A hybrid methodology for the frequency response function variability due to joint uncertainty

Abstract

In vibroacoustic engineering, the most probable cause of dynamic uncertainty are the joints since it is not easy to strictly control the properties of manufactured joints. Although uncertainty in joints is localized in a complex structure, it may affect the dynamic response of the whole structure especially at higher frequencies. Generally, uncertain industrial structures are modelled numerically by FE whereas the uncertainty is modelled by performing Monte Carlo Simulations (MCS). These combined approaches are named FE-MCS. Application of FE-MCS to analyse local uncertainty in a complex structure is computationally slow, as FE and MCS requires a high number of elements and sampling, respectively. A possible solution is to introduce a combined hybrid Wave Finite Element and FE (shortly hybrid WFE) model, treating the uniform structures as waveguides joined by a local FE joint representation. Then, Polynomial Chaos Expansion (PCE) can be applied to introduce and model the uncertainty. The methodology is developed herein and tested on two right angled beams forming a L-shaped joint. The joint thickness is assumed to have a uniform distribution as an uncertain parameter. The scattering coefficients and frequency response function for both beams, are selected as the resulting uncertain variables. The results are subsequently verified with FE-MCS simulations using 200 samples and a limited number of experiments. It is clearly shown that the methodology introduced is an efficient tool for the structures possessing local uncertainty in terms of computational load as well as producing good frequency response function predictions when compared to both FE-MCS simulations and experimental validation.