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基于时域有限差分算法将大气中近似到二阶微小项的非线性声波波动方程进行离散化,得到了模拟采用的差分波动方程.在此基础上,数值模拟了初始声压强弱不同的5个点声源组成的线阵列垂直或斜向辐射的连续正弦波在大气中传播时二维声场的分布情况.将线性条件下的模拟结果与非线性条件下的模拟结果进行比较后发现:弱非线性会对声场的分布和阵列聚焦增益产生一定的影响,使声场分布波形比线性条件下的声场分布波形更加靠近阵列,聚焦效果变差;强非线性会使波形发生更严重畸变,这是由于产生了基频以外的其他频率声波引起的;非线性对斜向传播时声场分布的影响与垂直传播时的影响效果基本相同,但由于斜向辐射时的声波几何扩展造成的轴向声压衰减要大于垂直辐射时的轴向声压衰减,因此聚焦增益和强非线性的影响都将小于垂直辐射时的情况.The difference wave equation is obtained by the discretization of nonlinear acoustic wave equation in atmosphere with in the second-order miniterm approximation based on the finite-difference time-domain method. And the two-dimensional field distribution of continuous sinusoidal wave vertically or obliquely radiated by a linear array of five monopole sound sources is numerically simulated at the different initial acoustic pressures. A comparison between nonlinear simulation and linear one show that weak nonlinearity has definite and apparent effects on the distribution of acoustic field and focused gain of array, leading the distribution of waveform to be closer to the array and the focusing gain to deteriorate, and that the strong nonlinearity has a strong waveform aberration, because the other waves of non-fundamental frequency appear. No evident distinction is found in the effect between the oblique propagation and the vertical propagation, though less focusing gain and influence caused by strong nonlinearity produced by the acoustic geometric spreading result in more attenuation of axial pressure in the case of oblique propagation.
[1] Garrett G S, Tjtta J N, Tjtta S 1982 J. Acoust. Soc. Am. 72 1056
[2] Averkiou M A, Hamilton M F 1997 J. Acoust. Soc. Am. 102 2539
[3] Li J L, Liu X Z, Zhang D, Gong X F 2006 Acta Phys. Sin. 55 2809 (in Chinese) [李俊伦、刘晓宙、章 东、龚秀芬 2006 55 2809]
[4] Xue H H, Liu X Z, Gong X F, Zhang D 2005 Acta Phys. Sin. 54 5233 (in Chinese) [薛洪惠、刘晓宙、龚秀芬、章 东 2005 54 5233]
[5] Du H W, Peng H, Jiang C H, Feng H Q 2007 Acta Phys. Sin. 56 6496 (in Chinese) [杜宏伟、彭 虎、江朝晖、冯焕清 2007 56 6496]
[6] Yu J, Zhang D, Liu X Z, Gong X F, Song F X 2007 Acta Phys. Sin. 56 5909 (in Chinese) [于 洁、章 东、刘晓宙、龚秀芬、宋富先 2007 56 5909]
[7] Li T B 2005 Computing Acoustics: the Equations and Calculation Methods of Sound Field (Beijing: Science Press) p221 (in Chinese) [李太宝 2005 计算声学:声场的方程和计算方法(北京:科学出版社) 第221页]
[8] Huijssen J, Bouakaz A, Verweij M D, Jone N D 2003 IEEE Ultrasonics Symposium (Hawaii: IEEE) p1851
[9] Cizek M, Rozman J 2007 Radioelektronika 17th International Conference (Brno: IEEE) p1
[10] Hallaja I M, Cleveland R O 1999 J. Acoust. Soc. Am. 105 L7
[11] Botteldooren D 1995 J. Acoust. Soc. Am. 98 3303
[12] Cotté B, Blanc-Benon P 2009 J. Acoust. Soc. Am. 125 EL202
