Computation of the scattering matrix of guided acoustical propagation by the Wave Finite Element approach

Abstract

This work aims to study the guided acoustical propagation. The Wave Finite Element method is applied rather than the classic Finite Element method. Finite Element libraries are used for an elementary portion modelling. The dynamic stiffness matrix is then calculated. Periodicity conditions lead to a simple eigenvalue problem and the wave basis can be extracted. The dynamic stiffness matrix of the coupling elements corresponding to the lined parts can be also calculated considering the acoustical impedance. The use of the coupling’s conditions provides the scattering matrix. Within the framework of this method, the dispersion curves, the evolution of the scattering coefficients and the forced response to pressure excitations for both single and coupled waveguides can be represented, and compared to the FE method. The WFE method, treated in literature, and its main interests are reviewed, while adding the impedance notion into the calculation of the scattering matrix.