转动地震动作用对结构动力响应影响分析

转动地震动作用对结构响应的影响有待深入研究。建立钢筋混凝土框架结构模型,对地震动平动分量和转动分量单独及耦合作用下的结构动力响应进行分析,结果表明：地震动转动分量与平动分量耦合作用时,会增大结构响应;结构顶层位移、层间扭转角、结构的扭转效应都显著增大;含有速度脉冲比无速度脉冲的转动分量与平动分量耦合作用对结构响应影响大;地震动转动分量的施加方向对结构动力响应有影响;在有速度脉冲的地震波作用下,转动分量单独作用也可使结构进入弹塑性状态。     

多维非平稳随机地震响应分析的混合型精细时程积分

在一维虚拟激励法的基础上,通过激励功率谱的分解,建立多维非平稳地震激励作用下结构随机响应的虚拟激励法。根据演变随机激励的调制函数取不同形式,推导不同的特解精细积分格式,并混合应用这些格式于结构响应时变功率谱分析,可获得高效精确的数值结果。最后,通过算例讨论地震动各分量相关性对非对称结构地震响应的影响,得到一些有意义的结论。     

基于部分分层抽样的高墩桥梁随机地震响应分析EI北大核心CSCD

为了表征桥梁结构不确定性和随机参数相关性对桥梁结构抗震性能的影响,从概率角度对桥梁进行抗震性能分析,基于部分分层抽样原理建立了时-频非平稳地震作用下桥梁非线性随机地震响应分析方法。基于地震动演化功率谱,采用谱表示方法生成非平稳地震动样本,并采用基于正交函数的思想对谱表示方法中的随机变量进行模拟,通过两个基本随机变量表征地震动的不确定性;采用基于数论的部分分层抽样方法对地震动-结构随机变量抽样,从而对桥梁非线性随机地震响应进行模拟,减小桥梁随机地震响应分析中的抽样方差;以一座实际高墩连续刚构桥为数值算例,对其进行了非线性随机地震响应分析,详细研究了桥梁结构不确定性和随机参数相关性对其地震可靠度的影响。研究结果表明:随机地震作用下,桥梁随机地震响应是典型的零均值非平稳随机过程,从地震动开始到结束,桥梁结构地震响应概率密度曲线存在由窄边宽,再由宽变窄的演化过程;随机地震作用下,桥梁结构关键响应的平均峰值因子存在一定差异,其通常在1.8~2.2变化;桥梁结构不确定性和随机参数相关性对高墩桥梁地震响应极值分布和地震可靠度的影响较为显著,忽略桥梁结构的不确定性和随机参数相关性将高估桥梁结构的地震可靠度。     

近场地震作用下RC框架鲁棒性分析

基于地震作用下结构的受力的特征,提出构件易损性及重要性系数的改进计算方法,以此定量分析结构在近场地震作用下的鲁棒性。通过分析比较RC框架在近场有无速度脉冲两组地震动,不同强度下的构件易损性系数、重要性系数和结构鲁棒性系数,揭示了RC框架结构在近场地震作用下抗连续倒塌鲁棒性的特点,并依此提出增强结构鲁棒性的措施。研究表明：相比于层间位移角等结构的整体响应指标,鲁棒性则更能具体地反应出结构在近场地震下的状态;与近场无速度脉冲型地震动相比,速度脉冲型地震动会对结构构件的易损性与重要性造成更为明显的影响,从而降低了整体结构的鲁棒性,对结构安全存在更为不利的影响。     

基于多元增量动力分析（MIDA）方法的RC核心筒结构地震易损性分析

RC核心筒结构在水平双向地震荷载作用下,结构地震响应的耦合作用会严重削弱筒体的变形能力和延性性能,加剧筒体结构破坏程度。本文引入地震动入射角来模拟结构可能遭遇到的更为客观、实际的水平双向地震激励,基于传统IDA方法,采用拉丁超立方体网络抽样法考虑地震动强度及地震动入射角对结构的共同影响,提出了多元增量动力时程分析(MIDA)方法。基于MIDA方法,利用有限元分析软件Perform-3D对20层RC核心筒结构进行多元增量动力时程分析,获取了能反映结构抗震性能的MIDA曲线,并基于性能定义出结构的四个极限性态点,进而获得结构的地震易损性曲线,对结构的易损性能进行了分析和评估。     

