(untitled) (Journal of Computational Mathematics, 1997)
We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babuška and Osborn. Some numerical examples are shown for the problem for which the exact analytical solutions are calculated. The results show that the convergence order is consistent with the one by the numerical analysis.