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。     

风荷激励下天线结构的随机振动分析

研究随机天线结构的风激随机振动响应问题。考虑天线结构物理参数、几何尺寸和结构阻尼的随机性,在基于随机因子法对结构进行动力特性分析的基础上,从结构风激随机振动响应在频域上的表达式出发,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,导出了随机天线结构在风荷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。以8米口径天线为例,分析了结构物理参数、几何尺寸和阻尼的随机性对天线结构风激位移响应均方值和应力响应均方值随机性的影响。     

刚架结构物理参数的随机性对其非平稳随机响应的影响

文中研究了随机刚架结构的非平稳随机响应问题。考虑结构在非平稳随机激励下其物理参数的随机性,从结构非平稳随机响应的表达式出发,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,导出了结构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的随机性对结构动力响应均方值随机性的影响,获得了若干有意义的结论。     

随机刚架结构在平稳随机激励下的动力响应分析

文中研究了随机刚架结构的平稳随机响应问题。考虑结构物理参数的随机性，导出了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的随机性对结构动力响应均方值随机性的影响，并获得了若干有意义的结论。     

随机结构随机激励下的响应灵敏度分析

对于随机激励下随机结构动力响应的灵敏度分析问题,提出基于点估计法的随机结构随机动力响应灵敏度分析方法.所提方法从随机结构响应均方值的均值表达式出发,首先将随机结构响应均方值的均值对基本随机变量分布参数灵敏度转化成求期望值问题,再由求解随机变量函数矩的点估计方法导出求解动力响应灵敏度的计算公式.算例分析表明该方法的计算结果是合理的,并且由于点估计法具有较高的效率和精度,因而所提方法具有一定的工程意义.     

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。     

模糊结构有限元分析的一种新方法

本文利用信息熵的概念,将模糊变量转变为随机变量,将模糊结构视为随机结构进行处理,从而提出了模糊结构有限元分析的一种新方法。当模糊结构转换的随机变量处于小扰动情况下,利用摄动法得到有限元递归方程组,解之可以得到响应量的均值和方差。     

基于四分之一车辆模型的具有随机结构参数车辆的随机动力分析

本文通过具有随机结构参数的四分之一车辆模型研究了具有不确定性结构参数的车辆在受到来自道路的随机激励作用下的振动响应问题。文中将簧上质量、簧下质量、悬挂阻尼、悬挂刚度以及轮胎刚度均认为是随机变量。将路面的不平整引起的对车辆的激励看作高斯随机过程并通过简单指数功率谱密度来建立力学模型。利用蒙特卡洛方法得出了车辆的固有频率和模态振型的均值、标准差以及变异系数。利用随机变量函数矩方法在频域中建立了车辆的随机响应的均方值的数字特征的计算表达式。通过工程算例表明了车辆结构参数的随机性对其动力响应的影响。本文所做的工作可拓展应用于车辆结构参数的灵敏度分析和动力优化设计。     

结构随机响应分析的一种直接积分法

对结构随机响应分析的数值积分方法进行了深入的研究。首先，直接从控制方程出发计算加速度，其次，给出了位移和速度的一种近似计算公式，最后，推导出响应均方值的离散计算表达式。就两个算例进行了数值仿真，结果表明该方法对于结构的随机响应分析是有效的。     

利用子结构模态的结构随机响应精确综合

提出基于固定界面子结构模态的结构随机响应精确综合方法。首先用固定界面子结构的中阶模态与精确剩余约束模态表达子结构频域位移;再利用界面力与位移的协调关系进一步消去界面自由度,建立双协调的精确缩聚变换;然后根据里兹法,得到结构精确综合的广义频响函数;并由此独立地计算各子结构的功率谱密度,进一步得到其均方值等响应统计;最后通过数值结果验证该方法的综合能力与准确性。     

The analyses of dynamic response and reliability of fuzzy-random truss under stationary stochastic excitation

A new two-factor method based on the probability and the fuzzy sets theory is used for the analyses of the dynamic response and reliability of fuzzy-random truss systems under the stationary stochastic excitation. Considering the fuzzy-randomness of the structural physical parameters and geometric dimensions simultaneously, the fuzzy-random correlation function matrix of structural displacement response in time domain and the fuzzy-random mean square values of structural dynamic response in frequency domain are developed by using the two-factor method, and the fuzzy numerical characteristics of dynamic responses are then derived. Based on numerical characteristics of structural fuzzy-random dynamic responses, the structural fuzzy-random dynamic reliability and its fuzzy numerical characteristic are obtained from the Poisson equation. The effects of the uncertainty of the structural parameters on structural dynamic response and reliability are illustrated via two engineering examples and some important conclusions are obtained.     

不均匀随机参数桁架结构的随机反应分析

以随机荷载作用下的不均匀随机参数桁架结构为研究对象,提出了求解结构反应数字特征的矩法。从结构有限元方程出发,推导出结构刚度矩阵对各单元的弹性模量、横截面积以及各节点坐标的导数,进一步导得结构位移反应对各随机参数的敏度。利用随机变量函数的矩法,导出了结构位移反应的均值和方差,依据单元位移应力的转换表达式,分析了应力反应的均值和方差。算例表明,结构反应的方差取决于各随机参数的分散性和参数间的相关性。     

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.     

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.     

Transient random interaction of dam reservoir systems

A simple gravity dam-reservoir system is selected for studying the interaction of structure-fluid systems under nonstationary random excitation. For an idealized random excitation with a zero start and a white power spectrum, the transient response mean square for the structural displacement is obtained by a simple time domain approach. Using this transient solution the random interaction effect is examined in detail. This transient interaction effect is important because it simulates random and time dependent earthquake ground accelerations.