Oscillations of immiscible liquids in a stationary cylindrical vessel and their mechanical analogs

When making engineering calculations for the dynamics of solid bodies with the cavity filled with fluid, we often use mechanical analogues of movements of the required hydrodynamic systems. So, in plane motions of a solid body with a cavity partly filled with fluid we use pendulous analogues of oscillations in fluids. The longitudinal oscillations of у deformable body with fluid fuel require mechanical oscillators. In oscillations around the longitudinal axis of symmetry, we use the physical and mathematical pendulums on the bifilar suspension, freely rotating around the longitudinal axis. This article deals with the oscillations of three incompressible fluids. Within the research we obtain differential equations for generalized coordinates that reflect the wave motions of fluids on the section surfaces, and we describe the mechanical analogues of oscillations of fluids.

References

[1] Chashechkin Yu.D. Fluid Mechanics: Consistent Analytical, Numerical and Laboratory Models of Stratified Flows. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2014, no. 6, pp. 67-95 (in Russ.).

[2] Ai Min Vin. Cryogenic Liquid Fluctuations in a Motionless Tank. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science & Education of the Bauman MSTU. Electronic Journal], 2014, no. 9. DOI: 10.7463/0914.0726215 Available at: http://technomag.bmstu.ru/en/doc/726215.html

[3] Babskiy V.G., Zhukov M.Yu., Kopachevskiy N.D., Myshkis A.D., Slobozhanin L.A., Tyuptsov A.D. Metody resheniya zadach gidromekhaniki dlya usloviy nevesomosti [Methods for Solving Fluid Mechanics Problems for Weightless Conditions]. Kiev, Naukova dumka Publ., 1992. 592 p.

[4] Ganichev A.I., Kachura V.P., Temnov A.N. Malye kolebaniya dvukh nesmeshi-vayushchikhsya zhidkostey v podvizhnom tsilindricheskom sosude. V kn.: Kolebaniya uprugikh konstruktsiy s zhidkost’yu [Small Oscillations of Two Immiscible Liquids in a Movable Cylindrical Vessel. In: The Oscillations of Elastic Structures with Liquid]. Novosibirsk, NETI Publ., 1974, pp. 82-88.

[5] Temnov A.N., Ai Min Vin. On the Motion of Stratified Liquid in the Cavity of Movable Solid. Jelektr. nauchno-tekh. izd. "Inzhenernyy zhurnal: nauka i innovacii" [El. Sci.-Tech. Publ. "Eng. J.: Science and Innovation"], 2012, iss. 7. DOI: 10.18698/2308-6033-2012-7-291 Available at: http://engjournal.ru/catalog/eng/teormech/291.html

[6] Goncharov D.A. Dynamics of two-layer liquid divided by an elastic dividing wall with an allowance for surface tension forces (with corrections). Nauka i obrazovanie. MGTU im. N.E. Baumana [Science & Education of the Bauman MSTU. Electronic Journal], 2013, no. 11. DOI: 10.7463/1113.0619258 Available at: http://technomag.bmstu.ru/en/doc/619258.html

[7] Pozhalostin A.A., Goncharov D.A., Kokushkin V.V. Small Oscillations of Two-Layer Liquid in View Permeability of Separator. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumcma, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2014, no. 5, pp. 109-116 (in Russ.).

[8] Gaziev E.L. Simulation of Natural Oscillations of the "Ideal Capillary Liquid - Barotropic Gas" System in a Cylindrical Container. Book of Abstracts of Crimean International Mathematics Conference (CIMC-2003). Simferopol’: KNTs NANU, 2013, vol. 3, pp. 51-52 (in Russ.).

[9] Kolesnikov K.S., Pozhalostin A.A., Shkapov P.M. Problems of Hydromechanical Systems Dynamics in Proceedings of the Zhukovsky Theoretical Mechanics Department. Jelektr. nauchno-tekh. izd. "Inzhenernyy zhumal: nauka i innovacii" [El. Sci.-Tech. Publ. "Eng. J.: Science and Innovation"], 2012, iss. 7. DOI: 10.18698/2308-6033-2012-7-285 Available at: http://engjournal.ru/catalog/eng/teormech/285.html

[10] Kononov Yu.N., Tatarenko E.A. Free oscillations of elastic membranes and two-layer liquid in rectangular channel with elastic bottom. Prikladnaya gidromekhanika [Applied Hydromechanics], 2008, no. 1, pp. 33-38 (in Russ.).

[11] Mikhayluk A.V., Timokha A.N. Variational formulations for a spectral problem with parameter on the interface of two mediums. Dopov. Nats. Akad. Ukr. Mat. Prirodozn. Tekh. Nauki, 1995, iss. 45, no. 10, pp. 38-40.

[12] Popov D.N., Panaiotti S.S., Ryabinin M.V. Gidromekhanika [Hydromechanics]. Moscow, MGTU im. N.E. Baumana Publ., 2014. 320 p.

[13] Martinson L.K., Malov Yu.I. Differentsial’nye uravneniya matematicheskoy fiziki [Differential Equations of Mathematical Physics]. Moscow, MGTU im. N.E. Baumana Publ., 2002. 185 p.

[14] Kolesnikov K.S. Dinamika raket [Rocket Dynamics]. Moscow, Mashinostroenie Publ., 2003. 520 p.

[15] Kalinichenko V.A., Aung Naing Soe. Faraday waves in a movable tank and their mechanical analog. Jelektr. nauchno-tekh. izd. "Inzhenernyy zhurnal: nauka i innovacii" [El. Sci.-Tech. Publ. "Eng. J.: Science and Innovation"], 2013, iss. 12. DOI: 10.18698/2308-6033-2013-12-1138 Available at: http://engjournal.ru/catalog/eng/teormech/1138.html