The modal stability procedure for dynamic and linear finite element analysis with variability

In this paper the modal stability procedure (MSP), for the calculation of natural frequencies and frequency response functions (FRFs) of finite element systems with random parameters, is investigated. The perturbed natural frequencies and FRFs are calculated in an approximate way by using the modal stability assumption. This method requires only one finite element analysis and a post-processing procedure. The MSP has been applied to an academic example: a 1D beams assembly, and to an industrial application: a windscreen. Small and large numbers of random parameters, as well as moderate and high variability levels, have been considered. Systematically, a comparison between the MSP and Monte Carlo simulation approach, considered as a reference, are reported and commented. A detailed study of the possibilities and the limitations of the method has been carried out. For the academic as well as for the industrial example, the results are satisfactory in terms of mean value, standard deviation, probability density functions of the natural frequencies and FRFs. Moreover, the MSP is very efficient from a computational time point of view.