考虑谱形影响的地震动强度指标研究进展

合理地选择与调整地震动记录是影响结构弹塑性时程分析结果可靠性的重要因素之一。该文首先选择15条地震动记录作为输入,以基本周期T₁对应的谱加速度S_a(T₁)作为地震动强度指标来调整原始地震动记录,对一榀六层三跨钢筋混凝土平面框架结构进行了增量动力分析,分析了结构线性和非线性地震响应指标如最大层间位移角与不同周期处谱加速度值的相关性。分析结果表明,不同周期处谱加速度值与结构地震响应的相关性不同,且相关程度与结构是否进入非线性和进入非线性的程度有关。这一结果表明,由于高阶振型的影响或进入非线性阶段的周期延长效应,仅按单一强度指标如S_a(T₁)调整地震动记录对结构进行动力分析,所得结果的离散性必然较大。因此发展考虑地震动谱形特征的强度指标是进一步完善结构地震反应分析和抗震性能评估的基础。基于此,该文较为系统地对目前已提出的能够考虑谱形的地震动强度指标及其应用现状进行了综述总结,以期为我国开展合理的地震动记录选择与调整等研究提供一定的参考。     

地震作用下高位层间隔震体系参数优化设计

对地震作用下高位层间隔震体系中隔震支座参数的优化设计进行了研究。通过两自由度体系近似模拟多自由度结构层间隔震体系,将地震波简化为白噪声,优化目标为使层间隔震上部与下部结构频域振动能量和最小,推导了隔震支座优化参数的理论表达式,隔震支座的优化刚度系数和阻尼系数与上部和下部结构的质量比密切相关。在数值算例中,通过比较过滤白噪声激励下多自由度体系中的隔震支座参数化研究结果和两自由度体系理论结果,发现二者吻合良好;实际地震波记录激励下多自由度结构体系的响应与两自由度体系的响应规律一致。研究结果表明,多自由度结构高位层间隔震体系的隔震支座优化参数可基于理论表达式得出,可为高位层间隔震体系的初步设计提供参考。     

随机地震激励作用下自复位结构的平稳响应

自复位结构是一种震后不需修复或仅需少量修复即可继续投入使用的新型抗震结构。目前有关自复位结构地震响应的研究多是在确定性激励下进行,鲜有涉及随机激励环境。假定地震动加速度过程为金井清过滤白噪声模型,研究了随机地震激励下单自由度自复位体系的平稳响应。应用广义谐波平衡技术分解旗帜形的恢复力,建立原系统的等效非线性随机系统。通过Stratonovich-Khasminskii极限定理作随机平均,得到关于幅值的近似一维扩散过程。建立并求解对应的FPK方程,得到关于幅值的稳态概率密度函数并进行参数分析。数值结果表明,能量耗散系数与屈服位移的减小能降低系统响应,同时,随着这两个参数的变化,系统会出现随机P分岔现象。通过蒙特卡罗数值模拟法验证了解析解的有效性。     

地震动强度指标与框架结构响应的相关性研究

随着当前结构性能设计及耗能减震技术的普遍应用,根据合理的地震动强度指标来选择和调整实测地震动记录进行结构地震动响应分析,对于保证结构抗震设计的可靠性具有重要的意义。该研究将13种常用的地震动强度指标按照加速度型指标、速度型指标和位移型指标分为3类,对强震作用下13种常用的地震动强度指标与不同周期框架结构响应参数的相关性开展了研究。研究结果表明:3类地震动强度指标中,加速度型指标与短周期框架结构响应参数的相关性最好;速度型指标与中周期和中长周期框架结构响应参数的相关性最好;位移型指标与中长周期框架结构响应参数的相关性相对较好;同一结构在线性反应阶段与非线性反应阶段的响应参数与地震动强度指标的相关性是变化的。     

