Combining parametric and non-parametric uncertainty modeling for the vibroacoustic analysis of random built-up structures

摘要

The effect of manufacturing uncertainties on the response of complex built-up structures has been the subject of much research effort over recent years. The most direct approach to modelling uncertainties is to consider specific system parameters to be random and to have known statistical properties;;this randomness can then be used in conjunction with a computational model of the system to yield the statistics of the response. This approach can be very computationally intensive, and a number of alternative non-parametric approaches have been developed to address this problem. One of these is known as the hybrid FESEA (Finite Element;;Statistical Energy Analysis) method, in which universal statistical distributions are used to describe the statistics of the natural frequencies and mode shapes of sub-components of the system. The assumptions behind this method require the sub-components to either conform to this statistical model or to be completely deterministic. These assumptions are relaxed in the present paper, where the method is combined with a parametric modelling approach, so that each subsystem is taken to obey the universal statistical laws, or to have parametric uncertainty. The effect of the parametric uncertainty on the response can be computed either with Monte-Carlo simulations, or with an approximate technique such as FORM (the First Order Reliability Method). The theory behind this approach is described here, and then the method is applied to an example plate structure. Good agreement is found between the present approach and a computationally intensive fully parametric model.