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首页> 外文期刊>International journal of structural stability and dynamics >RESPONSE STATISTICS OF LINEAR STRUCTURES WITH UNCERTAIN-BUT-BOUNDED PARAMETERS UNDER GAUSSIAN STOCHASTIC INPUT
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RESPONSE STATISTICS OF LINEAR STRUCTURES WITH UNCERTAIN-BUT-BOUNDED PARAMETERS UNDER GAUSSIAN STOCHASTIC INPUT

机译：高斯随机输入下具有不确定边界约束参数的线性结构的响应统计

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摘要

Uncertainty plays a fundamental role in structural engineering since it may affect both external excitations and structural parameters. In this study, the analysis of linear structures with slight variations of the structural parameters subjected to stochastic excitation is addressed. It is realistically assumed that sfficient data are available to model the external excitation as a Gaussian random process, while only fragmentary or incomplete information about the structural parameters are known. Under this assumption, a nonprobabilistic approach is pursued and the fluctuating properties are modeled as uncertain-but-bounded parameters via interval analysis. A method for evaluating the lower and upper bounds of the second-order statistics of the response is presented. The proposed procedure basically consists in combining random vibration theory with first-order interval Taylor series expansion of the mean-value and covariance vectors of the response. After some algebra, the sets of first-order ordinary differential equations ruling the nominal and first-order sensitivity vectors of response statistics are derived. Once such equations are solved, the bounds of the mean-value and covariance vectors of the response can be evaluated by handy formulas. To validate the procedure, numerical results concerning two different structures with uncertain-but-bounded stiffness properties under seismic excitation are presented.
机译：不确定性在结构工程中起着基本作用，因为它可能会影响外部激励和结构参数。在这项研究中，分析了线性结构的结构参数受随机激励的轻微变化。实际上，可以假设有足够的数据可用来将外部激励建模为高斯随机过程，而只有关于结构参数的零碎信息或不完整信息是已知的。在此假设下，采用非概率方法，并且通过区间分析将波动性建模为不确定但有界的参数。提出了一种评估响应的二阶统计量上下限的方法。所提出的过程主要包括将随机振动理论与响应的均值和协方差向量的一阶区间泰勒级数展开相结合。经过一些代数运算后，得出了确定响应统计的标称和一阶灵敏度向量的一阶常微分方程组。一旦解决了这些方程，就可以通过方便的公式评估响应的均值和协方差向量的范围。为了验证该程序，给出了在地震激励下具有不确定但有界刚度特性的两种不同结构的数值结果。

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