두 영역 분할법을 이용한 임의 형상 음향 공동의 고유치 해석

A two-domain method for eigenvalue analysis of arbitrarily-shaped acoustic cavities with convex or concave shapes is proposed in this paper. This method divides the concave acoustic cavity of interest into two convex regions. The sound pressure (approximate solution) of each convex region is assumed by linearly superposing plane waves generated at edges of the region. A sub-system matrix for each convex region is extracted by applying a provisional boundary condition to the approximate solution. Finally, a system matrix, of which the determinant provides the eigenvalues of the concave cavity, is made by considering the rigid-wall boundary condition at edges and the compatibility condition (the condition of continuity in sound pressure and its slope) at the interface between the two regions. In addition, a practical method for reducing the size of the system matrix is presented to facilitate the calculation of the determinant of the system matrix. Case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by the exact method or FEM.