[13] Castor K, Gerstoft P, Roux P, Kuperman W A, McDonald B E 2004 J. Acoust. Soc. Am. 116 2004
[14] Eccardt P C, Landes H, Lerch R 1996 IEEE Ultrasonics Symposium (San Antonio: IEEE) p991
[15] Pozuelo C C, Dubus B, Gallego-Juárez J A 1999 J. Acoust. Soc. Am. 106 91
[16] Qian Z W 1992 Nonlinear Acoustics (Beijing: Science Press) p30 (in Chinese) [钱祖文 1992 非线性声学 (北京:科学出版社) 第30页]
[17] Hamilton M F, Blackstock D T 1998 Nonlinear Acoustics (San Diego: Academic Press) p55
[18] Yang X R, Chen Y 2007 Amosphere Acoustics (Beijing: Science Press) p148 (in Chinese) [杨训仁、陈 宇 2007 大气声学 (北京:科学出版社) 第148页]
[19] Ma D Y, Shen H 2004 Handbook of Acoustics (Beijing: Science Press) p240 (in Chinese)[马大猷、沈 豪 2004 声学手册 (北京:科学出版社) 第240页]
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[1] Garrett G S, Tjtta J N, Tjtta S 1982 J. Acoust. Soc. Am. 72 1056
[2] Averkiou M A, Hamilton M F 1997 J. Acoust. Soc. Am. 102 2539
[3] Li J L, Liu X Z, Zhang D, Gong X F 2006 Acta Phys. Sin. 55 2809 (in Chinese) [李俊伦、刘晓宙、章 东、龚秀芬 2006 55 2809]
[4] Xue H H, Liu X Z, Gong X F, Zhang D 2005 Acta Phys. Sin. 54 5233 (in Chinese) [薛洪惠、刘晓宙、龚秀芬、章 东 2005 54 5233]
[5] Du H W, Peng H, Jiang C H, Feng H Q 2007 Acta Phys. Sin. 56 6496 (in Chinese) [杜宏伟、彭 虎、江朝晖、冯焕清 2007 56 6496]
[6] Yu J, Zhang D, Liu X Z, Gong X F, Song F X 2007 Acta Phys. Sin. 56 5909 (in Chinese) [于 洁、章 东、刘晓宙、龚秀芬、宋富先 2007 56 5909]
[7] Li T B 2005 Computing Acoustics: the Equations and Calculation Methods of Sound Field (Beijing: Science Press) p221 (in Chinese) [李太宝 2005 计算声学:声场的方程和计算方法(北京:科学出版社) 第221页]
[8] Huijssen J, Bouakaz A, Verweij M D, Jone N D 2003 IEEE Ultrasonics Symposium (Hawaii: IEEE) p1851
[9] Cizek M, Rozman J 2007 Radioelektronika 17th International Conference (Brno: IEEE) p1
[10] Hallaja I M, Cleveland R O 1999 J. Acoust. Soc. Am. 105 L7
[11] Botteldooren D 1995 J. Acoust. Soc. Am. 98 3303
[12] Cotté B, Blanc-Benon P 2009 J. Acoust. Soc. Am. 125 EL202
[13] Castor K, Gerstoft P, Roux P, Kuperman W A, McDonald B E 2004 J. Acoust. Soc. Am. 116 2004
[14] Eccardt P C, Landes H, Lerch R 1996 IEEE Ultrasonics Symposium (San Antonio: IEEE) p991
[15] Pozuelo C C, Dubus B, Gallego-Juárez J A 1999 J. Acoust. Soc. Am. 106 91
[16] Qian Z W 1992 Nonlinear Acoustics (Beijing: Science Press) p30 (in Chinese) [钱祖文 1992 非线性声学 (北京:科学出版社) 第30页]
[17] Hamilton M F, Blackstock D T 1998 Nonlinear Acoustics (San Diego: Academic Press) p55
[18] Yang X R, Chen Y 2007 Amosphere Acoustics (Beijing: Science Press) p148 (in Chinese) [杨训仁、陈 宇 2007 大气声学 (北京:科学出版社) 第148页]
[19] Ma D Y, Shen H 2004 Handbook of Acoustics (Beijing: Science Press) p240 (in Chinese)[马大猷、沈 豪 2004 声学手册 (北京:科学出版社) 第240页]
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