Implementation and application of the unconditionally stable explicit parametrically dissipative KR‐α method for real‐time hybrid simulation

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.     

Effects of near‐fault ground motions on the nonlinear dynamic response of base‐isolated r.c. framed buildings

Near‐fault ground motions are characterized by long‐period horizontal pulses and high values of the ratio between the peak value of the vertical acceleration, PGA_V, and the analogous value of the horizontal acceleration, PGA_H, which can become critical for base‐isolated (BI) structures. The objective of the present work is to check the effectiveness of the base isolation of framed buildings when using High‐Damping‐Rubber Bearings (HDRBs), taking into consideration the combined effects of the horizontal and vertical components of near‐fault ground motions. To this end, a numerical investigation is carried out with reference to BI reinforced concrete buildings designed according to the European seismic code (Eurocode 8). The design of the test structures is carried out in a high‐risk region considering (besides the gravity loads) the horizontal seismic loads acting alone or in combination with the vertical ones and assuming different values of the ratio between the vertical and horizontal stiffnesses of the HDRBs. The nonlinear seismic analysis is performed using a step‐by‐step procedure based on a two‐parameter implicit integration scheme and an initial‐stress‐like iterative procedure. At each step of the analysis, plastic conditions are checked at the potential critical sections of the girders (i.e. end sections of the sub‐elements in which a girder is discretized) and columns (i.e. end sections), where a bilinear moment–curvature law is adopted; the effect of the axial load on the ultimate bending moment (M‐N interaction) of the columns is also taken into account. The response of an HDRB is simulated by a model with variable stiffness properties in the horizontal and vertical directions, depending on the axial force and lateral deformation, and linear viscous damping. Copyright © 2011 John Wiley & Sons, Ltd.     

Real time hybrid simulation: from dynamic system,motion control to experimental error

Real‐time hybrid simulation (RTHS) has increasingly been recognized as a powerful methodology to evaluate structural components and systems under realistic operating conditions. It is a cost effective approach compared with large scale shake table testing. Furthermore, it can maximally preserve rate dependency and nonlinear characteristics of physically tested (non)structural components. Although conceptually very attractive, challenges do exist that require comprehensive validation before RTHS should be employed to assess complicated physical phenomena. One of the most important issues that governs the stability and accuracy of an RTHS is the ability to achieve synchronization of boundary conditions between the computational and physical substructures. The objective of this study is to propose and validate an H_∞ loop shaping design for actuator motion control in RTHS. Controller performance is evaluated in the laboratory using a worst‐case substructure proportioning scheme. A modular, one‐bay, one‐story steel moment resisting frame specimen is tested experimentally. Its deformation is kept within the linear range for ready comparison with the reference closed‐form solution. Both system analysis and experimental results show that the proposed H_∞ strategy can significantly improve both the stability limit and test accuracy compared with several existing strategies. Another key feature of the proposed strategy is its robust performance in terms of unmodeled dynamics and uncertainties, which inevitably exist in any physical system. This feature is essential to enhance test quality for specimens with nonlinear dynamic behavior, thus ensuring the validity of the proposed approach for more complex RTHS implementations. Copyright © 2012 John Wiley & Sons, Ltd.     

金属橡胶支座剪切性能试验研究

针对一种金属橡胶支座,研究其剪切性能。进行3种压应力下的拟静力试验,分析竖向压力和水平剪切变形对支座剪切性能的影响;以试验数据为基准,建立支座剪切性能与压应力之间的相关性经验公式,提出能够近似模拟试验曲线的三线性恢复力模型。试验研究表明,随着支座剪切变形的增大,支座等效刚度及耗能增大,等效阻尼比减小,屈服力基本保持不变,滞回曲线由梭形逐渐变为反S型,当剪切应变大于25%时支座出现刚度硬化现象;随着支座压应力增大,支座的耗能、屈服力、等效刚度及等效阻尼比均增大。     

Inelastic response of RC frame buildings with seismic isolation

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 (F_y/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.     

