NONLINEAR FORCED OSCILLATIONS OF A BUBBLE IN A LIQUID

A. G. Petrov; Петров А. Г.

doi:10.31857/S2686740023040119

NONLINEAR FORCED OSCILLATIONS OF A BUBBLE IN A LIQUID

Authors: Petrov A.G.¹
Affiliations:
1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Issue: Vol 511, No 1 (2023)
Pages: 55-59
Section: МЕХАНИКА
URL: https://journals.rcsi.science/2686-7400/article/view/135944
DOI: https://doi.org/10.31857/S2686740023040119
EDN: https://elibrary.ru/VSXFSH
ID: 135944

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Abstract
About the authors
References
Supplementary files
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Abstract

Forced nonlinear oscillations of a gas bubble in a liquid are investigated when the frequency of fluctuations in the external pressure of the liquid is equal to the natural frequency of the bubble (resonance). By the method of averaging, a simple formula is derived for the dependence of the oscillation amplitude of a gas bubble on the amplitude of the external pressure and the thermophysical characteristics of the gas and the viscosity of the liquid. Its good agreement with numerical calculations is shown up to the value of the oscillation amplitude of the bubble radius comparable to its equilibrium value.

Keywords

gas bubbles, forced nonlinear oscillations, homobaricity, liquid

About the authors

A. G. Petrov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: petrovipmech@gmail.com
Russia, Moscow

References

Plesset M., Prosperetty A. Bubble Dynamics and Cavitation // Ann. Rev. Fluid Mech. 1977. V. 9. P 145.
Leighton T. The Acoustic Bubble. London: Academic Press, 1994. 633 p.
Нигматулин Р.И. Динамика многофазных сред. М.: Н̈аука, 1987. Т. 1. 464 с.
Brennen C. Cavitation and Bubble Dynamics. N.Y.: Oxford University Press, 1995. 254 p.
Minnaert M. Musical Air Bubbles and the Sounds of Running Water // Philosophical Magazine. 1933. V. 16. P. 235.
Pfriem H. Zur thermischen Dämpfung in kugelsymme trisch schwingenden Gasblasen // Akust. Z. 1940. Bd. 5. S. 202.
Devin C. Survey of Thermal, Radiation, and Viscous Damping of Pulsating Air Bubbles in Water // J. Acoust. Soc. Am. 1959. V. 31. P. 1654.
Prosperetti A. The thermal behaviour of oscillating gas bubbles // J. Fluid Mechanics. 1991. V. 222. P. 587–616.
Avdeev A.A. Gas bubble pulsations in an acoustic field (resonance and boundaries of the polytropic approximation) // High temperature. 2014. V. 52. P. 851–860.
Khabeev N.S., Shagapov V.S. Towards the problem of homobaricity in bubble dynamics // Int. J. of Math. Trends and Techn. 2020. V. 66. Iss. 9. P. 156–159.
Голубятников А.Н., Украинский Д.В. О динамике сферического пузырька в неньютоновских жидкостях // Изв. РАН. МЖГ. 2021. № 4. С. 52–62.
Седов Л.И. Механика сплошной среды. Т. 2. М.: Наука, 1994. 560 с.
Журавлев В.Ф., Климов Д.М. Прикладные методы в теории колебаний. М.: Наука, 1988. 326 с.
Вановский В.В., Петров А.Г. Колебания газового пузырька в жидкости при резонансе частот радиальной и произвольной осесимметричной моды колебаний 2: 1 // ДАН. 2011. Т. 437. № 3. С. 331–335.
Вановский B.B., Петров А.Г. Резонансный механизм дробления газового пузырька в жидкости // ДАН. 2012. Т. 444. № 4. С. 385–389.