This paper proposes an efficient and reliable eigenvalue solution technique for analytical stochastic dynamic stiffness (SDS) formulations of beam built-up structures with parametric uncertainties. The SDS formulations are developed based on frequency-dependent shape functions in conjunction with both random-variable and random-field structural parameters. The overall numerical framework is aimed towards representing the broadband dynamics of structures using very few degrees of freedom. This paper proposes a novel approach combining the Wittrick–Williams(WW) algorithm, the Newton iteration method and numerical perturbation method to extract eigensolutions from SDS formulations. First, the eigenvalues and eigenvectors of the deterministic DS formulations are computed by the WW algorithm and the corresponding mode finding technique, which are used as the initial solution. Then, a numerical perturbation technique based on the inverse iteration and homotopy method is proposed to update the eigenvectors and eigenvalues. The robustness and efficiency of the proposed method are guaranteed through several technique arrangements. Through numerical examples, the proposed method is demonstrated to be robust within the whole frequency range. This method provides an efficient and reliable tool for stochastic analysis of eigenvalue problems relevant to free vibration and buckling analysis of built-up structures.

本文提出了一种有效且可靠的特征值求解技术，用于分析具有参数不确定性的梁组合结构的分析随机动态刚度 (SDS) 公式。SDS 公式是基于与频率相关的形状函数以及随机变量和随机场结构参数而开发的。整体数值框架旨在使用很少的自由度来表示结构的宽带动力学。本文提出了一种结合 Wittrick-Williams(WW) 算法、牛顿迭代法和数值微扰法的新方法，以从 SDS 公式中提取特征解。首先，确定性 DS 公式的特征值和特征向量由 WW 算法和相应的模式查找技术计算，用作初始解决方案。然后，提出了一种基于逆迭代和同伦方法的数值微扰技术来更新特征向量和特征值。所提出的方法的鲁棒性和效率是通过几种技术安排来保证的。通过数值例子，证明了所提出的方法在整个频率范围内是鲁棒的。该方法为与组合结构的自由振动和屈曲分析相关的特征值问题的随机分析提供了一种有效且可靠的工具。通过数值例子，证明了所提出的方法在整个频率范围内是鲁棒的。该方法为与组合结构的自由振动和屈曲分析相关的特征值问题的随机分析提供了一种有效且可靠的工具。通过数值例子，证明了所提出的方法在整个频率范围内是鲁棒的。该方法为与组合结构的自由振动和屈曲分析相关的特征值问题的随机分析提供了一种有效且可靠的工具。