方形多铅芯橡胶支座力学性能研究

本文通过对方形多铅芯橡胶支座竖向压缩性能试验,水平剪切性能试验以及其等效刚度、屈服强度、屈服后刚度、等效阻尼比等水平特征参数与水平剪切应变和竖向压应力的关系,特别是对其在不同方向上压缩剪切变形状态下的性能试验,分析了这种隔震支座各种水平特征参数在不同方向上变化的相关规律。得出在这种类型橡胶隔震支座在双向水平荷载同时作用下,竖向性能和水平性能较为稳定,是较为理想的桥梁结构的减隔震装置。     

Accurate real‐time hybrid earthquake simulations on large‐scale MDOF steel structure with nonlinear viscous dampers

This paper presents real‐time hybrid earthquake simulation (RTHS) on a large‐scale steel structure with nonlinear viscous dampers. The test structure includes a three‐story, single‐bay moment‐resisting frame (MRF), a three‐story, single‐bay frame with a nonlinear viscous damper and associated bracing in each story (called damped braced frame (DBF)), and gravity load system with associated seismic mass and gravity loads. To achieve the accurate RTHS results presented in this paper, several factors were considered comprehensively: (1) different arrangements of substructures for the RTHS; (2) dynamic characteristics of the test setup; (3) accurate integration of the equations of motion; (4) continuous movement of the servo‐controlled hydraulic actuators; (5) appropriate feedback signals to control the RTHS; and (6) adaptive compensation for potential control errors. Unlike most previous RTHS studies, where the actuator stroke was used as the feedback to control the RTHS, the present study uses the measured displacements of the experimental substructure as the feedback for the RTHS, to enable accurate displacements to be imposed on the experimental substructure. This improvement in approach was needed because of compliance and other dynamic characteristics of the test setup, which will be present in most large‐scale RTHS. RTHS with ground motions at the design basis earthquake and maximum considered earthquake levels were successfully performed, resulting in significant nonlinear response of the test structure, which makes accurate RTHS more challenging. Two phases of RTHS were conducted: in the first phase, the DBF is the experimental substructure, and in the second phase, the DBF together with the MRF is the experimental substructure. The results from the two phases of RTHS are presented and compared with numerical simulation results. An evaluation of the results shows that the RTHS approach used in this study provides a realistic and accurate simulation of the seismic response of a large‐scale structure with rate‐dependent energy dissipating devices. Copyright © 2015 John Wiley & Sons, Ltd.     

An improved rheology model for the description of the rate-dependent cyclic behavior of high damping rubber bearings

An improved rheology model, inspired from explicit experiments is conceived to represent rate-dependent cyclic shear behavior of high damping rubber bearings at subzero and room temperatures. Total stress has been decomposed into nonlinear rate independent elasto-plastic stress, nonlinear elastic stress and nonlinear visco-elasto-plastic overstress branches. To represent nonlinear viscosity behavior, ‘overstress branch’ has been generalized by putting linear elastic spring in parallel to nonlinear elasto-plastic model, placed in series with nonlinear dashpot. Constitutive relations for model elements have been designated for respective fundamental phenomenon observed in constant strain rate experiments. An optimum calculation approach is developed to determine a unique set of overstress parameters capable not only of representing constant strain rate cyclic tests but also sinusoidal tests with variable input strain rates. Essential abilities of the proposed model and adequacy of estimated parameters have been confirmed by comparing numerical simulation results with experiments conducted at −30 °C, −10 °C and 23 °C.     

橡胶座非线性弹性回转剪切特性的理论和试验研究

本文系统地研究分析了橡胶隔震支座(以下简称为橡胶座)回转、剪切相关的基础理论,提出了能够反映剪切应变特性的非线性回转刚度等概念。基于非线性回转刚度与Haringx弹性体计算模型,给出了计算橡胶座回转、压缩、剪切特性的计算理论。针对回转剪切计算理论采用天然橡胶和铅芯橡胶座原型试件进行了回转刚度试验,以及变动回转、变动压力等状态的剪切试验,结果表明建立的计算理论能够较理想地分析橡胶座回转剪切相关的力和弯矩等力学特性。     

瑞利阻尼对砂土场地非线性地震响应的影响分析

在地震荷载作用下,自由场地会产生土体侧向变形和地表响应放大现象。由于土体的高度非线性,计算自由场地地震响应时,不同的阻尼比及剪切模量取值是造成其计算结果与试验结果相差较大的原因之一。目前动力计算常采用瑞利阻尼方法,其系数取值会在一定程度上影响计算结果。选用两模态简化瑞利阻尼系数计算方法,分析土体阻尼比及控制频率的取值对计算结果的影响,对比离心机模型试验,利用开源有限元平台OpenSees,采用适合于土体动力分析的多屈服面本构模型(PDMY),建立剪切梁模型模拟三维自由场地,并分析瑞利阻尼参数对自由场地地震响应和侧向变形计算结果的影响。结果表明,针对相对密度为60%的Nevada干砂,阻尼比为4%、控制频率比为5时,场地响应计算结果与试验结果较为符合。综合分析显示场地非线性响应时域计算时,应特别注意选用的瑞利阻尼参数值。     

