Generalized Transfer Matrix Method for periodic planar media

Sound transmission through infinite planar multilayered structures characterized by in-plane periodicity is accurately and efficiently predicted by exploiting free wave propagation and Bloch modes. A through-thickness transfer matrix is derived for each layer by manipulating the dynamic stiffness matrix related to a finite element model of a unit cell. The transfer matrices of all the layers composing the structure account for the Bloch modes generated in heterogeneous layers. The proposed technique is equally appealing for in-plane homogeneous structures since few elements and no Bloch modes are needed in this case, ensuring high efficiency. In such a framework, the acoustic radiation or transmission of multilayered systems excited by an oblique plane wave can be assessed. The proposed approach is validated in case of structures consisting of heterogeneous layers by comparison with alternative approaches.