The motion of a liquid in a flexible container is important for rocket structural dynamics. The purpose of this paper is to study the dynamic response of the liquid, the sloshing frequencies and the stability of the free surface of the liquid in an elastic container.
The variational principle for the problem of an incompressible, inviscid fluid in an elastic container is presented by considering the pressure energy of the fluid, the surface energy, and the Lagrangian of the elastic thin shell. The corresponding linearized equations are studied in terms of eigenvalues and eigenfunctions.
The effects of the gravitation, the surface tension, the rigidity of the container, the free surface contact angle and its dynamic variation, on the natural frequencies and the stability of the free surface are discussed.
It is found that the flexibility of the container always lowers the natural frequencies and also induces a mean oscillatory motion of the liquid that creates an oscillatory force on the container in the vertical direction. The equilibrium contact angle and its dynamic variation have an important effect on the limit of stability.
The motion of a liquid in a circular cylindrical container with a flat flexible bottom is worked out in detail analytically by means of eigenfunctions.Some results are presented graphically.A numerical scheme using finite elements method is developed for an arbitrary container.Methods for improving the solution systematically are indicated.