小应变硬化模型(HSS)在Rayleigh波作用下场地响应分析中的应用

为研究冲击荷载或地震作用下产生的,以Rayleigh波为主的面波对浅层地表土体动力响应特征以及数值模拟中土层阻尼的设置方法,以厦门地区浅层的素填土及粉质黏土为研究对象,采用有限元动力分析,土体本构采用小应变硬化模型(HSS),利用模型本身的滞回环特性,输入变化的小应变参数,考察HSS模型的小应变参数对场地动力响应的影响,并与土体采用摩尔-库伦模型结合Rayleigh阻尼("MC+Rayleigh阻尼")的计算结果进行对比。研究表明:当采用带有滞回环的HSS模型时,波速随初始剪切模量Gref0的增大而增大,但振幅减小,残余变形量也有所减小;小应变参数γ0.7对波的影响较小;HSS模型能够给出残余变形量,而"MC+Rayleigh阻尼"由于本构模型为理想弹塑性模型,在卸载重加载条件下表现为纯弹性行为,无法反映出卸载重加载过程中塑性应变的积累及其累积阻尼效应;但HSS模型还不能够全面反映循环加载作用下塑性体积应变的累积,因此在考虑滞回阻尼的基础上,仍然建议借助Rayleigh阻尼来更加全面地模拟土体的实际阻尼特性。     

橡胶砂芯组合砌块动力特性及隔震效应数值分析

在混凝土空心砌块的空腔中填入橡胶砂形成的组合砌块（RSMCB）可作为简易隔震层应用于村镇建筑防震减灾。建立RSMCB的三维数值分析模型,进行循环剪切试验以及隔震分析,研究不同橡胶砂配比、竖向压应力、盖板尺寸和盖板埋深对隔震砌块动刚度和阻尼比的影响,分析不同的上部配重、输入地震波、橡胶砂配比、盖板尺寸和铺设方式对RSMCB垫层隔震效果的影响。结果表明:（1）橡胶砂芯组合砌块应变软化现象明显。（2）RSMCB的水平动刚度随橡胶砂配比增大而减小,随盖板埋深、盖板尺寸以及竖向压应力的增大而增大。（3）阻尼比随橡胶砂配比、竖向压应力、盖板尺寸和埋深的增大而减小,橡胶砂芯组合砌块隔震消能效果显著。在隔震数值模拟中,输入加速度在经过橡胶砂芯组合砌块垫层过滤后均有不同程度的降低,且被过滤掉大部分高频波。隔震效应随着盖板尺寸的增大而减小,上部结构配重越大,隔震效应越明显,橡胶砂配比为30%时RSMCB垫层隔震效应更好。橡胶砂芯组合砌块符合在村镇欠发达地区低成本隔震的要求,表现出广阔的应用前景。     

A study on using pre‐bent steel strips as seismic energy‐dissipative devices

Buckling is usually conceived as an unstable structural behavior leading to lateral instability of axially loaded members, if not properly supported. However, a pre‐bent strip would become an excellent seismic energy‐dissipative device if it is deformed in a guided direction and range. Geometrically large lateral deformation of the steel strips in buckling leads to inelastic behavior of the material and dissipates energy as a consequence. The purpose of this study is to propose a new type of seismic damper in the form of braces based on pre‐bent steel strips. The nonlinear elastic stiffness of monotonously loaded pre‐bent strips in both compression and tension is derived. The energy‐dissipative characteristics of the proposed damping device are investigated via component tests under cyclic loads. Experimental results indicate that the force–displacement relationship of pre‐bent strips in cyclic loads exhibits mechanical characteristics of displacement‐dependent dampers. A series of seismic performance tests has been conducted further to verify the feasibility and effectiveness of using the proposed device as seismic dampers. Encouraging test results have been obtained, suggesting feasibility of the proposed device for earthquake‐resistant design. Copyright © 2008 John Wiley & Sons, Ltd.     

