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本文利用Bessel波的谐波展开式, 采用T矩阵方法的推导思路, 建立了水下任意刚性散射体在Bessel波照射下的声散射场计算公式. 以水下刚性椭球体和两端附连半球的刚性圆柱体为例, 计算了在不同波锥角β 下的反向散射形态函数, 同时, 依据镜反射波和绕行波的干涉物理模型, 给出了预报Bessel波照射下的反向散射形态函数峰峰间隔值的计算模型. 仿真结果表明本文提出的Bessel波照射下反向散射形态函数峰峰间隔值预报方法是准确有效的, 同时也说明, 本文建立的基于T矩阵法计算水下任意刚性散射体在Bessel波束下的声散射场方法是有效的, 这拓展了T矩阵法的应用领域.Study on underwater acoustic scattering is very important for detection, location, and recognition of underwater targets. In the past decades, most investigations in this respect were focused on the case of plane wave incidence. But the Bessel beam is a kind of approximate non-diffracting beam with an excellent directing property, so more attention should be paid on it. So far, according to the literature, the studies about underwater acoustic scattering of a Bessel beam mainly focused on spheres and spherical shells using the partial wave series form. When the scatterers become complex objects, the partial wave series form fails to deal with these kinds of problems. To overcome this shortage, the T-matrix method has been introduced to calculate the underwater scattering of a Bessel beam by complex rigid objects. #br#In this paper, the underwater acoustic scattering of a Bessel beam by rigid objects with arbitrary shapes calculated by T-matrix method is studied. By means of the harmonic expansion of Bessel beam, the expression of the incident coefficient can be derived. Through the transmission matrix that relates the known coefficients of expansion of an incident wave to the unknown expansion coefficients of the scattered field, the acoustic scattering formula of a Bessel beam by a rigid scatterer with arbitrary shape is established. In this paper, the backscattering fields of rigid spheroids and finite cylinders with two spheroidal endcaps are discussed, and the backscattering form function modulus |F| is curved as a function of dimensionless frequency ka. Subsequently, the peak to peak intervals in backscattering form function caused by the interference of the specular wave and the Franz wave are also analyzed in geometry. The calculated results show that the frequency interval obtained from the curves agrees well with those obtained by geometric analysis for the rigid objects. Meanwhile, for both the rigid spheroid and finite cylinder, the highlight model is successfully applied to explain the phenomenon in which the amplitude of backscattering form function changes with the cone angle of the Bessel beam. From the above numerical results and analysis, the T-matrix method has been successfully introduced to calculate the acoustic scattering of the Bessel beam by complex objects, which extends the application of the T-matrix method and provides a useful tool to explore the characteristics of the Bessel beam.
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Keywords:
- T-matrix method /
- Bessel beam /
- form function /
- Franz wave
[1] Williams K L, Marston P L 1985 J. Acoust. Soc. Am. 78 1093
[2] Houston B H, Bucaro J A, Photiadis D M 1995 J. Acoust. Soc. Am. 98 2851
[3] Gabrielli P, Mercier-Finidori M 2001 J. Sound Vib. 241 423
[4] Li W 2004 Ph.D. Dissertation (Singapore: National University of Singapore)
[5] Durnin J 1984 J. Opt. Soc. Am. A 4 651
[6] Marston P L 2007 J. Acoust. Soc. Am. 121 753
[7] Marston P L 2007 J. Acoust. Soc. Am. 122 247
[8] Li W, Qu H F 2013 Acta Acustica 38 42
[9] Waterman P C 1969 J. Acoust. Soc. Am. 54 1417
[10] Li W, Zhao Y, Zhang T, Liu J X 2007 Technical Acoustics 26 844 (in Chinese) [李威, 赵耀, 张涛, 刘敬喜 2007 声学技术 26 844]
[11] Fan J, Zhu B, Tang W 2001 Acta Acustica 26 545 (in Chinese) [范军, 朱蓓丽, 汤渭霖 2001 声学学报 26 545]
[12] Fan J, Liu T, Tang W 2002 Technical Acoustics 21 153 (in Chinese) [范军, 刘涛, 汤渭霖 2002 声学技术 21 153]
[13] Marston P L 2008 J. Acoust. Soc. Am. 124 2905
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[1] Williams K L, Marston P L 1985 J. Acoust. Soc. Am. 78 1093
[2] Houston B H, Bucaro J A, Photiadis D M 1995 J. Acoust. Soc. Am. 98 2851
[3] Gabrielli P, Mercier-Finidori M 2001 J. Sound Vib. 241 423
[4] Li W 2004 Ph.D. Dissertation (Singapore: National University of Singapore)
[5] Durnin J 1984 J. Opt. Soc. Am. A 4 651
[6] Marston P L 2007 J. Acoust. Soc. Am. 121 753
[7] Marston P L 2007 J. Acoust. Soc. Am. 122 247
[8] Li W, Qu H F 2013 Acta Acustica 38 42
[9] Waterman P C 1969 J. Acoust. Soc. Am. 54 1417
[10] Li W, Zhao Y, Zhang T, Liu J X 2007 Technical Acoustics 26 844 (in Chinese) [李威, 赵耀, 张涛, 刘敬喜 2007 声学技术 26 844]
[11] Fan J, Zhu B, Tang W 2001 Acta Acustica 26 545 (in Chinese) [范军, 朱蓓丽, 汤渭霖 2001 声学学报 26 545]
[12] Fan J, Liu T, Tang W 2002 Technical Acoustics 21 153 (in Chinese) [范军, 刘涛, 汤渭霖 2002 声学技术 21 153]
[13] Marston P L 2008 J. Acoust. Soc. Am. 124 2905
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