm is developed including the effects of stick—slip phases. Effect of time delay is included in the formulation. The developed algorithm is used to evaluate the accuracy and limitations of the algorithm with continuous sliding assumption. Response to various earthquake motions, simulated using the two control algorithms, is presented. Comparisons with experimental results are also presented. Effects of stick—slip phases on the response are evaluated.     

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。     

罕遇地震下村镇建筑复合隔震系统的地震响应特征及设计参数

为研究罕遇地震下复合隔震村镇建筑的地震响应特征及设计参数,采用ABAQUS有限元软件建立了复合隔震结构、滑移隔震结构、砂垫层隔震结构以及传统的砌体结构四种模型,通过对比4种模型在不同滑移层摩擦系数及不同地震烈度下的加速度、位移及底部剪力等动力响应差异,得出复合隔震体系的地震响应特征及主要设计参数。结果表明:复合隔震体系具有最优的隔震效果,且滑移层摩擦系数越小,地震烈度越大,隔震效果越好。根据预设40%隔震率的要求,确定出不同抗震设防烈度区的滑移层摩擦系数取值范围。     

非平整曲面隔震结构的多质点计算模型及地震响应研究

针对强地震作用下隔震结构隔震层变形过大的现象提出了曲面隔震结构体系,该结构隔震层为曲面布置,在地震和结构重力作用下,上部结构可绕曲率中心进行曲面运动。建立了非平整曲面隔震结构多质点计算分析模型,通过数值分析进一步研究非平整曲面隔震层的曲率半径对结构地震响应的影响规律。分析结果表明:在罕遇地震作用下,曲面隔震结构对隔震层及上部结构的位移控制效果显著,同时当曲率半径为10~15倍重心高度时具有良好的隔震效果。     

On the rocking–sliding instability of rigid blocks under ground excitation: Some new findings

Rocking (overturning) instability analyses of rigid blocks based on the assumption that the friction between the block and the ground is sufficiently large to exclude the effect of sliding, are reconsidered by including the effect in question. Both modes of overturning instability – without impact and after one impact – are thoroughly discussed in connection with small sliding, whose value depends on the values of kinetic (dry) friction coefficient and the external frequency excitation. Using an energy approach the analytical derivation of the nonlinear differential equations of motion of free-standing rigid blocks under one-sine ground pulse including the effect of sliding, are comprehensively established. The serious difficulties in solving this problem on one hand the change of the kinetic friction coefficient during the motion and on the other hand the reliable evaluation of the actual friction effect when rocking is included, are effectively confronted. This is achieved through a reliable approximation of an equivalent (reduced) coefficient assuming that the major part of friction takes place from the initiation of motion and terminates shortly after the onset of rocking. In cases of slender blocks closed form solutions for overturning due to simultaneous rocking–sliding without or after one impact, are conveniently derived. Among other findings, it was explored that the single block in question for small values of the external frequency (long periods of excitation) the sliding effect is beneficial (stabilizing the block), while for large values of external frequency this effect is detrimental (destabilizing the block).     

农居结构隔震技术研究现状

从地基隔震、基础隔震和混合隔震三类隔震技术3个方面分别阐述了农居结构隔震技术的国内外研究现状。重点介绍了常用的摩擦滑移隔震技术以及隔震滑移位移问题;针对农居工程建设的现状,提出了几个亟待解决或需进一步研究完善的问题。可为从事该研究和设计工作的相关人员提供一定的参考。     

Seismic fragility and reliability of structures isolated by friction pendulum devices: seismic reliability‐based design (SRBD)

The paper deals with the seismic reliability of elastic structural systems equipped with friction pendulum isolators (friction pendulum system). The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the friction pendulum system device behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. With reference to medium soil condition, the uncertainty in the seismic inputs is taken into account by considering a set of artificial records, obtained through Monte Carlo simulations within the power spectral density method, with different frequency contents and characteristics depending on the soil dynamic parameters and scaled to increasing intensity levels. The sliding friction coefficient at large velocity is also considered as random variable modeled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities exceeding different limit states related to both r.c. superstructure and isolation level defining the seismic fragility curves through an extensive parametric study carried out for different structural system properties. Finally, considering the seismic hazard curves related to a site near L'Aquila (Italy), the seismic reliability of the r.c. superstructure systems is evaluated, and seismic reliability‐based design abacuses are derived with the aim to define the radius in plan of the friction pendulum devices in function of the structural properties and reliability level expected. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

应力增量触发断层岩体能量释放模拟与地震成因探讨—以龙门山断裂带为例

本文以龙门山断裂带为背景,基于岩体应变能基本理论,使用FLAC软件模拟地震能量源和能量释放形式,计算结果显示:在0.01 MPa水平应力增量作用下,龙门山断裂带及附近区域可释放的应变能约为3.24×1013 J;使得断层面之间发生滑移,克服断层面滑动摩擦所需消耗的能量约为2.10×1013 J;岩体在重力方向上产生位移,克服重力做功所消耗的能量约为1.14×1013 J。由此可推断:在一定区域内,应力触发释放能量值与克服断层面滑动摩擦和克服重力做功所消耗的能量之和大致相当;应变能可能会在某一区域范围内集中释放,形成地震效应。本次应力增量触发断层周围岩体能量释放事件中,在映秀—北川断裂与灌县—安县断裂之间的局部区域集中释放的能量为7.67×1012 J,相当于一次M_S5.39地震发生所释放的能量。      

Seismic isolation of buildings with sliding concave foundation (SCF)

In this paper, a new base isolation system, namely the sliding concave foundation (SCF), is introduced and the behaviour of the buildings using such a system is theoretically investigated. A building supported on the new system behaves like a compound pendulum during seismic excitation. The pendulum behaviour accompanied by the large radius of foundation curvature shifts the fundamental period of the system to a high value (e.g. more than 8sec), in a frequency range where none of the previously recorded earthquakes had considerable energy. This results in a large decrease in the structural responses. Since small friction forces are essential on the contact surfaces, PTFE sheets can be used as sliding surfaces. Although the pure frictional sliding systems have the same efficiency as the SCF, in reducing the responses of the superstructure, the main advantage of the new system is a significant decrease in sliding displacement. The performance of the SCF subjected to a number of harmonic and non‐harmonic base excitations is studied and its ability to reduce the structural responses is examined. Some numerical examples are solved for a single‐degree‐of‐freedom (SDOF) structure and the responses are compared with the responses of the same SDOF structure on a fixed base or a pure frictional sliding support system. The comparisons confirm the effectiveness of the new system. Copyright © 2002 John Wiley & Sons, Ltd.     

土体-结构界面接触对地下结构动力反应的影响

迄今为止,关于土体与结构交界面的接触效应对地下结构地震反应的影响尚未引起研究者们的重视,成果鲜有报道。本文基于接触面对法和非线性有限元波动分析方法,建立了考虑土体与结构界面接触效应的地下结构非线性地震反应分析模型和计算方法,并利用大型有限元软件ANSYS进行了求解。分析结果表明：土体与结构界面的接触效应对地下结构地震反应有明显影响,可能增大地下结构节点的峰值加速度、峰值位移和峰值应力反应;随着接触摩擦系数的增大,接触点的相对滑移逐渐减小,而接触应力的变化则无明显规律。