In various technical applications, assessing the impact of non-Gaussian processes on responses of dynamic systems is crucial. While simulating time-domain realizations offers an efficient solution for linear dynamic systems, this method proves time-consuming for finite element (FE) models, which may contain thousands to millions of degrees-of-freedom (DOF). Given the central role of kurtosis in describing non-Gaussianity - owing to its concise, parametric-free and easily interpretable nature - this paper introduces a highly efficient approach for deriving response kurtosis and other related statistical descriptions. This approach makes use of the modal solution of dynamic systems, which allows to reduce DOFs and responses analysis to a minimum number in the modal domain. This computational advantage enables fast assessments of non-Gaussian effects for entire FE models. Our approach is illustrated using a simple FE model that has found regular use in the field of random vibration fatigue.

翻译：在各种工程应用中，评估非高斯过程对动态系统响应的影响至关重要。虽然时域实现模拟为线性动态系统提供了有效的解决方案，但对于可能包含数千至数百万自由度（DOF）的有限元（FE）模型而言，该方法耗时严重。鉴于峰度在描述非高斯性中的核心作用——因其简洁、无参数且易于解释的特性——本文提出了一种高效推导响应峰度及其他相关统计描述的方法。该方法利用动态系统的模态解，可将自由度和响应分析在模态域中降至最少。这一计算优势使得能够对整个有限元模型进行非高斯效应的快速评估。我们通过一个在随机振动疲劳领域常用的简单有限元模型来阐述所提方法。