Transfer Matrix approaches for the prediction of impact sound radiation from layered floors

In this work, an efficient and accurate framework for the prediction of the direct impact sound insulation of layered floors is presented. Both floor models of infinite lateral extent and with simply supported boundaries are considered. For the infinite floors, closed-form mechanical admittance expressions are provided which relate directly to the transfer matrix elements of the conventional transfer matrix method (TMM). For floors with simply supported boundaries, an image source argument is employed for underpinning the modal version of the TMM, or mTMM, which approximately accounts for the boundary conditions by considering admissible trace wavenumbers only. It is demonstrated that both for the TMM and the mTMM, the radiated sound power can be evaluated directly in the frequency–wavenumber domain from a simple integral. The accuracy of the mTMM is confirmed in a numerical verification using detailed finite element models. The method is also extensively validated with laboratory measurements for a set of five heavy floors with stiff and resilient layers. A very good agreement between measurements and mTMM predictions is generally observed. The TMM and mTMM approaches yield very similar results above the critical frequency of the base floor, yet at lower frequencies, the inclusion of the finite-size and boundary conditions effects make the mTMM substantially more accurate.