Theory of fuzzy random vibration with fuzzy parameters

In this paper, based on our previous papers [1–4], the general theory of fuzzy random vibration with fuzzy parameters is studied. In order to better describe the random excitation with fuzziness in mathematics, first, the random variable and random process with a fuzzy parameter are defined and their probability distributions and statistical moments are discussed. Secondly, by simulating the fuzzy random excitation as a random process with a fuzzy parameter, the fundamental method and numerical method are presented for analysing the fuzzy random response of linear or nonlinear oscillators subjected to this kind of excitation. Finally, the methods are applied to the fuzzy random vibration of aseismic structures and a concrete example is given.This paper is supported by the Natural Science Foundation of China.     

含模糊参数的随机振动

本文在抗震结构模糊随机振动的研究基础上,进一步研究含模糊参数的随机振动分析方法,为了较好地描述具有模糊性的随机干扰,首先在Zadeh定义的模糊变量的基础上,定义了含模糊参数的随机变量和含模糊参数的随机过程,并讨论了它们的概率分布和数字特征;然后将模糊随机干扰模拟为含模糊参数的随机过程,提出了在这种模糊随机干扰下振动体系的模糊随机反应分析的基本方法和数值方法;最后对于抗震结构的模糊随机振动给出了具体的分析和算例     

线性随机桁架结构的平稳随机响应分析

研究了随机桁架结构的平稳随机响应问题。同时考虑结构的物理参数、几何尺寸的随机性，从结构平稳随机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，导出了随机桁架结构在平稳随机激励下位移响应均方值的均值、均方差和变异系数的计算表达式。通过算例考察了随机荷载激励下结构物理参数、几何尺寸的随机性对结构随机响应的影响。     

Pseudolinear vibroimpact systems: Non-white random excitation

Response analyses of vibroimpact systems to random excitation are greatly facilitated by using certain piecewise-linear transformations of state variables, which reduce the impact-type nonlinearities (with velocity jumps) to nonlinearities of the common type — without velocity jumps. This reduction permitted to obtain certain exact and approximate asymptotic solutions for stationary probability densities of the response for random vibration problems with white-noise excitation. Moreover, if a linear system with a single barrier has its static equilibrium position exactly at the barrier, then the transformed equation of free vibration is found to be perfectly linear in case of the elastic impact. The transformed excitation term contains a signature-type nonlinearity, which is found to be of no importance in case of a white-noise random excitation. Thus, an exact solution for the response spectral density had been obtained previously for such a vibroimpact system, which may be called pseudolinear, for the case of a white-noise excitation. This paper presents analysis of a lightly damped pseudolinear SDOF vibroimpact system under a non-white random excitation. Solution is based on Fourier series expansion of a signum function for narrow-band response. Formulae for mean square response are obtained for resonant case, where the (narrow-band) response is predominantly with frequencies, close to the system's natural frequency; and for non-resonant case, where frequencies of the narrow-band excitation dominate the response. The results obtained may be applied directly for studying response of moored bodies to ocean wave loading, and may also be used for establishing and verifying procedures for approximate analysis of general vibroimpact systems.     

随机疲劳裂纹扩展新模型

疲劳裂纹扩展的随机特性是工程结构可靠性分析和制定检查、维修计划野性 须考虑的因素,提出疲劳裂纹随机扩展模型,不仅考虑了时间参数影响,而且还考虑了初始裂纹尺寸分布影响。模型适应范围广,由于采用了一次二阶矩近似方法简化随机过程计算,便于工程应用。     

桅杆风致破坏机理研究

桅杆风致破坏的情况屡见不鲜。桅杆的非线性是相当复杂的,它是由拉索的几何非线性和拉索的张力产生的,拉索的张力又依赖于拉索的几何位置。研究指出由于在经常性风荷载作用下,桅杆产生空间混沌振动,并由此产生疲劳破坏的结果,但这些研究仅限于确定性情况。本文中将研究扩展到随机问题,数值计算结果表明该系统存在随机混沌现象,其响应平均值与平均应力指出混沌性质。为了进一步研究桅杆破坏机理,因此在本文中,既考虑突发性故障问题,又考虑随机疲劳寿命问题,并给出时间与应力极值概率。     

SOME PROBLEMS IN THE Z-C-X SPACE

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Dynamic response and reliability analysis of random structures

The finite element method determining dynamic response of random structuressubjected to random dynamic load is studied,the formulas for dynamic response ofrandom structures and reliability based on random resistibility are proposed in thispaper.     

混凝土破裂过程的三维数值模型

利用混合同余法产生了随机变量,将混凝土中的骨料简化为球体,采用循环比较法将随机变量赋给球心坐标(X,Y,Z),实现了混凝土骨料的空间随机分布,最终建立了三维混凝土数值模型。对模型整体进行单元剖分,将骨料、砂浆、界面层分别投影到该有限元网格中,采用多次网格划分技术完成模型网格划分。通过对算例进行有限元计算,结果表明该模型基本上反映了混凝土骨料分布的实际情况,较好地模拟了混凝土的不均匀性与各向异性,验证了建立该模型的方法是可行的。     

平稳随机激励下随机智能桁架结构振动主动控制中的优化

研究了平稳随机激励下随机智能桁架结构振动主动控制中主动杆的配置位置和闭环控制系统增益的优化问题。考虑结构物理参数、几何尺寸、阻尼同时具有随机性以及作用荷载为平稳随机激励，基于系统最小储存能，构建了具有位移响应均方值、应力响应均方值可靠性约束的主动杆配置和控制增益的优化模型；并对结构平稳随机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。