Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure
Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure
复制标题
随机特征值问题在线性随机结构受迫响应分析中的应用
DOI：
10.1007/s00419-013-0750-9
复制
发表时间：
2013
影响因子：
2.8
通讯作者：
D. Ghosh
中科院分区：
文献类型：
--
作者：
D. Ghosh
随机特征值问题出现在结构特性不确定的线性系统的频率和振型确定中。在表征此随机特征值问题的多种方法中，一种计算速度快、精度高的方法是使用多项式混沌展开 (PCE) 的弱公式。在该方法中，特征值和特征向量在PCE中展开，并通过伽辽金投影最小化残差。当前工作的目标是（i）在随机载荷下的动态响应计算中实现这种 PCE 特征的随机特征值问题，以及（ii）探索计算优势和挑战。在所提出的方法中，响应量也用 PCE 表示，后跟伽辽金投影。与扰动法和蒙特卡罗模拟的数值比较表明，当载荷具有随机幅度但频率含量确定时，该方法比一阶扰动法给出更准确的结果，并且在较低的计算时间内与蒙特卡罗模拟具有相当的精度。然而，当载荷的频率成分变得随机时，或者对于一般的随机过程载荷，该方法会失去其准确性和计算效率。还解决了实施中的问题、限制和进一步的挑战。
The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.
影响因子：
5.6
作者：
Wolfram Martens;U. Wagner;V. Mehrmann
通讯作者：
Wolfram Martens;U. Wagner;V. Mehrmann