Hybrid deterministic-statistical analysis of vibro-acoustic systems with domain couplings on statistical components

Recently a hybrid analysis method has been developed in which the various components of a complex vibro-acoustic system can be modeled either deterministically or statistically. The coupling between these two types of component is effected by using a diffuse field reciprocity relation, which relates the cross-spectrum of the forces at the boundary of a statistical component to the vibrational energy level of the component. In practical applications, components may be coupled over a domain, rather than just at the component boundaries—for example, the coupling between a plate and an acoustic volume involves the surface of the plate. It is shown in the present work that the reciprocity relation and the hybrid method can be extended to this situation, so that, for example, it is possible to couple a statistical model of a plate to a finite element model of an acoustical cavity, or to a statistical acoustical cavity. The coupling of statistical acoustical and structural components is not new, but rather is done routinely within statistical energy analysis (SEA); this part of the present work demonstrates that the relevant coupling loss factors can be found by using the hybrid method. The analysis is illustrated by various numerical examples.