A finite element structural-acoustic model of coupled membranes

A simple model displaying structural-acoustic behavior is considered. The model comprises of two parallel infinitely-long flat membranes lying on elastic foundations and the acoustic medium separating them. The structural-acoustic coupling manifests itself in that a vibrational excitation of one of the membranes triggers vibrations in the other. The governing equations are stated, and the associated finite element formulation is constructed. The model is then analyzed numerically and its vibrational properties are investigated. The proposed model is especially simple, being two-dimensional and involving a small number of parameters, but at the same time it brings to light some important features associated with structural-acoustic coupling. Therefore it may serve as a benchmark for evaluating structural-acoustic numerical schemes and as an educational tool for studying structural-acoustic coupling in a simple context.