An FRF bounding method for randomly uncertain structures with or without coupling to an acoustic cavity

Abstract

An efficient frequency response function (FRF) bounding method is proposed using asymptotic extreme-value theory. The method exploits a small random sample of realised FRFs obtained from nominally identical structures to predict corresponding FRF bounds for a substantially larger batch. This is useful for predicting forced-vibration levels in automotive vehicle bodies when parameters are assumed to vary statistically. Small samples are assumed to come either from Monte Carlo simulation using a vibration model, or via measurements from real structures. The basis of the method is to undertake a hypothesis test and if justified, repeatedly fit inverted Type I asymptotic threshold exceedance models at discrete frequencies, for which the models are not locked to a block size (as in classical extreme-value models). The chosen FRF ‘bound’ is predicted from the inverse model in the form of the ‘ m-observational return level’, namely the level that will be exceeded on average once in every m structures realised. The method is tested on simulated linear structures, initially to establish its scope and limitations. Initial testing is performed on a sdof system followed by small and medium-sized uncoupled mdof grillages. Testing then continues to: (i) a random acoustically coupled grillage structure; and (ii) a partially random industrial-scale box structure which exhibits similar dynamic characteristics to a small vehicle structure and is analysed in NASTRAN. In both cases, structural and acoustic responses to a single deterministic load are examined. The paper shows that the method is not suitable for very small uncoupled systems but rapidly becomes very appropriate for both uncoupled and coupled mdof structures.