Wave-based approach for dynamical analysis of a coupled rectangular cavity: fundamental properties of eigenpairs

This study is concerned with an eigenvalue problem of a vibro-acoustic coupled system. In the conventional modal coupling method, the particle velocity normal to the surface of a panel is always calculated as zero, and the wave motion in the cavity cannot be directly treated. To overcome the problem, this study presents a novel formulation for a coupled system that expresses the correct boundary condition at the coupling plane and the wave motion in the cavity. First, a transfer matrix is introduced which can describe the characteristics of the sound field based on the wave dynamics. It is then clarified that if the panel vibration is regarded as the input to the cavity, the boundary condition of the sound field at the coupling plane should be a rigid wall. This is followed by the formulation of the eigenvalue problem of a vibro-acoustic coupled system. Finally, some numerical simulations are conducted, thereby clarifying the principles of the shift of natural frequencies and mode shapes, the accuracy of boundary condition at a coupling plane, and the orthogonality of coupled modes.