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

Abstract

In various technical applications, assessing the impact of non-Gaussian and non-stationary processes on responses of dynamic systems is crucial. While simulating time-domain realizations offers an effective 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 is based on the modal solution of dynamic systems, which allows to reduce DOF and response analyses to a minimum 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.