An extension to random point process theory for predictiong the vibration response of uncertain structures

In the high-frequency range, there have been advances in the use of non-parametric uncertainty models to predict the vibration response of uncertain structures. In particular, the Statistical Energy Analysis (SEA) approach has been combined with the Random Point Process Theory (RPPT) to yield the non-parametric ensemble variance of the subsystem energies without requiring Monte Carlo Simulations (MCS) to be performed to propagate the uncertainty. The assumptions behind the RPPT are that the generalised forces acting on a single subsystem and the mode shapes (computed at the points where the forces are applied) are statistically independent and identically distributed. These assumptions are valid for a large variety of cases; however, it has been found that correlation effects can have a significant effect on the response variance in some cases, particularly when the modal overlap is high. In this paper, the correlation effects are quantified for the case of a system driven by multiple random point loads. It is then shown how these correlation effects can be accounted for in response predictions: closed form analytical solutions are derived for the case of a single random point load, and an efficient numerical method is derived for multiple point loads. The approach is illustrated by application to a randomly driven plate system.