The Effect of Wall Elasticity and Surface Tension on the Forced Oscillations of a Liquid in a Cylindrical Container. Part I. Analysis

摘要

The stability of a fluid contained in a circular cylindrical tank with a flat, flexible bottom under a periodic axial excitation was studied. An analytical difficulty for the solution of the linearized equations in the form of infinite series was discussed. A variational approach is formulated. An approximate solution results in a pair of coupled ordinary differential equations with periodic coefficients. A method of handling the stability of the solutions of such a system of equation is presented. Numerical results will be discussed in a later article. (Author)