摘要Mechanisms for the evolution of a single spherical bubble subjected to sound excitation in water are studied from the viewpoint of nonlinear dynamics. First, the shooting method is combined with a Poincaré map to obtain the fixed point for the case of forced oscillation in volume. Then, the stabilities are judged by Floquet theory and the bifurcation theorem. Moreover, the transitions of bubble oscillation in volume due to sound excitation in water are explained from the viewpoint of nonlinear dynamics in detail. The results show that with an increase in sound frequency, the period-1 oscillation becomes unstable, and oscillation behaves in a double-periodic manner, then a quasi-periodic manner, and finally chaotically. Additionally, with an increase of the amplitude of the sound pressure, the bubble eventually oscillates with chaos via a series of period-doubling bifurcations.
Abstract：Mechanisms for the evolution of a single spherical bubble subjected to sound excitation in water are studied from the viewpoint of nonlinear dynamics. First, the shooting method is combined with a Poincaré map to obtain the fixed point for the case of forced oscillation in volume. Then, the stabilities are judged by Floquet theory and the bifurcation theorem. Moreover, the transitions of bubble oscillation in volume due to sound excitation in water are explained from the viewpoint of nonlinear dynamics in detail. The results show that with an increase in sound frequency, the period-1 oscillation becomes unstable, and oscillation behaves in a double-periodic manner, then a quasi-periodic manner, and finally chaotically. Additionally, with an increase of the amplitude of the sound pressure, the bubble eventually oscillates with chaos via a series of period-doubling bifurcations.
REN Sheng, ZHANG Jia-Zhong**, LI Kai-Lun. Mechanisms for Oscillations in Volume of Single Spherical Bubble Due to Sound Excitation in Water[J]. 中国物理快报, 2012, 29(2): 20504-020504.
REN Sheng, ZHANG Jia-Zhong, LI Kai-Lun. Mechanisms for Oscillations in Volume of Single Spherical Bubble Due to Sound Excitation in Water. Chin. Phys. Lett., 2012, 29(2): 20504-020504.
[1] Lauterborn W and Ohl C 1997 Ultrason. Sonochem. 4 65
[2] Lauterborn W, Kurz T, Geisler R, Schanz D and Lindau O 2007 Ultrason. Sonochem. 14 484
[3] Rayleigh L 1917 Philos. Mag. 34 94
[4] Plesset M and Prosperetti A 1977 Annu. Rev. Fluid. Mech. 9 145
[5] Keller J and Miksis M 1980 J. Acoust. Soc. Am. 68 628
[6] Prosperetti A, Crum L and Commander K 1988 J. Acoust. Soc. Am. 83 502
[7] Feng Z C and Leal L G 1997 Annu. Rev. Fluid. Mech. 29 201
[8] Franc J P and Michel J M 2004 Fundamentals of Cavitation (Dordrecht: Kluwer Academic Publisher)
[9] Cunha F R, Sousa A J and Morais P C 2002 J. Magn. Magn. Mater. 252 271
[10] Zhu S L and Zhong P 1999 J. Acoust. Soc. Am. 106 3024
[11] Ji B, Luo X W, Zhang Y, Ran H J, Xu H Y and Wu Y L 2010 Chin. Phys. Lett. 27 096401
[12] Parlitz U, Englisch V, Scheffczyk C and Lauterborn W 1990 J. Acoust. Soc. Am. 88 1061
[13] Behnia S, Jafari A, Soltanpoor W and Jahanbakhsh O 2009 Chaos Solitons Fractals 41 818
[14] Behnia S, Sojahrood A J, Soltanpoor W and Jahanbakhsh O 2009 Ultrason. Sonochem. 16 502
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