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.

这项研究与振动声耦合系统的特征值问题有关。在传统的模态耦合方法中，垂直于面板表面的粒子速度始终被计算为零，并且无法直接处理腔体内的波动。为了克服这个问题，本研究为耦合系统提出了一种新颖的公式，该公式表达了耦合平面上正确的边界条件以及空腔中的波动。首先，介绍了一个可以基于波动力学描述声场特性的传递矩阵。然后澄清的是，如果将面板振动视为腔的输入，则在耦合平面处的声场的边界条件应为刚性壁。接下来是振动声耦合系统的特征值问题的表述。最后，进行了一些数值模拟，从而阐明了固有频率和模式形状的偏移，耦合平面上边界条件的精度以及耦合模式的正交性的原理。