On the Frequency Spectrum of Free Vibrations of Membranes and Plates in Contact with a Fluid

A parallelepiped-shaped container, which is completely filled with a perfect incompressible fluid, is considered. The container is covered with an elastic lid, which is modeled by a membrane or a constant-thickness plate. The other faces of the container are nondeformable. The frequency spectrum of small free vibrations of the lid has been obtained taking into account the apparent mass of the fluid the movement of which is assumed to be potential. The main specific feature of the problem formulation is that the volume of the fluid under the cover remains unchanged in the course of vibrations. As a result, the shape of the deflection of the lid should satisfy the equation of constraint, which follows from the condition of preservation of the volume of the fluid under the lid.