LRB隔震桥梁空间变异性地震随机响应分析

对装有铅芯橡胶支座（Lead—Rubber—Bearing，LRB）的隔震大跨连续梁桥进行了考虑地震动空间变异性的随机响应分析。地面运动加速度功率谱模型为零均值的平稳高斯过程，描述为过滤白噪声施加于支撑各点。地震动空间变异性综合考虑空间不相干效应、行波效应和局部场地土效应。推导了LRB隔震结构多点激励运动方程，并运用随机等价线性化方法以计入铅芯橡胶支座（LRB）的滞回非线性性能。对一大跨LRB隔震梁桥进行了一致激励和综合考虑地震动空间变异性的三种工况计算，得到了各工况下响应的拟静力项、动力项和总响应项的各自最大值的均值，并进行了对比分析。结果表明，对于带有铅芯橡胶支座的减隔震大跨连续梁桥，多点激励效应不容忽视，一致激励会对结构产生不安全的估计。     

Non-Gaussian solution for random rocking of slender rigid block

This paper adopts a random vibration approach to study the response of the slender rigid block to seismic action. The problem is strongly non-linear because of (i) the restoring term and (ii) the quadratic dissipation of energy due to the inelastic impacts, modeled as an impulsive process. The excitation process is firstly assumed to be a Gaussian white noise; secondly, a non-stationary filtered Gaussian white noise is assumed to simulate seismic shaking more accurately. The solution of the associated Fokker-Planck equation in terms of moments of the response is obtained by means of a non-Gaussian closure technique, that enables the complete statistical definition of the approximated transient response process to be achieved. The mean upcrossing rates and the response spectra in terms of displacement are evaluated. The reliability of the solutions derived is assessed by comparing them with Monte Carlo simulations.     

Importance sampling for reliability assessment of dynamic systems under general random process excitation

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally efficient approach intended for dynamic systems driven by Gaussian white noise, and this approach can be extended to random process inputs that can be represented as transformations of Gaussian white noise. In practice, dynamic systems may be subjected to inputs that may be better modeled as non-Gaussian and/or non-stationary random processes, which are not easily transformable to Gaussian white noise. We propose a computationally efficient scheme, based on importance sampling, which can be implemented directly on a general class of random processes — both Gaussian and non-Gaussian, and stationary and non-stationary. We demonstrate that this approach is in fact equivalent to Girsanov transformation when the uncertain inputs are Gaussian white noise processes. The proposed approach is demonstrated on a linear dynamic system driven by Gaussian white noise and Brownian bridge processes, a multi-physics aero-thermo-elastic model of a flexible panel subjected to hypersonic flow, and a nonlinear building frame subjected to non-stationary non-Gaussian random process excitation.     

Simulation by Slepian method of plastic displacements of Gaussian process excited multistory shear frame

The object of study is a stationary Gaussian white noise excited multi-degree-of-freedom (MDOF) linear elastic, ideal plastic, linearly damped, statically determinate oscillator with several potential elements of ideal plastic yielding. Specifically the study is exemplified for a plane multistory shear frame with rigid traverses where all the connecting columns except the columns in one or more of the bottom floors have finite symmetrical yield limits. The white noise excitation acts on the mass of the first floor making the movement of the elastic bottom floors simulate a ground motion that interacts with the structure above the bottom floors. The method of study is so-called Slepian model simulation and is in principle the same for other statically determinate MDOF elasto-plastic oscillators of the considered type. The method is fast as compared to direct simulation and provides results that give good insight in the behavior of the plastic displacement response process.     

Equivalent linearization of MDOF systems under external Poisson white noise excitation

Equivalent linearization (EQL) techniques are developed and evaluated for multidimensional systems under external Poisson white noise excitation. Especially, a simulation strategy for the calculation of the linearization coefficients is proposed. The methods are illustrated by several examples that have been treated under Gaussian white noise excitation in the literature. It is shown that EQL for MDOF systems under Poisson white noise excitation is able to deal with problems of nearly the same dimension as under Gaussian white noise excitation.     

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined.As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, we must pass from the solution of the artificial system (driven by parametric noise) to that of the original one (driven by external noise, that is known). Moreover, introducing this invertible nonlinear transformation into the Itô’s rule for the original system driven by external input, one can derive the Itô’s rule for systems driven by a parametric type excitation, directly. In this latter case one can see how natural is the presence of the Wong–Zakai correction term or the presence of the hierarchy of correction terms in the case of normal and Poissonian white noise, respectively. Direct transformation on the Fokker–Planck and on the Kolmogorov–Feller equation for the case of parametric input are found.     

