基于概率密度演化的基础隔震结构随机响应分析

针对抗震结构和基础隔震结构,应用概率密度演化方法对其进行多遇地震作用下的线性随机响应分析。通过引入工程地震动物理随机函数模型,采用数论选点法对多维外荷载随机变量进行离散代表点的生成并求得其赋得概率,利用离散代表点合成地震动加速度时程样本作为输入结构的随机激励,对于每条地震波,相当于对结构进行确定性动力反应分析。在求得结构响应及其相关导数后,应用TVD差分格式求解广义概率密度演化方程即可得到所求响应的时变概率密度及其演化。结果表明：基础隔震结构在随机地震作用下相比抗震结构具有良好的减震性能,隔震层的设置能够减小结构位移响应的标准差,减少了结构响应的离散型;概率密度演化方法不仅能够给出结构响应的二阶统计矩,还能全面地反映结构响应的时变概率信息,位移响应的概率密度函数分布不服从正态分布或其他常用分布,且随着时间演化。     

空间网格结构多维多点随机地震响应分析的高效算法

将林家浩教授提出的“虚拟激励法”进一步推广应用于空间网格结构多维多点非平稳随机地震响应分析,推导了多维虚拟激励随机振动分析方法的理论公式,给出了峰值响应估计方法,并讨论了多维地震动的随机模型及参数选取,通过编制的专用计算机程序分析了网壳结构的随机地震响应。本方法自动包含了参振振型间及各输人地震分量间的相关项,计算精确、快速,非常适合分析频率密集型空间网格结构的随机地震响应,是一种高效的随机振动分析算法。     

非一致激励条件下工程场地地震动相干函数的数值模拟--Ⅱ分析方法的应用

在文《非一致激励条件下工程场地地震动相干函数的数值模拟———Ⅰ分析原理和方法》中,通过将随机振动的虚拟激励原理与工程波动理论散射问题的求解方法相结合,提出了开放系统中非一致激励条件下工程场地地震动随机场的数值模拟方法。本文将建议方法应用于具有非一致随机激励的复杂工程场地的地震动相干函数分析之中,讨论了受局部场地条件影响的地震动相干函数的若干特征。     

随机结构动力可靠度分析的极值概率密度方法

提出了随机结构动力可靠度分析的极值概率密度方法。基于概率密度演化的基本思想,构造一个虚拟随机过程,使得随机结构动力反应的极值为该虚拟随机过程的截口随机变量。进而．采用概率密度演化方法,建立概率密度演化方程并求解给出随机结构动力反应的极值分布。在安全域内积分即可给出结构动力可靠度,当安全界限为随机变量时,采用这一方法几乎不增加额外的工作量,与随机模拟结果的比较表明,本文建议方法具有良好的精度和效率。     

多点激励下结构随机地震反应分析的反应谱方法

基于随机振动理论,提出了多点激励作用下线性系统随机地震反应分析的均值反应谱方法,给出了结构峰值反应的均值、标准差以及反应平均频率的反应谱组合公式。这可以将反应谱方法推广应用到多点激励结构的抗震可靠度分析中。鉴于组合公式中谱参数和相关系数需要由烦琐的数值积分得到,本文进一步针对它们给出合理的简化计算式,从而使得建议的反应谱方法的计算效率大大增加。最后,以一个双塔斜拉桥为例,对本文方法进行了验证。基于建议方法的计算结果与Monte Carlo模拟结果吻合较好。与经典的多点激励反应谱方法(MSRS法)比较,本文方法具有其无法比拟的计算效率。     

基于不同参数的基础隔震结构非线性概率密度演化

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。     

地震多点激励结构随机分析方法

将多点地震激励简化为平稳向量随机过程，地对其时－空相关特性，采用两步相关谱展开，使相关向量随机过程转化为正交向量随机过程，通过结构振型分解法直接求得结构随机响应；进一步可计算各种响应功率谱密度。本文方法不仅考虑了结构的多点激励及行波效应，而且考虑了结构振型之间的相关性，计算过程简单，是结构随机振动分析的一种有效方法。     

基于概率密度演化的隔震结构随机地震响应

本文考虑地震动的随机性,运用概率密度演化方法对基础隔震结构的随机响应进行研究.上部结构与隔震层分别采用刚度退化的Bouc-Wen模型与Bouc-Wen模型,建立隔震结构的概率密度演化方程,直接应用四阶龙格-库塔方法迭代求解隔震结构的非线性的响应,得出隔震结构在8度罕遇地震下每层的位移概率.结果显示隔震结构较非隔震结构上部结构的位移大大地减小了,上部结构具有足够的安全性.结构整个概率密度演化过程显示了隔震结构的响应信息,概率密度演化方法能够有效评估隔震结构的抗震性能.     

