A.N.Timokha Planimetry of vibrocapillary equilibria with small wave numbers |
Acoustic bulletin, Vol. 5 ¹ 1, (2002) |
| For case of two-dimensional potential flows, time-averaged geometrical configurations (vibroequilibria) of limited volume of ideal liquid in a rectangular vessel, showing high-frequency forwards vibrations, are analysed. A concept of quasipotential energy and supposition of smallness of the wave numbers is used. Particular exact analytical solutions are stated. The study of a general case is based on straight numeral minimization of a functional of quasipotential energy. Auxiliary boundary problem on the wave function, being a limitation-tie, is solved by modified Nystrom-Kress method. Theoretical description is given for experimental phenomena of "flattening" and vibrostabilization of free liquid surface, "overturn" ("reorientation" of the liquid, its localization near one of vertical walls) and "dip" (even spreading of the liquid between the walls with a "cavity" forming in the center), that occur under horizontal vibrations of the vessel. Numerical results for vibroequilibria under conditions of the Earth gravitation (large Bond's numbers) and zero-gravity (lack of mass forces) are discussed. Non-uniqueness of solution and dependence of vibroequilibrium on transitional processes are stated. It is confirmed theoretically that an "overturn" is more probable for small depths, while a "dip" is typical for non-small depths of the liquid. Preliminary theoretical results, describing the " flattening" and vibrostabilization of a drop hanging on vibrating plate are obtained, including the case of negligibly small surface-tension (large Bond's numbers). |
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KEY WORDS: vibroequilibrium, quasipotential energy vibrostabilization, the Bond number |
| TEXT LANGUAGE: Russian |