Slepian simulation of distributions of plastic displacements of earthquake excited shear frames with a large number of stories

The object of this study is a stationary Gaussian white noise excited plane multistory shear frame with a large number of rigid traverses. All the traverse-connecting columns have finite symmetrical yield limits except the columns in one or more of the bottom floors. The columns behave linearly elastic within the yield limits and ideally plastic outside these without accumulating eigenstresses. Within the elastic domain, the frame is modeled as a linearly damped oscillator. The white noise excitation acts on the mass of the first floor making the movement of the elastic bottom floors simulate a ground motion that interacts with the structure above the bottom floors. As in a recent work by the authors, the paper is about application of the so-called Slepian model simulation, but in this paper supplemented by a simplification principle that allows a manageable calculation for the considered type of elasto-plastic oscillator also when it has a large number of elasto-plastic columns.     

斜拉桥系统地震易损性评估的Pair Copula技术

大跨度斜拉桥作为高次超静定结构,通常包含主塔、斜拉索、主梁、辅助墩及连接墩等较多构件,由于地震作用下各构件相互影响,准确模拟构件地震响应之间的相关性对斜拉桥整体系统的易损性评估十分关键。因Pair Copula能较好地模拟构件两两之间的相关性,理论上可将Pair Copula分层迭代模拟斜拉桥整体系统,进而提出基于Pair Copula迭代模型的斜拉桥系统地震易损性评估方法。基于结构不确定性参数及地震动不确定性,采用拉丁超立方抽样技术建立桥梁-地震动概率地震响应分析样本;通过非线性动力时程及相关性分析,量化构件地震响应之间的相关性;采用极大似然估计拟合Pair Copula模型,基于AIC及BIC准则对其进行优选;通过Pair Copula分层迭代,建立斜拉桥整体模型并对其进行地震易损性评估。工程实例表明,基于Pair Copula分层迭代技术能准确模拟多构件之间的相关性,假定构件地震响应完全不相关,会显著高估斜拉桥整体系统的地震易损性。     

POD-based filters for the representation of random loads on structures

Random loads on structures are often represented as stationary Gaussian multi-variate random processes, whose components are correlated with each other according to characteristic patterns. Numerous techniques usually applied in structural dynamics require having the input constituted by a vector of independent random processes or even white noises. The application of such techniques in many practical contexts requires the introduction of suitable pre-filters to reproduce the exact correlation and harmonic content of the real external excitation. The present paper describes the development and the implementation in the time and in the frequency domain of digital filters based on the proper orthogonal decomposition (POD). Two different approximated approaches are discussed and verified through numerical examples.     

框架结构在双向地震动作用下的最大结构反应

实际地震由水平地震动和竖向地震动组成。由于水平地震动可能沿任何方向发生,通常把引起结构最大动力反应的水平地震动角度称为地震对该结构的最不利入射角度。确定地震动的最不利入射角度是研究双向地震作用下结构动力响应的关键问题。该文提出了一种基于弹性时程分析的地震动最不利入射角度的确定方法,并给出了该方法的图形解法。该文通过具体算例证实,当结构为线弹性时,该方法给出的是动力响应的精确解。当结构进入非线性阶段,产生塑性变形时,该文对该方法引起的误差进行了讨论,发现误差随强度折减系数(Rd)的增加而增大,在Rd小于6时,误差通常不超过10%,证明该文所提出的方法在结构发生塑性变形时依然具有很好的适用性。     

Precise integration strategy for aseismic LQG control of structures

Although LQG regulators have been used in many engineering fields, the relevant control technique still requires further development, particularly when the disturbances are random and non‐stationary. Therefore this paper presents a new method for non‐stationary seismic random excitations in which LQG control is applied to adjacent tall buildings which are connected together by active hydraulic actuators. The ground motion is induced by non‐stationary uniformly modulated white noise excitation of the bedrock which passes through a single layered soil which is regarded as a single‐peak filter. This represents an advance on other papers in the literature, which use stationary random white noise or filtered white noise as the ground excitation. The method uses the pseudo excitation method in conjunction with two different precise integration schemes to analyse structural non‐stationary seismic random responses via solution of the differential Riccati equations of this transient LQG control process. Unlike previous work in the literature, the performance index used has a finite time region, rather than an infinite one. Reasonable control effects are demonstrated via numerical simulation for two adjacent 20‐storey buildings which are connected by hydraulic activators. Copyright © 2006 John Wiley & Sons, Ltd.