双气泡振子系统的非线性声响应特性分析
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摘要
对初始半径不同的双气泡振子系统在声波作用下的共振行为和声响应特征进行了分析.利用微扰法分析了双泡系统的非线性共振频率,由于气泡间耦合振动的非线性影响,双泡系统存在双非线性共振频率.倍频共振和分频共振现象的存在使得双泡系统振幅-频率响应曲线有多共振峰,且随着非线性增强,共振区向低频区移动.通过对气泡平衡半径、双泡平衡半径比以及气泡间距的分析发现,耦合作用较强的情形发生在系统共振频率附近、气泡半径比接近1以及气泡间距小于10R_(10)的范围内,同时观察到了此消彼长的现象,充分体现了气泡在声场中能量转换器的特征.
It is of great importance to investigate the dynamics of the multiple bubble system for revealing the mechanism of cavitation. Because of the secondary radiation of the oscillating bubbles, the coupled vibration of neighboring bubbles arises. Previous studies have reported that time delays appear to be more important when the coupled bubbles are close to each other. In this paper, we investigate the acoustical response of two bubble oscillators theoretically and numerically. Firstly, we modify the dynamic model equation by use of Taylor series being accurate up to terms of second order in radial displacement of bubbles. Based on the perturbation theory,the eigenmodes of the coupled-bubble system are analyzed, and two different resonant frequencies are obtained.Secondly, the effects of time delays on the coupled oscillation are analyzed numerically by use of phase diagram.When bubbles are driven by low-intensity ultrasound, we can neglect the effect of the time delay for the coupled-bubble system. Thirdly, the theoretical and numerical curve of amplitude versus frequency are compared with each other. There are two peaks on each curve on which present are two resonant regions. The relative position of the resonant peaks of the two bubbles in each region is similar for the two analytical methods. Finally, the effect of equivalent radius of bubble, equivalent radius ratio, bubble center distance, and driving pressure amplitude on the radial motion are numerically explored. With the increase of the intensity of the acoustic wave, the resonant peaks shift toward the low-frequency region. The coupled oscillation of the two bubbles of different radii could be intensified when these conditions are satisfied, such as resonant driving, equal radius, and the range of center distance smaller than 10 R10. We can observe a transition phenomenon and outof-phase fluctuation of the bubble oscillation in the strong coupling region. Therefore, bubbles play an important role of energy translator in the ultrasound applications.
It is of great importance to investigate the dynamics of the multiple bubble system for revealing the mechanism of cavitation. Because of the secondary radiation of the oscillating bubbles, the coupled vibration of neighboring bubbles arises. Previous studies have reported that time delays appear to be more important when the coupled bubbles are close to each other. In this paper, we investigate the acoustical response of two bubble oscillators theoretically and numerically. Firstly, we modify the dynamic model equation by use of Taylor series being accurate up to terms of second order in radial displacement of bubbles. Based on the perturbation theory,the eigenmodes of the coupled-bubble system are analyzed, and two different resonant frequencies are obtained.Secondly, the effects of time delays on the coupled oscillation are analyzed numerically by use of phase diagram.When bubbles are driven by low-intensity ultrasound, we can neglect the effect of the time delay for the coupled-bubble system. Thirdly, the theoretical and numerical curve of amplitude versus frequency are compared with each other. There are two peaks on each curve on which present are two resonant regions. The relative position of the resonant peaks of the two bubbles in each region is similar for the two analytical methods. Finally, the effect of equivalent radius of bubble, equivalent radius ratio, bubble center distance, and driving pressure amplitude on the radial motion are numerically explored. With the increase of the intensity of the acoustic wave, the resonant peaks shift toward the low-frequency region. The coupled oscillation of the two bubbles of different radii could be intensified when these conditions are satisfied, such as resonant driving, equal radius, and the range of center distance smaller than 10 R10. We can observe a transition phenomenon and outof-phase fluctuation of the bubble oscillation in the strong coupling region. Therefore, bubbles play an important role of energy translator in the ultrasound applications.
