Analysis of bending wave transmission using beam tracing with advanced statistical energy analysis for periodic box-like structures affected by spatial filtering

For bending wave transmission across periodic box-like arrangements of plates, the effects of spatial filtering can be significant and this needs to be considered in the choice of prediction model. This paper investigates the errors that can occur with Statistical Energy Analysis (SEA) and the potential of using Advanced SEA (ASEA) to improve predictions. The focus is on the low- and mid-frequency range where plates only support local modes with low mode counts and the in situ modal overlap is relatively high. To increase the computational efficiency when using ASEA on large systems, a beam tracing method is introduced which groups together all rays with the same heading into a single beam. Based on a diffuse field on the source plate, numerical experiments are used to determine the angular distribution of incident power on receiver plate edges on linear and cuboid box-like structures. These show that on receiver plates which do not share a boundary with the source plate, the angular distribution on the receiver plate boundaries differs significantly from a diffuse field. SEA and ASEA predictions are assessed through comparison with finite element models. With rain-on-the-roof excitation on the source plate, the results show that compared to SEA, ASEA provides significantly better estimates of the receiver plate energy, but only where there are at least one or two bending modes in each one-third octave band. Whilst ASEA provides better accuracy than SEA, discrepancies still exist which become more apparent when the direct propagation path crosses more than three nominally identical structural junctions.