Efficient modeling of sound transmission through finite-sized thick and layered wall and floor systems

Built-up wall and floor systems such as roof panels, floors with floating screeds, etc., have found widespread application in building construction. Achieving sufficient sound insulation with these systems is challenging because of their relatively low weight and complex vibro-acoustic behavior. A fast and sufficiently accurate acoustic design tool is needed. The semi-analytical transfer matrix method is able to efficiently compute the response of a thick or multilayered structure in the frequency-wavenumber domain but has important limitations. First, the system is assumed to be of infinite extent. At lower frequencies however, neglecting the modal behavior of the wall can lead to large prediction errors. Second, integration over all possible incident plane waves is necessary to obtain the diffuse transmission loss, resulting in a high computation time. The transfer matrix approach is therefore extended in two ways. The modal behavior of rectangular walls and floors with simply supported boundary conditions is approximately accounted for. Using the diffuse reciprocity relationship, a hybrid modal transfer matrix-statistical energy analysis method is then developed such that integration of plane-wave transmission over all angles of incidence is no longer necessary, largely decreasing the computational effort. The model is validated against alternative numerical prediction models and experimental data.