Acoustic modeling and eigenanalysis of coupled rooms with a transparent coupling aperture of variable size

Abstract

This paper is concerned with the modeling and acoustic eigenanalysis of coupled spaces with a coupling aperture of variable size. A modeling method for this problem is developed based on the energy principle in combination with a 3D modified Fourier cosine series approach. Under this theoretical framework, the energy exchange property and acoustically transparent characteristics of the opening are taken into account via the inflow and outflow sound powers through the opening without any assumptions. The sound pressure in the subrooms is constructed in the form of the three-dimensional modified Fourier series with several auxiliary functions introduced to ensure the uniform convergence of the solution over the entire solution domain. The accuracy of the natural frequencies and mode shapes of three exemplary coupled rooms systems is verified against numerical data obtained by finite element method, with good agreement achieved. The present method offers a unified procedure for a variety of cases because the modification of any parameter from one case to another, such as the size and location of the coupling aperture, is as simple as modifying the material properties, requiring no changes to the solution procedures.