Meta-models of the Eigensolution of Uncertain Structures

The measurement of frequency response functions (FRFs) on nominally identical items reveals usually a considerable scatter induced by some inherent variabilities. In this paper a stochastic parametric approach is suggested in order to analyze the variability of the FRFs, where random as well as uncertain structural properties are modeled as a function of independent random variables with prescribed probability distributions. This work focuses on the establishment of a functional relation (meta-model) between the random variables and the modal properties to be utilized for assessing the variability of the FRFs. The proposed procedure aims to extract a close approximation of the modal properties from the set modal solutions obtained by Monte Carlo and FE analyses, of which the sample size should be as small as possible for computational efficiency. An adaptive sampling procedure has been developed for this purpose which allows a balancing between efficiency and accuracy. The concept of modal superposition is then used for calculating the FRFs. The main advantage is the fast approximate evaluation of the FRF in order to identify critical domains of the random input parameter space within some particular frequency bands. This information is used as a basis to obtain refined accurate results by FE calculations in the important domain, which is of interest in context with reliability analysis. This is demonstrated by a numerical example.