Fast assessment of non-Gaussian inputs in structural dynamics exploiting modal solutions

TL;DR

This paper presents a fast, modal-based method to assess non-Gaussian effects, specifically kurtosis, in large finite element models of dynamic systems, significantly reducing computational effort.

Contribution

It introduces a novel modal solution approach to efficiently compute response kurtosis and non-Gaussian statistics in large FE models, improving assessment speed.

Findings

The method accurately estimates kurtosis in FE models.

It reduces computational time compared to traditional simulation methods.

Validated on a standard FE model used in random vibration fatigue.

Abstract

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.