Open AccessThe article considers approximate numerical methods to determine own frequencies of cryogenic liquid fluctuations stratification of which changes under any law. The increasing use of cryogenic liquids, liquefied gas, superfluid solutions, and slush liquids in modern mechanical engineering define relevance of a perspective. Interest in the considered problem is also caused by the fact that in cryogenic liquid along with superficial waves there can be internal wave movements penetrating all thickness of liquid in a tank and therefore playing important role in many hydro-dynamic processes.
This article considers problems of determining the own frequencies of cryogenic liquid fluctuations, partially filling cylindrical tank of any cross section. It is supposed that the change of the liquid particles density due to thermal stratification of entire liquid mass can proceed continuously under any law. To solve numerically a similar problem, a method of trigonometric series (MTS) and a method of final elements (MFE) were used. When using the MTS method the unknown solution and variable coefficients of the equation were presented in the form of trigonometric series. Further, after multiplication of series and the subsequent mathematical operations the frequency equation was obtained. Bubnov-Galyorkin's approach was used to obtain solutions by the MFE method. Reliability of received numerical results is confirmed by coincidence with frequency results calculated by analytical formulas of solutions of differential equations with constant frequency of buoyancy.