In order to solve the problem of phased nonlinear acoustic field could not be modeled by one order parabolic approximation KZK equation, equivalent parametric array primary frequency natural directivity acoustic field model was built based on primary frequency collimate characteristic, and the equivalent relation between this field and the primary frequency phased acoustic field was built, so the problem of phased nonlinear acoustic field modeling was transferred to equivalent parametric array source condition calculation, and an operator split time domain finite difference numerical calculation method was derived, the rectangular aperture parametric array phased nonlinear field calculation based on KZK equation was realized. Let the SES2000 parametric array acoustic field as subjects, the phased nonlinear acoustic model and the corresponding field calculation method were examined by computer simulation and pool contrast experiment.
[1] Olav R G, Kenneth G F, Johnny D, et al. Detecting atlantic herring by parametric sonar[J]. J. Acoust. Soc. Am, Express Letters, 2010, 127(4):EL153-EL159.
[2] Egor V D, Bojan B G. Acoustic radiation force in tissue-like solids due to modulated sound field[J]. Journal of the Mechanics and Physics of Solids, 2012, 60:1791-1813.
[3] Akiyoshi I, Nobuo T and Hiroyuki I. Global active noise control using a delayed driving parametric array loudspeaker[J]. The Japan Society of Mechanical Engineers, 2013, 79(799):604-617.
[4] Milan C and Michal B. Non-paraxial model for a parametric acoustic array[J]. J. Acoust. Soc. Am, 2013, 134(2):933-938.
[5] Hideyuki N, Claes M H and Tomoo K. Numerical simulation of length-limited parametric sound beam[C]. International Congress on Ultrasonics, 2012, 1433:547-550.
[6] David G. B, Mark B M and William L K. Parametric acoustic array development at the US Navy’s New London, Connecticut laboratory[C]. Acoustical Society of America, Physical Acoustics, 2009, 6:1-22.
[7] Karsten W, Thomas B, Tobias W. Parametric underwater communications[C]. 11th European Conference on Underwater Acoustics, 2012, 17:1-10.
[8] Akira A, Tamaki U, Fumitaka M, et al. Sub-bottom synthetic aperture imaging sonar system using an AUV and an autonomous surface tracking vehicle for searching for buried shells of toxic chemicals[C]. Waterside Security conference, 2010, 1-3.
[9] Maxim S and Tony W H S. Simulation of nonlinear Westervelt equation for the investigation of acoustic streaming and nonlinear propagation effects[J]. J. Acoust. Soc. Am, 2013, 134(5):3931-3942.
[10] 杨德森, 兰朝凤, 时胜国, 等. 水中声波非线性相互作用的声吸收研究[J]. 振动与冲击, 2012, 31(8):52-56.
YANG De-sen, LAN Chao-feng, SHI Sheng-guo, et al. Sound absorption of sound under interaction among underwater nonlinear acoustic variable parameters[J]. Journal of Vibration and Shock, 2012, 31(8): 52-56.
[11] LIU Wei, YANG Jun and TIAN Jing. Time-domain modeling of finite-amplitude sound beams in three-dimensional Cartesian coordinate system[J]. Chinese Journal of Acoustics, 2012, 31(4):408-422.
[12] 杜宏伟. 生物医学超声中若干非线性问题的研究[D]. 合肥:中国科学技术大学, 2007.
DU Hong-wei. Researches on nonlinear problems in the biomedicine ultrasonic[D]. He Fei: University of Science and Technology of China, 2007.
[13] Kenneth G F, David T I F and Philip R A. Calibration sphere for low-frequency parametric sonars[J]. J. Acoust. Soc. Am, 2007, 121(3):1482-1490.
[14] Paul L M J van N, Mikhail G D, Martin D V, et al. Comparison of fundamental, second harmonic and superharmonic imaging: A simulation study[J]. J. Acoust. Soc. AM, 2011, 130(5):3148-3157.
[15] SHI Chuang and GAN Woon-seng. Steerable parametric loudspeaker with preprocessing methods[C]. Proceedings of Meetings on Acoustics, 2013, 19:1-6.
[16] 李太宝. 计算声学—声场的方程和计算方法[M]. 北京:科学出版社, 2005.
LI Tai-bao. Computational Acoustics: equation and calculation method of sound field[M]. Beijing: Science Press, 2005.
[17] YANG Jun, SHA Kan, GAN Woon-seng, et al. A Fast Field Scheme for the Parametric Sound Radiation from Rectangular Aperture Source[J]. CHIN. PHYS. LETT, 2004, 21(1):111-113.
[18] Aanonsen S I, Barkve T, Tjøtta J N, et al. Distortion and harmonic generation in the nearfield of a finite amplitude sound beam. J. Acoust. Soc. Am, 1984, 75: 749-768.
[19] Kaya O A, Şahin A and Kaleci D. Pressure field of rectangular transducers at finite amplitude in three dimensions[J]. Ultrasound in Med.& Biol, 2006, 32(2):271-280.
[20] Egor V D and Bojan B G. On the KZK-type equation for modulated ultrasound fields[J]. Wave Motion, 2013, 50:763-775.
[21] Lee Y S. Numerical solution of the KZK equation for pulsed finite amplitude sound beams in thermoviscous fluids[J]. Texas: University of Texas, 1993.
[22] Marco M V. 3D harmonic echocardiography[D]. Rotterdam: Erasmus University, 2007.
[23] Lucilla D M, Jacques M, Pierre C. Nonlinear multi-frequency generation for underwater application[J]. Applied Acoustic, 2012, 73:900-903.
[24] Kenneth B O and Leon A F. Sound field calculation for rectangular sources[C]. IEEE Transactions on Ultrasonics, 1989, 36(2):242-248