TMD结构基于双过滤白噪声随机地震激励的系列响应的简明解

针对既有方法在分析TMD结构基于双过滤白噪声激励下结构响应的解表达式复杂而导致计算效率低的问题,提出了一种简明封闭解法。首先,利用双过滤白噪声谱的滤波方程与TMD结构的地震动方程联立,可将TMD结构基于复杂的双过滤白噪声激励准确的表示为易于求解的运动方程;其次,基于复模态法获得TMD耗能结构位移、层间位移的系列响应的复特征值及复模态参与系数;然后基于随机振动理论获得了TMD结构随机地震动系列响应（相对于地面绝对位移和结构层间位移）的功率谱统一形式的二次正交解,进而获得了TMD结构系列随机响应的0-2阶谱矩和方差的简明封闭解。最后研究了基于首超破坏准、Markov过程假设及串联失效模式的TMD结构的体系动力可靠度。通过一算例分析,表明了本文方法的正确性和高效性。因此,本文方法可用于各类线性结构基于复杂的随机地震动响应的分析及其动力可靠度计算。     

非平稳随机激励下线性结构动力响应的小波多尺度分析

为了能够有效地建立随机激励作用下结构动力响应均方值、频率与时间之间的关系,基于小波多尺度分析理论,探讨了非平稳随机激励下线性结构动力响应均方值的2种计算方法：(1)先采用显式时域法求解线性结构在不同激励样本下的动力响应样本,然后基于小波多尺度分析技术对各动力响应样本进行多尺度分析;(2)先将不同的激励样本进行小波多尺度分析得到不同尺度下的激励样本,然后再基于显式时域法高效求解线性结构在不同尺度激励样本下的响应样本。最后,基于导出的响应均方值多尺度计算公式得到总的响应均方值。在数值算例部分,采用Meyer小波对结构动力响应实施了小波多尺度分析。算例结果表明,位于结构基频共振区域的那部分激励能量对位移响应均方值有较大的贡献,而对速度响应均方值和加速度响应均方值影响较为复杂。同时,数值算例还表明所提计算方法不受非平稳激励形式的限制,且可以在频域空间高效地识别出激励不同频率区间的能量对结构动力响应均方值的贡献情况。     

基于等效单自由度体系的结构地震输入能量的研究

通过对多自由度体系结构在地震作用下的能量分析,考虑地震动因素和结构自身特性,提出一种框架结构地震总输入能量的简化求解方法.实例计算结果表明:基于等效单自由度体系来估计多自由度体系的地震总输入能,是一种计算简便且较为准确的方法.     

行波效应对大跨度空间结构随机地震响应的影响

深入研究了行波效应对大跨度空间结构随机地震响应的影响,进一步完善了大跨度空间结构随机地震响应分析理论。推导了双支座、单自由度体系地震响应功率谱密度函数的解析表达式,研究了不同频率体系的响应峰值随地面视波速的变化规律,分析了多支撑点、多自由度体系的地震响应功率谱矩阵的特点,发现多自由度体系地震响应随地面视波速的变化规律与单自由度体系相似。数值模拟了某体育馆网壳结构在不同地面视波速情况下的随机地震响应,结果表明,考虑地震动行波效应后,结构地震响应随地面视波速的变化而显著变化,当视波速较低时其变化规律很复杂;且支撑点附近、受拟静力位移影响较大的部分杆件的地震响应明显增大,远离支撑点处、受拟静力位移影响较小的部分杆件的地震响应稍有减小。由此得出结论,对于大跨度空间结构的随机地震响应分析,必须考虑地震动的行波效应,尤其当受拟静力位移影响较大的部分杆件对结构抗震设计起控制作用时;且应对可能出现的地面视波速进行全面分析,作为结构抗震设计依据。     

剪切型结构的抗震强度折减系数研究

为了研究剪切型结构抗震强度需求的变化规律,本文基于单自由度体系的非线性时程分析,研究了不同场地条件下延性折减系数与位移延性系数和结构自振周期的关系;采用修正等效单自由度体系位移延性折减系数的方法,研究了剪切型多自由度体系的延性折减系数;以基于中国建筑抗震规范设计的代表不同抗震能力要求的RC框架结构为分析对象,通过静力弹塑性分析,研究了RC框架结构的体系超强能力。分析结果表明场地类别、位移延性水准和结构振动周期对单自由度体系的延性折减系数有显著的影响;多自由度体系的抗震延性折减系数明显比其相应的等效单自由度体系的抗震延性折减系数小;RC框架结构的超强系数一般随结构楼层数的增加而减小,随抗震设防烈度的增大而减小,内框架的超强系数比边框架的超强系数大。     

Response spectrum method for multi-support seismic excitations

A new response spectrum method is developed for seismic analysis of linear multi-degree-of-freedom, multiply supported structures subjected to spatially varying ground motions. Variations of the ground motion due to wave passage, loss of coherency with distance and variation of local soil conditions are included. The method is based on fundamental principles of random vibration theory and properly accounts for the effects of correlation between the support motions as well as between the modes of vibration of the structure.     

