zbMATH — the first resource for mathematics

Finite element approximation of eigenvalue problem for a coupled vibration between acoustic field and plate. (English) Zbl 0891.73062
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, and a numerical example is shown for the problem for which the exact analytical solutions can be calculated.

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 Hydro- and aero-acoustics
74K20 Plates
74H45 Vibrations in dynamical problems in solid mechanics