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

Abstract

UDC 517.9 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. The solution of numerous problems of the mechanics of continua for composed domains can often be significantly simplified if we split the domain into separate subdomains by introducing the corresponding conjugation conditions on the interfaces. In the construction of approximate solutions of these problems in the indicated statement, we encounter certain difficulties caused by the necessity of satisfying the conjugation conditions. The problem of linear natural oscillations of a perfect incompressible liquid in an immobile vessel in terms of the potential of shiftsˆ.x;y;z/ takes the form [1]