模糊随机桁架结构的非平稳随机振动分析

利用一种新的双因子法研究了模糊随机桁架结构的非平稳随机振动问题。同时考虑结构物理参数和几何尺寸的模糊随机性,首先从时域上推导出了位移响应的模糊随机相关函数矩阵;进而得出了位移和应力响应在频域上的模糊随机均方值,并用随机变量的矩法得到了结构响应均方值模糊随机变量的模糊数字特征。最后用算例验证了该方法的可行性。     

模糊随机桁架结构在模糊随机激励下的动力响应

研究了模糊随机参数桁架结构在模糊随机荷载激励下的复合模糊随机振动动力响应的问题。同时考虑结构的物理参数、几何尺寸和外载荷幅值的模糊随机性,从Duham e l积分式出发,利用振型迭加法求出了结构动力响应模糊随机变量的表达式;再由随机函数的矩法推导出结构模糊随机动力响应的模糊数字特征。最后,通过算例考察了结构参数和作用荷载的模糊随机性对结构动力响应的影响,并用M on te C arlo数值法对算例进行模拟,验证了文中模型和分析方法是可行有效的。     

Dynamic Response Analysis of Fuzzy Stochastic Truss Structures under Fuzzy Stochastic Excitation

A novel method (Fuzzy factor method) is presented, which is used in the dynamic response analysis of fuzzy stochastic truss structures under fuzzy stochastic step loads. Considering the fuzzy randomness of structural physical parameters, geometric dimensions and the amplitudes of step loads simultaneously, fuzzy stochastic dynamic response of the truss structures is developed using the mode superposition method and fuzzy factor method. The fuzzy numerical characteristics of dynamic response are then obtained by using the random variable’s moment method and the algebra synthesis method. The influences of the fuzzy randomness of structural physical parameters, geometric dimensions and step load on the fuzzy randomness of the dynamic response are demonstrated via an engineering example, and Monte-Carlo method is used to simulate this example, verifying the feasibility and validity of the modeling and method given in this paper.     

Design of a mega-sub-controlled building system under stochastic wind loads

Vibration control of high-rise buildings under wind loads with application of the mega-sub-control method is studied in this paper. A building with a megasub-configuration consists of two major structural components - a megastructure as the main structural frame and several sub-structures for residential and/or commercial usage. The authors have previously proposed a ‘megasub-control method’ in which the sub-structures are designed to serve as vibration control dampers. The control objective is to suppress certain critical building responses such as inter-story drifts of the mega-structure for the purpose of structural safety and acceleration response of the sub-structures for the purpose of protecting contents and improving human comfort. The feasibility of this method has been explored by the authors in previous publications. In this study, the procedure of optimally designing dynamic parameters of a megasub-controlled building under stochastic wind loads is developed, together with two possible structural configurations which provide a mega-sub-control mechanism. The mega-structure of a mega-sub-building is modeled as a cantilever beam to retain the dominant bending mode characteristics of highrise buildings, and the sub-structure as a shear building to retain the shear mode. The fluctuating wind speed is modeled as a non-white random process in both time and space domains. The power spectral density (PSD) of critical building responses is obtained using the random vibration theory. The mean square value (MSV) of those responses, as functions of the dynamic parameters including the stiffness and damping ratio of the sub-structures, are evaluated from their PSD by numerical integration in the frequency domain. The optimal values of the dynamic parameters are determined by minimizing the MSV of certain critical building responses. An example building is used to demonstrate the design procedure and the numerical simulation of the response quantities in the time domain is carried out to verify the MSV of the building responses obtained from the random vibration theory in the frequency domain. The results show that the proposed design procedure is suitable to apply to a mega-sub-building with different sub-structural configurations. The MSV obtained from the random vibration theory in the frequency domain and from the numerical simulation in the time domain exhibit an excellent agreement. It is also found that the megasub-control method is robust in the sense that slight change in the dynamic parameters affects the building's performance very little. With the design procedure developed, and the corresponding favorable building response demonstrated, this paper has enhanced the feasibility of application of the mega-sub-control method to actual high-rise buildings for wind vibration suppression.     

