Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version)

Russian Russian English English About Journal | Issues | Editorial Board | Contact Us
 


IssuesArchive of Issues2017-4pp.305-316

Archive of Issues

Total articles in the database: 10482
In Russian (ΟΜΜ): 9683
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 81, Issue 4 / 2017 | Next article >>
V.V. Vanovskii and A.G. Petrov, "Spring analogy of non-linear oscillations of a bubble in a liquid at resonance," J. Appl. Math. Mech. 81 (4), 305-316 (2017)
Year 2017 Volume 81 Issue 4 Pages 305-316
DOI 10.1016/j.jappmathmech.2017.12.008
Title Spring analogy of non-linear oscillations of a bubble in a liquid at resonance
Author(s) V.V. Vanovskii (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia, vladimir.vanovsky@gmail.com)
A.G. Petrov (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia)
Abstract Two non-linear oscillatory systems are considered. The first is a point mass on a spring with vertical vibration of the suspension point with a frequency that coincides with the frequency of free vertical oscillations and is two times greater than the frequency of free horizontal oscillations. The friction force in the spring is taken into account. For an initial deviation of the point mass from the vertical, after a long enough time the energy of the vertical oscillations is almost completely transferred into the energy of horizontal oscillations. Using an averaging method, an asymptotic solution is constructed, describing the transient process setting up a periodic solution. Comparison of the analytical solution with the numerical one demonstrates its high accuracy. The second system is an axisymmetrical bubble in a liquid under the variable pressure. An analogy between this system and the previous one is established. Vibration of the suspension point of a spring pendulum corresponds to variable liquid pressure, and the vertical and horizontal oscillation modes of the swinging spring correspond to the radial and deformational oscillation modes of the bubble, and the ratio of the frequencies of these modes is also taken to be equal to two. The friction force in the spring corresponds to energy dissipation under radial oscillations of the bubble. In our calculations of energy dissipation, we take into account the liquid viscosity, thermal dissipation, and acoustic radiation due to liquid compressibility. During transfer of the energy of the radial oscillations, the amplitude of the resonant deformational mode of the bubble oscillations grows anomalously, which makes it possible for the bubble to break up with small energy dissipation under the action of a time-varying external pressure field.
Received 20 October 2016
Link to Fulltext
<< Previous article | Volume 81, Issue 4 / 2017 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 245, 119526 Moscow, Russia (+7 495) 434-2149 pmm@ipmnet.ru pmmedit@ipmnet.ru https://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Journal of Applied Mathematics and Mechanics
webmaster
Rambler's Top100