Vibration response bound prediction of uncertain structures via an extreme-value based modelling

Abstract

In engineering, in the final analysis stage of the production, many samples of the same product may exhibit different vibro-acoustics behaviour. This uncontrollable variability on free and forced vibration responses is called as quncertaintyq. Uncertainties may be or may not be on negligible levels depending on frequency of operation. Generally, the effects of the uncertainty becomes more observable as the frequency increases. Uncertainty, in general, is caused by variability in inner structure of the material, small differences in geometry, and fluctuations of excitation driving the structure, initial and boundary conditions of the structure. For a more realistic vibro-acoustics analysis, it is necessary to perform analyses taking this uncertainty into account from the initial design stage of the production. In this study, an extreme-value based modelling, which is able to predict the limits of the effects of uncertainty on vibro-acoustics responses, is introduced. This is performed for a cantilever beam and a refrigerator compressor whose reference modal parameters (Natural frequency, modal coefficient and modal damping factor) have already been obtained experimentally (reference model) and have been sampled as a normal random distribution with 5% standard deviation of the mean value. 100 uncertain vibration responses are obtained from 100 different samples of modal parameters generated based upon the reference values using Monte-Carlo simulation. Finally, bounds of these uncertain vibration responses are succesfully obtained via an extreme-value based model..