Assessment of the seismic non-linear behavior of ductile wall structures due to synthetic earthquakes

In this paper, different methods for generating synthetic earthquakes are compared in terms of related non-linear seismic response of ductile structures. The objective of the investigation is to formulate recommendations for the use of synthetic earthquakes for reliable seismic analysis. The comparison is focused on the accuracy of the reproduction of the characteristics of the structural non-linear response due to recorded earthquakes. First the investigations are carried out for non-linear single-degree-of-freedom systems. Later, the results are validated for a set of realistic buildings modelled as multi-degree-of-freedom systems. Various options of the classical stationary simulation procedure of SIMQKE and a non-stationary simulation procedure proposed by Sabetta and Pugliese are examined and compared. The adopted methodology uses a set of recorded earthquakes as a reference. Hundred synthetic accelerograms are generated for each examined simulation option with the condition that the related elastic responses are similar to those of the reference set. The non-linear single-degree-of-freedom systems are defined using six recognized hysteretic models and four levels of increasing non-linearity. The non-linear responses computed for the reference set and the studied simulation options are then statistically compared in terms of displacement ductility and energy. The results show that the implementation of the classical stationary procedure always leads to a significant underestimation of the ductility demand and a significant overestimation of the energy demand. By contrast, non-stationary time histories produce much better results. The results with the multi-degree-of-freedom systems are shown to confirm these conclusions.     

Approximate analysis method for displacement responses of structures with active variable stiffness systems

The performance of structures with active variable stiffness (AVS) systems exhibits strong nonlinearity due to the variety with time of the stiffness of each storey unit, in which the AVS system is installed. Hence, the classical dynamic analysis method for linear structures, such as the mode-superposition method, is not applicable to structures with AVS systems. In this paper, an approximate analysis method is proposed for displacement responses of structures with AVS systems. Firstly, an equivalent relationship between single-degree-of-freedom (SDOF) structures equipped with AVS systems and so-called fictitious linear structures is established. Then, an approximate mode-superposition (AMS) method is presented for multi-degree-of-freedom (MDOF) structures equipped with AVS systems. The accuracy of this method is investigated through extensive parametrical study using different types of earthquake excitations, and some modification is made to the method. Numerical calculation results indicate that the modified AMS method is effective for estimating the maximum displacements relative to the ground and the maximum interstorey drifts of MDOF structures equipped with AVS systems. Supported by: National Natural Science foundation of China, Grant number 59895410     

A METHOD OF ESTIMATING THE PARAMETERS OF TUNED MASS DAMPERS FOR SEISMIC APPLICATIONS

The optimum parameters of tuned mass dampers (TMD) that result in considerable reduction in the response of structures to seismic loading are presented. The criterion used to obtain the optimum parameters is to select, for a given mass ratio, the frequency (tuning) and damping ratios that would result in equal and large modal damping in the first two modes of vibration. The parameters are used to compute the response of several single and multi-degree-of-freedom structures with TMDs to different earthquake excitations. The results indicate that the use of the proposed parameters reduces the displacement and acceleration responses significantly. The method can also be used in vibration control of tall buildings using the so-called ‘mega-substructure configuration’, where substructures serve as vibration absorbers for the main structure. It is shown that by selecting the optimum TMD parameters as proposed in this paper, significant reduction in the response of tall buildings can be achieved. © 1997 John Wiley & Sons, Ltd.     

Stochastic considerations in seismic analysis of structures

A method is presented for stochastic modelling of a design earthquake by a power spectral density function for seismic analysis of structures. The method can be adopted with information currently available in the form of design response spectra for earthquake motion. Accurate seismic responses of structures can be easily obtained using such stochastic models. The methods for accurate response analysis of structures with closely spaced modes and for generation of floor response spectra of a building using a prescribed ground response spectrum directly are also presented. The hypothesis that a design earthquake can be modelled by a power spectral density function is used only implicitly in developing these methods.     

Optimum hysteretic damper design for multi-story timber structures represented by an improved pinching model

Timber structures are characterized by a pinching phenomenon that leads to reduced dissipative capability. A few hysteretic models have been proposed to simulate the mechanical behavior of timber structures, among which the one composed of a bilinear element and a slip element in parallel has been popular in practice. Based on this model, this paper expands on the existing seismic control design methodology to determine the capacity of hysteretic dampers for multi-story timber structures. The equivalent linearization method for a single-degree-of-freedom timber structure with added hysteretic damper is established and is verified through nonlinear timber history analysis over a wide range of structural parameters. The design formulas for determining the damper capacity for a multi-degree-of-freedom system are derived, based on the concept of adjusting the distribution of equivalent stiffness of structure. The seismic control design is applied to many buildings with randomly generated parameters and the effectiveness is confirmed through a nonlinear time history analysis with four sets of seismic excitations. An extended study has shown that the shear force pattern plays an important role in the seismic control design results and thus the performance of structures. The effectiveness of the control of residual deformations by adding dampers is also studied.