引文
[1]Ooi A,Nikolovska A,Manasseh R 2008 J.Acoust.Soc.Am.124 815
[2]Allen J S,Kruse D E,Dayton P A,Ferrara K W 2003 J.Acoust.Soc.Am.114 1678
[3]Mohd Y N S,Babgi B,Alghamdi Y,Aksu M,Madhavan J,Ashokkumar M 2016 Ultrason.Sonochem.29 568
[4]Ashokkumar M 2011 Ultrason.Sonochem.18 864
[5]Prosperetti A,Crum L A,Commander K W 1988 J.Acoust.Soc.Am.83 502
[6]Wang C H,Cheng J C 2013 Chin.Phys.B 22 014304
[7]Zhang Y N,Li S C 2016 Ultrason.Sonochem.29 129
[8]Doinikov A A 2004 J.Acoust. Soc.Am.116 821
[9]Yasui K,Lee J,Tuziuti T,Towata A,Kozuka T,Yasuo I2009 J.Acoust.Soc.Am.126 973
[10]Hegedus F,Klapcsik K 2015 Ultrason.Sonochem.27 153
[11]Hu J,Lin S Y,Wang C H,Li J 2013 Acta Phys.Sin.62114301(in Chinese)[胡静,林书玉,王成会,李锦2013物理学报62 114301]
[12]Takahira H,Yamane S,Akamatsu T 1995 JSME Int.J.Ser.B 38 432
[13]Naohiro S,Keita A,Toshihiko S 2017 Ultrasonics 77 160
[14]Chew L W,Klaseboer E,Ohl S W,Khoo B C 2011 Phys.Rev.E 84 066307
[15]Versluis M,Schmitz B,Heydt A V D,Lohse D 2000 Science289 2114
[16]Masato I 2009 Phys.Rev.E 79 016307
[17]Jiang L,Liu F B,Chen H S,Wang J D,Chen D R 2012Phys.Rev.E 85 036312
[18]Bonabi R S,Rezaee N,Ebrahimi H,Mirheydari M 2010 Phys.Rev.E 82 016316
[19]Masato I 2007 Phys.Rev.E 76 046309
[20]An Y 2011 Phys.Rev.E 83 066313
[21]Doinikov A A,Manasseh R,Ooi A 2005 J.Acoust.Soc.Am.117 47
[22]Sugita N,Toshihiko S 2017 Ultrasonics 74 174
[23]Ikeda T,Harata Y,Hiraoka R 2015 Nonlinear Dyn.81 1759
[24]Dzaharudin F,Suslov S A,Manasseh R,Ooi A 2013 J.Acoust.Soc.Am.134 3425
[2]Allen J S,Kruse D E,Dayton P A,Ferrara K W 2003 J.Acoust.Soc.Am.114 1678
[3]Mohd Y N S,Babgi B,Alghamdi Y,Aksu M,Madhavan J,Ashokkumar M 2016 Ultrason.Sonochem.29 568
[4]Ashokkumar M 2011 Ultrason.Sonochem.18 864
[5]Prosperetti A,Crum L A,Commander K W 1988 J.Acoust.Soc.Am.83 502
[6]Wang C H,Cheng J C 2013 Chin.Phys.B 22 014304
[7]Zhang Y N,Li S C 2016 Ultrason.Sonochem.29 129
[8]Doinikov A A 2004 J.Acoust. Soc.Am.116 821
[9]Yasui K,Lee J,Tuziuti T,Towata A,Kozuka T,Yasuo I2009 J.Acoust.Soc.Am.126 973
[10]Hegedus F,Klapcsik K 2015 Ultrason.Sonochem.27 153
[11]Hu J,Lin S Y,Wang C H,Li J 2013 Acta Phys.Sin.62114301(in Chinese)[胡静,林书玉,王成会,李锦2013物理学报62 114301]
[12]Takahira H,Yamane S,Akamatsu T 1995 JSME Int.J.Ser.B 38 432
[13]Naohiro S,Keita A,Toshihiko S 2017 Ultrasonics 77 160
[14]Chew L W,Klaseboer E,Ohl S W,Khoo B C 2011 Phys.Rev.E 84 066307
[15]Versluis M,Schmitz B,Heydt A V D,Lohse D 2000 Science289 2114
[16]Masato I 2009 Phys.Rev.E 79 016307
[17]Jiang L,Liu F B,Chen H S,Wang J D,Chen D R 2012Phys.Rev.E 85 036312
[18]Bonabi R S,Rezaee N,Ebrahimi H,Mirheydari M 2010 Phys.Rev.E 82 016316
[19]Masato I 2007 Phys.Rev.E 76 046309
[20]An Y 2011 Phys.Rev.E 83 066313
[21]Doinikov A A,Manasseh R,Ooi A 2005 J.Acoust.Soc.Am.117 47
[22]Sugita N,Toshihiko S 2017 Ultrasonics 74 174
[23]Ikeda T,Harata Y,Hiraoka R 2015 Nonlinear Dyn.81 1759
[24]Dzaharudin F,Suslov S A,Manasseh R,Ooi A 2013 J.Acoust.Soc.Am.134 3425