Boundary effects on the vibration statistics of a random plate

This paper considers the estimation of statistics of displacement of a vibrating rectangular plate with random wave scatterers. The influence of uncertainty is investigated using point impedance theory. Coherent boundary effects are seen, which decrease when the number of scatterers increases. The boundary effect is investigated using images and the first side and corner reflections are found to be a minimum requirement to estimate the spatial correlation. Statistics for point driven response are investigated under the assumption that the statistics of the natural frequencies follow those of the Gaussian Orthogonal Ensemble (GOE). The estimates are compared with Monte Carlo simulation results, and they show good agreement.

► Two-point correlation is estimated for a displacement of a vibrating rectangular plate with uncertainties.
► Effect of randomness is modelled using a point impedance theory.
► Boundary effect in the random plate is predicted using mirror images of the correlation.
► Ensemble average and covariance of the plate vibration subjected to a point excitation are modelled under GOE statistics.