Determination of the Frequencies and Modes of Natural Oscillations of Liquids in Composed Vessels

We develop a variation method for the solution of the spectral problems for free oscillations of liquids in axially symmetric vessels of complex geometry. The problem is formulated in terms of the conjugation method. We obtain a generalized functional for which the conjugation conditions on the adjacent parts of the introduced subdomains are natural boundary-value conditions. We use the Trefts method for the reduction of the original problem to a problem of solution of an algebraic problem of low dimension. The results of calculations confirm the efficiency of the proposed method.