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Based on the hypothesis that the wall of an elastic tube can be described as a membrane-type elastic structure, the coupled oscillation in a system of bubble clusters and local position of the elastic wall is explored, and the model of the nonlinear oscillation of bubbles is developed. According to the successive approximation method, the nonlinear resonance frequencies the and forced oscillation are analyzed theoretically. Results indicate that the resonance frequency of bubbles is mainly affected by the interaction of bubbles in clusters. Furthermore, there is a maximum frequency of ultrasound that will excite vibrations of the bubbles in clusters, and the response of multi-valued amplitudes exists in the region of high frequency.
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Keywords:
- elastic tube /
- nonlinear resonance /
- interaction /
- acoustical response
[1] Yao L, Song Q, Bai W, Zhang J, Miao D, Jiang M, Wang Y, Shen z, Hu Q, Gu X, Huang M, Zheng G, Gao X, Hu B, Chen J, Chen H 2014 Biomaterials 35 3384
[2] Khokhlova T D, Canney M S, Khokhlova V A, Sapozhnikov O A, Crum L A, Bailey M R 2011 J. Acoust. Soc. Am. 130 3498
[3] Li T, Liu Z 2010 Medical Hypotheses 74 679
[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] Wang X, Chen H, Zheng Y, Ma M, Chen Y, Zhang K, Zeng D, Shi J 2013 Biomaterials 34 2057
[8] Freund J B 2008 J. Acoust. Soc. Am. 123 2867
[9] Gao F R, Hu Y T, Hu H P 2007 Int. 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] Leighton T G, White P R, Marsden M A 1995 Acta. Acust. 3 517
[12] Oguz H N, Prosperetti A 1988 J. Acoust. Soc. Am. 103 3301
[13] Sassaroli E, Hynynen K 2004 J. Acoust. Soc. Am. 115 3235
[14] Martynov S, Stride E, Saffari N 2009 J. Acoust. Soc. Am. 126 2963
[15] Wang C H, Cheng J C 2012 Acta. Phys. Sin. 61 194303 (in Chinese)[王成会, 程建春 2012 61 194303]
[16] Wang C H, Cheng J C 2013 Acta. Phys. Sin. 62 114301 (in Chinese)[王成会, 程建春 2013 62 114301]
[17] Wang C H, Cheng J C 2013 Sci. Sin-Phys. Mech. Astron. 43 230 (in Chinese) [王成会, 程建春 2013 中国科学 43 230]
[18] Jang N W, Gracewski S M, Abrahamsen B, Buttaccio T, Halm Robert, Dalecki D 2009 J. Acoust. Soc. Am. 126 EL34
[19] Sadighi-Bonabi R, Rezaee N, Ebrahimi H and Mirheydari M 2010 Phys. Rev. E 82 016316
[20] Rezaee N, Sadighi-Bonabi R, Mirheydari M, Ebrahimi H 2011 Chin. Phys. B 20 087804
[21] Ida M 2009 Phys. Rev. E 79 016037
[22] Zhang Y L, Zheng H R, Tang M X, Zhang D 2011 Chin. Phys. B 20 114302
[23] Jiang L, Liu F, Chen H S, Wang J D, Chen D R 2012 Phys. Rev. E 85 036312
[24] Hu J, Lin S Y, Wang C H, Li J 2013 Acta. Phys. Sin. 62 134303 (in Chinese)[胡静, 林书玉, 王成会, 李锦 2013 62 134303]
[25] Wang C H, Cheng J C 2013 Chin. Phys. B 22 014304
[26] An Y 2012 Phys. Rev. E 85 016305
[27] An Y 2011 Phys. Rev. E 84 066313
[28] Martynov S, Stride E, Saffari N 2009 J. Acoust. Soc. Am. 126 2963
[29] Landau L D, Lifshitz E M 1976 Mechanics (Third Edition) (London: Pergamon Press) p58
[30] Chen H, Kreider A, Brayman A A, Bailey M R, Matula T J 2011 Phys. Rev. L 106 034301
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[1] Yao L, Song Q, Bai W, Zhang J, Miao D, Jiang M, Wang Y, Shen z, Hu Q, Gu X, Huang M, Zheng G, Gao X, Hu B, Chen J, Chen H 2014 Biomaterials 35 3384
[2] Khokhlova T D, Canney M S, Khokhlova V A, Sapozhnikov O A, Crum L A, Bailey M R 2011 J. Acoust. Soc. Am. 130 3498
[3] Li T, Liu Z 2010 Medical Hypotheses 74 679
[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] Wang X, Chen H, Zheng Y, Ma M, Chen Y, Zhang K, Zeng D, Shi J 2013 Biomaterials 34 2057
[8] Freund J B 2008 J. Acoust. Soc. Am. 123 2867
[9] Gao F R, Hu Y T, Hu H P 2007 Int. 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] Leighton T G, White P R, Marsden M A 1995 Acta. Acust. 3 517
[12] Oguz H N, Prosperetti A 1988 J. Acoust. Soc. Am. 103 3301
[13] Sassaroli E, Hynynen K 2004 J. Acoust. Soc. Am. 115 3235
[14] Martynov S, Stride E, Saffari N 2009 J. Acoust. Soc. Am. 126 2963
[15] Wang C H, Cheng J C 2012 Acta. Phys. Sin. 61 194303 (in Chinese)[王成会, 程建春 2012 61 194303]
[16] Wang C H, Cheng J C 2013 Acta. Phys. Sin. 62 114301 (in Chinese)[王成会, 程建春 2013 62 114301]
[17] Wang C H, Cheng J C 2013 Sci. Sin-Phys. Mech. Astron. 43 230 (in Chinese) [王成会, 程建春 2013 中国科学 43 230]
[18] Jang N W, Gracewski S M, Abrahamsen B, Buttaccio T, Halm Robert, Dalecki D 2009 J. Acoust. Soc. Am. 126 EL34
[19] Sadighi-Bonabi R, Rezaee N, Ebrahimi H and Mirheydari M 2010 Phys. Rev. E 82 016316
[20] Rezaee N, Sadighi-Bonabi R, Mirheydari M, Ebrahimi H 2011 Chin. Phys. B 20 087804
[21] Ida M 2009 Phys. Rev. E 79 016037
[22] Zhang Y L, Zheng H R, Tang M X, Zhang D 2011 Chin. Phys. B 20 114302
[23] Jiang L, Liu F, Chen H S, Wang J D, Chen D R 2012 Phys. Rev. E 85 036312
[24] Hu J, Lin S Y, Wang C H, Li J 2013 Acta. Phys. Sin. 62 134303 (in Chinese)[胡静, 林书玉, 王成会, 李锦 2013 62 134303]
[25] Wang C H, Cheng J C 2013 Chin. Phys. B 22 014304
[26] An Y 2012 Phys. Rev. E 85 016305
[27] An Y 2011 Phys. Rev. E 84 066313
[28] Martynov S, Stride E, Saffari N 2009 J. Acoust. Soc. Am. 126 2963
[29] Landau L D, Lifshitz E M 1976 Mechanics (Third Edition) (London: Pergamon Press) p58
[30] Chen H, Kreider A, Brayman A A, Bailey M R, Matula T J 2011 Phys. Rev. L 106 034301
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