Transfer-matrix-based approach for an eigenvalue problem of a coupled rectangular cavity

ABSTRACT This study concerns an eigenvalue problem of a vibro-acoustic coupling system. In the conventional method, the dynamics of a vibro-acoustic coupling system is calculated with modal coupling methodology which uses eigenfunctions of a rigid-walled cavity. Therefore, particle velocity on the surface of a panel is always calculated as zero, while it should be coincident with the velocity of the panel. To overcome the problem, this paper presents a new methodology for deriving accurate eigen-pairs of a vibro-acoustic coupling system. First, a transfer matrix is introduced which can describe the characteristics of the sound field. This is followed by the derivation of the sound pressure on the coupled rectangular panel. Then, the vibrational velocity of the panel is derived with the sound pressure being used as the input. Furthermore, the eigenvalue problem is formulated based on the equations of vibration and sound field. Finally, the numerical simulation is carried out, demonstrating the validity of the proposed method.