Implementation of impedance boundary condition in scaled boundary FEM for mid-frequency acoustics of a cavity

At the Inter-Noise 2017 conference, the authors had proposed employing the semi-analytical framework based scaled boundary finite element method (SBFEM), to study interior acoustics problems in the mid-frequency range. The method was shown to be quite accurate in computing the natural frequencies and modes, well into the mid-frequency range, with significantly less computational resources than the conventional finite element method (FEM). However, only the Dirichlet and Neumann type boundary conditions were used in the study. In most acoustic cavity numerical simulations impedance boundary conditions need to be imposed, to represent acoustic treatments on the walls. In this paper, the SBFEM formulation is extended to handle such boundary conditions as well as wall excitations. The boundary is represented by a Lagrangian description; other choices such as iso-geometric representation are also possible. The proposed method is validated with an analytical solution for a constant impedance boundary condition. For practical complex valued impedance cases, the results from the present approach are compared with conventional finite element method. The computational efficiency of SBFEM is demonstrated over conventional FEM for the mid-frequency range, using a two-dimensional rectangular cavity.