Study on effects of damping in laminated rubber bearings on seismic responses for a ⅛ scale isolated test structure

The effects of damping in various laminated rubber bearings (LRB) on the seismic response of a ?‐scale isolated test structure are investigated by shaking table tests and seismic response analyses. A series of shaking table tests of the structure were performed for a fixed base design and for a base isolation design. Two different types of LRB were used: natural rubber bearings (NRB) and lead rubber bearings (LLRB). Three different designs for the LLRB were tested; each design had a different diameter of lead plug, and thus, different damping values. Artificial time histories of peak ground acceleration 0.4g were used in both the tests and the analyses. In both shaking table tests and analyses, as expected, the acceleration responses of the seismically isolated test structure were considerably reduced. However, the shear displacement at the isolators was increased. To reduce the shear displacement in the isolators, the diameter of the lead plug in the LLRB had to be enlarged to increase isolator damping by more than 24%. This caused the isolator stiffness to increase, and resulted in amplifying the floor acceleration response spectra of the isolated test structure in the higher frequency ranges with a monotonic reduction of isolator shear displacement. Copyright © 2002 John Wiley & Sons, Ltd.     

低硬度橡胶隔震支座基本力学性能及恢复力特性

本研究对低硬度橡胶隔震支座的材料性能（主要包括力学性能）进行了系统的试验开发及理论研究。研究用低硬度橡胶隔震支座包括天然橡胶隔震支座及铅芯橡胶隔震支座两大类18种规格总计近30个大直径隔震支座。研究内容涉及橡胶隔震支座竖向刚度、水平刚度及阻尼等基本力学性能；压缩界限，屈曲及极限剪切变形等界限性能；温度、压力、剪切变形、老化和徐变等相关性及长期特性；同时还对橡胶材料其他性能进行了系统的试验研究。本文主要介绍低硬度天然橡胶隔震支座及铅芯橡胶隔震支座的基本力学性能，如竖向、水平刚度和恢复力等特性。     

Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility

The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil.However,it is often customary to idealize the soil as rigid during the analysis of such structures.In this paper,seismic response time history analyses of base-isolated buildings modelled as linear single degree-of-freedom(SDOF) and multi degree-of-freedom(MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are conducted.The flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots.In the analysis,a large number of parametric studies for different earthquake excitations with three different peak ground acceleration(PGA) levels,different natural periods of the building models,and different shear wave velocities in the soil are considered.For the isolation system,laminated rubber bearings(LRBs) as well as high damping rubber bearings(HDRBs) are used.Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the following conclusions:(1) soil flexibility may considerably influence the stiff superstructure response and may only slightly influence the response of the flexible structures;(2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the system with LRBs;(3) although the peak response is affected by the incorporation of soil flexibility,it appears insensitive to the variation of shear wave velocity in the soil;(4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building,indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions,base isolations and shear wave velocities;(5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories,especially for earthquakes with low and moderate PGA levels;and(6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications,especially at the level of the lower stories.     

Comparison of web plate numerical models for self‐centering steel plate shear walls

Previous research has shown that self‐centering steel plate shear walls (SC‐SPSWs) are capable of achieving enhanced seismic performance at multiple hazard levels, including recentering following design‐level earthquakes. When modeling SC‐SPSWs numerically, these studies considered an idealized tension‐only steel plate shear wall (SPSW) web plate behavior. Research has shown that web plate behavior is more complex than predicted by the idealized model, and web plates can provide more strength, stiffness, and energy dissipation than predicted by the idealized model. The idealized model of web plate behavior is used widely in SPSW numerical models where the moment‐resisting boundary frame provides supplemental hysteretic damping and stiffness; however, in SC‐SPSWs, where the post‐tensioned boundary frame is designed to remain elastic during an earthquake, accounting for the more complex web plate behavior can have a significant impact on seismic performance estimates from numerical simulation. This paper presents different methods for modeling SC‐SPSWs. Responses from these models are compared with experimental results. A simple modification of the tension‐only model, referred to as the tension‐compression strip model, is shown to provide a reasonable approximation of SC‐SPSW behavior. Results from nonlinear response history analyses of SC‐SPSWs with the tension‐only and tension‐compression web plate models are compared to assess how the approximation of web plate behavior affects SC‐SPSW seismic performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamic systems with high damping rubber: Nonlinear behaviour and linear approximation

High damping rubber (HDR) shows a quite complex constitutive behaviour, which is nonlinear with respect to strain and is dependent on the strain rate. In addition, it exhibits a transient response during which the material properties change (scragging or more generally the Mullins effect). A number of recent works were dedicated to analysing and modelling material behaviour. This paper studies the nonlinear dynamics of systems with restoring force produced by HDR‐based devices in order to propose a procedure to define equivalent linear models considering both transient and stationary behaviours. The reliability of these linear models is tested by evaluating the upper and lower bounds of the seismic response of a structural system equipped with HDR‐based devices (structural system with dissipative bracings and isolated systems). Copyright © 2008 John Wiley & Sons, Ltd.