复合随机振动系统的动力可靠度分析

建议了一类新的复合随机振动系统动力可靠度分析方法。基于复合随机振动系统反应分析的密度演化方法,根据首次超越破坏准则,对密度演化方程施加相应的边界条件,进而求解密度演化方程,在安全域内积分给出结构的动力可靠度。结合精细时程积分方法与具有TVD性质的差分格式,研究了基于密度演化方法求解结构动力可靠度问题的数值方法。以受到随机地震作用、具有随机参数的八层层间剪切型结构为例,进行了结构动力可靠度分析并与随机模拟结果进行了比较。研究表明,建议的方法具有较高的精度和效率。     

基于模糊因子法的模糊桁架结构动力特性分析

研究了模糊桁架结构动力特性的分析方法,在结构的物理和几何参数同时为模糊变量的情况下,利用模糊因子建立了结构的刚度矩阵和质量矩阵;从结构振动的瑞利商表达式出发,利用区间运算法则推导出结构模糊特征值的表达式。通过算例考察了结构各参数的模糊性对其动力特性模糊性的影响,并获得了一些有意义的结论。该法对模糊结构进行一次动力分析便可求得动力特性,且可充分地反映任一模糊参数对结构模糊动力特性的影响。     

Dynamic response and reliability analysis of structures with uncertain parameters

An original approach for dynamic response and reliability analysis of stochastic structures is proposed. The probability density evolution equation is established which implies that incremental rate of the probability density function is related to the structural response velocity. Therefore, the response analysis of stochastic structures becomes an initial‐value partial differential equation problem. For the dynamic reliability problem, the solution can be derived through solving the probability density evolution equation with an initial value condition and an absorbing boundary condition corresponding to specified failure criterion. The numerical algorithm for the proposed method is suggested by combining the precise time integration method and the finite difference method with TVD scheme. To verify and validate the proposed method, a SDOF system and an 8‐storey frame with random parameters are investigated in detail. In the SDOF system, the response obtained by the proposed method is compared with the counterparts by the exact solution. The responses and the reliabilities of a frame with random stiffness, subject to deterministic excitation or random excitation, are evaluated by the proposed method as well. The mean, the standard deviation and the reliabilities are compared, respectively, with the Monte Carlo simulation. The numerical examples verify that the proposed method is of high accuracy and efficiency. Moreover, it is found that the probability transition of structural responses is like water flowing in a river with many whirlpools, showing complexity of probability transition process of the stochastic dynamic responses. Copyright © 2004 John Wiley & Sons, Ltd.     

随机参数梁在考虑热弹耦合下的动力响应分析

以随机参数梁为研究对象,分析其在温度载荷和力载荷共同作用并考虑热弹耦合关系时的动力响应。建立了热弹耦合动力学有限元模型,给出了在时间域内差分离散、相互交替迭代的耦合计算方法。利用随机因子法推导了结构温度场和动力响应的数字特征表达式,其中温度场的求解利用θ 时间积分法,动力响应则利用Newmark-β 积分法。在求出结构各时间步温度场和动力响应数字特征的基础上,应用耦合算法获得了整个时间域内的结构响应数字特征。通过悬臂梁算例分析了热弹耦合项对动力响应的影响,并考察了诸随机参数分散性对结构动力响应分散性的影响。     

索膜结构的抖振动力特性研究

研究了索膜结构在脉动风作用下的动力特性。采用Wilson-q逐步积分法和Newton-Raphson迭代法推导了索膜结构在抖振力作用下的非线性动力增量平衡方程,求得结构的时程响应曲线。通过实例分析,探讨了结构参数变化对自振频率的影响;研究抖振力作用下索膜结构响应的频谱特性,从而得出索膜结构的抖振响应特性。     

