Petites oscillations d'un liquide dans un vase fermé par une membrane élastique. (Small oscillations of a liquid in a rigid container closed by an elastic membrane)
The problem of the small oscillations of a liquid in a rigid container closed by an elastic membrane is investigated. In the first part, the container is fixed. In the general case, the existence of the eigenfrequencies of the system is proved by means of the methods of the functional analysis. An analytic solution is given in the case of a circular cylindrical container. The second part deals with a moving container. The equations of motion are obtained by means of a variational principle and are written in the form of an operational equation in a suitable Hilbert space. The existence of the eigenfrequencies arises from the theory of the completely continuous self-adjoint operators in an Hilbert space.
completely continuous self-adjoint operators
scientific article; zbMATH DE number 4085205