Free and forced oscillations of a frictionless liquid in a long rectangular tank with structural obstructions at the free liquid surface

Summary

If a free liquid surface is partly covered with a solid wall, the natural frequencies and the response of the liquid in the container may be drastically changed. The fundamental natural frequency of a frictionless and incompressible liquid in an infinitely long rectangular container is determined for increasing structural coverage of the free surface. With increasing coverage of the surface by a rigid structural member, the natural frequencies increase drastically and reduce the sloshing motion. The response to translational excitation is evaluated also numerically.

The procedure may be applied to arbitrary coverages of a three-dimensional rectangular container, and may also be used as a test case for purely numerical procedures such as the finite element method.