压电主动杆位置和增益在随机智能桁架结构振动控制中的优化

对结构物理参数、几何尺寸、作用荷载和控制力同时具有随机性时 ,随机压电智能桁架结构中主动杆的配置位置和闭环控制系统增益进行了优化 ,基于系统最小储存能 ,构建了具有动应力、动位移可靠性约束的主动杆配置和控制增益的优化模型 ;并对结构动力响应的数字特征进行了推导。通过算例 ,验证了该优化配置模型的合理性和有效性 ,获得了若干有意义的结论。     

模糊参数平面连续体结构的拓扑优化设计

研究了具有模糊参数的连续体结构在模糊载荷作用下的拓扑优化设计问题。利用信息熵将模糊变量转换为随机变量,构建了随机载荷作用下的随机参数的连续体结构的拓扑优化设计数学模型,以结构的形状拓扑信息为设计变量,结构总质量均值极小化为目标函数,满足单元应力可靠性为约束条件,利用分布函数法对应力可靠性约束进行了等价显式化处理。基于随机因子法,利用代数综合法导出了应力响应的数字特征的计算表达式。采用双方向渐进结构优化(BESO)方法求解。通过两个算例验证了该文模型及求解方法的合理性和有效性。     

薄膜结构随机风场模拟和耦合风振响应分析

发展了一种以脉动风速曲线的人工模拟为基础的非线性随机振动的时域分析方法。应用自回归滑动平均(ARMA)模型对大跨度薄膜结构随机风场进行了数值仿真;采用Wilson-θ逐步积分法和Newton-Raphson迭代法推导了薄膜结构在抖振力作用下的非线性动力增量平衡方程,可考虑风与结构物的耦合作用,进一步求出结构的时程响应曲线和统计特性;对参数变化对结构抖振响应的影响进行了分析,从而分析索膜结构的抖振响应特性。     

圆柱壳在水下爆炸载荷下的流-固耦合响应分析

研究了无限域流场中两端简支圆柱壳受球形炸药爆炸冲击载荷作用的响应特性。运用Hamilton变分原理,推导出了考虑流固耦合作用圆柱壳受水下爆炸冲击载荷作用的运动方程,并分别展开成Fourier级数的形式,最后在时域上差分离散,用Galerkin方法求解,得到了在水下爆炸冲击载荷下圆柱壳的响应分析。文章着重就圆柱壳在迎爆面和背爆面的不同位置的变形位移和变形速度进行了对比分析,同时还比较了流体动压力对结构响应的影响。并将分析结果与有限元计算软件MSC.DYTRAN计算结果比较,验证了算法的可靠性。     

有限测点下结构复合反演的混合法

回顾了近年来输入信息未知条件下结构识别的复合反演算法，并对输出信息测试不完备条件下的复合反演问题做了深入的研究。提出了时频域混合的复合反演算法。该算法首先在时域内利用子结构上的测试信息反演未知输入，然后在频域内依据反演得到的未知输入和有限测点上的响应信息构造目标函数来识别结构参数。该算法适用于具有多个未知输入的情况，与仅适用于单个未知输入条件下的复合反演算法相比，具有更广泛的应用价值。最后用一数值算例说明了本文算法的可行性。     

随机子空间识别在悬索桥实验模态分析中的应用

为了从大型悬索桥的脉动实验结果得出精确的结构动力特性,以便进行结构的抗风、抗震研究和实时监测,本文利用随机子空间系统识别方法对虎门悬索桥进行了模态分析。这种时域识别方法基于状态空间模型,仅利用结构输出反应,避免了传统的人工识别和迭代过程,但必须利用稳定图形确定模型阶数。同有限元数值计算结果作比较后可看出,该法能识别出10个频率在0.5Hz以下的自振频率,并且可得到较好的结构阻尼,说明随机子空间系统识别方法是分析大型桥梁脉动实验特征参数的有力工具。     

Numerical and experimental investigations on the vibration band-gap properties of periodic rigid frame structures

