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Based on the model for the one-dimensional coupled oscillation of bubble-liquid column in tube, a theoretical investigation of the forced oscillation of a cylindrical gaseous bubble in a microtubule is presented. For the case that the two acoustic pressures of microtubule ends are not homogenous, the linear natural frequency is not affected, but its oscillating amplitude is influenced by the effective acoustic pressure amplitude. The relations between the amplitudes of fundamental, third and one third harmonic oscillations and the acoustic frequency are analyzed using the succession-level approximation method. Numerical results show that the bubble oscillates nonlinearly if the effective value of acoustic pressure exceeds 0.1MPa. It is found that the amplituds of fundamental, third and one third harmonic oscillations are multivalued, and the response of third harmonic oscillation is stronger in the region of lower frequencies. Furthermore, the third harmonic oscillation may be probably induced in the region of ω/ω0 ≥ 1.
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Keywords:
- cylindrical gaseous bubble /
- forced oscillations /
- nonlinear oscillations /
- acoustical response
[1] Hu Y T, Qin S P, Hu T, Ferrara K, Jiang Q 2005 Int. J. Nonlin. Mech. 40 341
[2] Qin S P, Hu Y T, Jiang Q 2006 IEEE. T. Ultrason. Ferr. 53 1322
[3] Freund J B 2008 J. Acoust. Soc. Am. 123 2867
[4] Cancelos S, Moraga F J, Lahey R T, Shain W, Parsons R H 2010 J. Acoust. Soc. Am. 128 2726
[5] Qin S P, Ferrara K W 2007 Ultrasound Med. Biol. 33 1140
[6] Miao H Y, Gracewski S M, Dalecki D 2009 J. Acoust. Soc. Am. 126 2374
[7] Martynov S, Stride E, Saffari N 2009J. Acoust. Soc. Am. 126 2963
[8] Sassaroli E, and Hynynen K 2005 Phys. Med. Biol. 50 5293
[9] Gao F R, Hu Y T, Hu H P 2007Int. J. Solids. Struct. 44 7197
[10] Zhen H R, Dayton P A, Caskey C, Zhao S K, Qin S P, Ferrara K W 2007 Ultrasound Med. Biol. 33 1978
[11] Wang Z Y, Tong A Y 2008 Int. J. Therm. Sci. 47 221
[12] Wang C H, Lin S Y 2010 Sci. China Phys. Mech. Astron. 53 496
[13] Leighton T G, White P R, Marsden M A 1995 Acta Acust. 3 517
[14] Oguz H N, Prosperetti A 1998 J. Acoust. Soc. Am. 103 3301
[15] Sassaroli E, Hynynen K 2004 J. Acoust. Soc. Am. 115 3235
[16] Chen X M, Prosperetti A 1998 J. Acoust. Soc. Am. 104 1389
[17] Jang N W, Gracewski S M, Abrahamsen B, Buttaccio T, Halm Robert, Dalecki D 2009 J. Acoust. Soc. Am. 126 EL34
[18] Du G H, Zhu Z M, Gong X F 2001 Fundamentals of Sound (Nanjing: Nanjing University Press) p502 (in Chinease) [杜功焕, 朱哲民, 龚秀芬 2001声学基础 (南京: 南京大学出版社)第 502页]
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[1] Hu Y T, Qin S P, Hu T, Ferrara K, Jiang Q 2005 Int. J. Nonlin. Mech. 40 341
[2] Qin S P, Hu Y T, Jiang Q 2006 IEEE. T. Ultrason. Ferr. 53 1322
[3] Freund J B 2008 J. Acoust. Soc. Am. 123 2867
[4] Cancelos S, Moraga F J, Lahey R T, Shain W, Parsons R H 2010 J. Acoust. Soc. Am. 128 2726
[5] Qin S P, Ferrara K W 2007 Ultrasound Med. Biol. 33 1140
[6] Miao H Y, Gracewski S M, Dalecki D 2009 J. Acoust. Soc. Am. 126 2374
[7] Martynov S, Stride E, Saffari N 2009J. Acoust. Soc. Am. 126 2963
[8] Sassaroli E, and Hynynen K 2005 Phys. Med. Biol. 50 5293
[9] Gao F R, Hu Y T, Hu H P 2007Int. J. Solids. Struct. 44 7197
[10] Zhen H R, Dayton P A, Caskey C, Zhao S K, Qin S P, Ferrara K W 2007 Ultrasound Med. Biol. 33 1978
[11] Wang Z Y, Tong A Y 2008 Int. J. Therm. Sci. 47 221
[12] Wang C H, Lin S Y 2010 Sci. China Phys. Mech. Astron. 53 496
[13] Leighton T G, White P R, Marsden M A 1995 Acta Acust. 3 517
[14] Oguz H N, Prosperetti A 1998 J. Acoust. Soc. Am. 103 3301
[15] Sassaroli E, Hynynen K 2004 J. Acoust. Soc. Am. 115 3235
[16] Chen X M, Prosperetti A 1998 J. Acoust. Soc. Am. 104 1389
[17] Jang N W, Gracewski S M, Abrahamsen B, Buttaccio T, Halm Robert, Dalecki D 2009 J. Acoust. Soc. Am. 126 EL34
[18] Du G H, Zhu Z M, Gong X F 2001 Fundamentals of Sound (Nanjing: Nanjing University Press) p502 (in Chinease) [杜功焕, 朱哲民, 龚秀芬 2001声学基础 (南京: 南京大学出版社)第 502页]
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