The spectral element method (SEM) is extended to study the vibration band-gap characteristics of periodic rigid frame structures composed of Timoshenko beams. The tensional and bending elements are taken into account for deducing the element stiffness matrices which are assembled to establish the spectral equations of motion of the whole rigid frame structure. The validity and accuracy of the natural frequencies and frequency responses obtained by the SEM are verified by comparing the present numerical results with the results of the experiments and the finite element method (FEM). The results indicate that the SEM is very suitable for analyzing the dynamic response and vibration band-gap properties of the periodic frame structures, and the SEM is more effective and accurate than the FEM, especially for the high frequency responses. The influences of the structural and material parameters on the vibration band-gaps are analyzed, and some new configurations of the periodic rigid frame structures are designed to obtain more and wider frequency band-gaps and consequently to improve the structural vibration isolation capability.     

Non-Deterministic Structural Response and Reliability Analysis Using a Hybrid Perturbation-Based Stochastic Finite Element and Quasi-Monte Carlo Method

The random interval response and probabilistic interval reliability of structures with a mixture of random and interval properties are studied in this paper. Structural stiffness matrix is a random interval matrix if some structural parameters and loads are modeled as random variables and the others are considered as interval variables. The perturbation-based stochastic finite element method and random interval moment method are employed to develop the expressions for the mean value and standard deviation of random interval structural displacement and stress responses. The lower bound and upper bound of the mean value and standard deviation of random interval structural responses are then determined by the quasi-Monte Carlo method. The structural reliability is not a deterministic value but an interval as the structural stress responses are random interval variables. Using a combination of the first order reliability method and interval approach, the lower and upper bounds of reliability for structural elements, series, parallel, parallel-series and series-parallel systems are investigated. Three numerical examples are used to demonstrate the effectiveness and efficiency of the proposed method.     

基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析EI北大核心CSCD

提出一种基于贝叶斯推理的非线性结构模型修正方法,同时考虑激励的随机性,建立了复合随机振动系统的动力可靠度分析方法。利用实测结构动力响应主分量的瞬时特征参数作为非线性指标构建似然函数,结合拒绝延缓自适应(Delayed Rejection and Adaptive Metropolis,DRAM)算法和高斯过程替代模型实现了非线性结构模型修正及其参数的不确定性量化。根据首次超越破坏准则,利用广义概率密度演化方法,分别对仅考虑激励随机性的确定性模型和同时考虑结构参数与激励不确定性的复合随机振动模型进行动力可靠度分析,并利用蒙特卡洛随机抽样方法验证了计算结果的准确性。研究结果表明:基于振动响应瞬时特征参数的贝叶斯推理方法能够快速、准确地实现结构的非线性模型修正及其参数的不确定性量化。与具有初始设计参数名义值的确定性模型相比,考虑参数不确定性的复合随机模型的动力可靠度总体偏低,因此,在结构安全评估中应考虑非线性模型参数不确定性的影响,使评估结果更加安全、可靠。     

平稳随机激励下线性随机桁架结构动力响应分析

考虑桁架结构的物理参数、几何尺寸的随机性，利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法，从结构平稳随机响应在频域上的表达式出发，导出了随机桁架结构在平稳随机激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例考察了结构物理参数和几何尺寸的随机性对结构位移响应均方值和应力响应均方值随机变量随机性的影响，并获得了一些有意义的结论。     

基于小波包能量谱的结构损伤预警方法研究

基于小波包分析推导了结构动力系统在不同分析尺度上的状态方程和观测方程,在此基础上研究了结构动力响应在不同分析尺度上的时-频特性以及系统矩阵和测量噪声在各个分析尺度上的递推性。理论分析证明,采用结构动力响应的小波包能量谱进行结构损伤预警具有较好的损伤敏感性和噪声鲁棒性。根据瞬态激励的特性提出对激励和响应的时域互相关序列进行小波包分解得到小波包能量谱,并在此基础上计算结构损伤预警指标。通过一钢筋混凝土板静力承载力的振动试验分析,对板不同受力阶段的损伤状态进行了判别,并与实际损伤程度进行了比较。