非线性声场中的参量激发

陈海霞; 林书玉

doi:10.7498/aps.70.20202093

摘要

本文基于求解单频声波方程近似解的方法, 得到了非线性声场中谐波的声压与介质性质、初始声压幅值及频率之间的定量关系. 并对两列相对声压幅值和相对频率不同情况下的声场分布进行了研究. 通过分析单、双频声源辐射场中的谐波分布和传播规律发现: 在非线性声场中会不断地出现新的谐波, 激发的各阶谐波随着声波传播距离的增大逐渐增强而后减弱. 在声源的附近, 谐波的声压随基波声压振幅的增大而增大; 但在基波的频率增大时反而会减小. 在输入总声能相同的情况下, 与单频声场相比双频声源辐射场的声能量分布较均匀, 声的传播距离较大, 远场中的谐波含量较大. 结果表明, 基波的频率越高, 衰减得越快, 谐波的积累越缓慢; 声压的极值越大, 基波声能量转移得越多, 产生的谐波越多, 基波的衰减越快, 声压对远场声能的负效应增大; 如果改用多频声源, 并适当地控制输入声波的组成成分, 可以达到改善声场分布均匀性、增大声辐射距离的效果.

关键词:

Abstract

The formula for the nonlinear propagation of harmonics is obtained by using the generalized Navier-Stokes equations and the modified equations of state, considering the presence of heat transfer and fluid viscidity. The quantitative relationship among the harmonic pressure, initial sound pressure amplitude, frequency and the media property is obtained by approximately solving the single-frequency acoustic equation. In this paper, the hamonics’ distributions and propagations in the radiation field of single- and double-frequency sound source with different driving pressures and frequencies are discussed. It is found that new harmonics constantly appear in the sound field, and each-order harmonic of excitation gradually increases and then weakens with the increase of distance. The amplitude of harmonic pressure increases with the increase of the driving acoustic pressure near the sound source, but decreases with the increase of the frequency. Compared with the single-frequency field, the dual-frequency field has a large propagation distance, a very uniform acoustic energy distribution, and a large harmonic content in the far-field when the input total sound energy is constant. The physical mechanism is that the higher driving frequency causes a faster acoustic loss, a slower harmonic accumulation, and a smaller sound propagation distance. The higher driving pressure causes the much fundamental sound energy to be transferred, the more harmonics to be generated, the fundamental wave to be attenuated faster, and the negative effect of sound pressure on far-field sound energy to be increased. Through the analysis, it is found that the multi-frequency sound source can increase the propagation distance of sound, and improve the uniformity of sound energy distribution.

Keywords:

作者及机构信息

陕西师范大学物理学与信息技术学院, 陕西省超声学重点实验室, 西安　710062

通信作者: 林书玉, sylin@snnu.du.cn

基金项目: 国家自然科学基金(批准号: 11674206, 11874253)资助的课题

Authors and contacts

Shaanxi Key Laboratory of Ultrasonics, School of Physics & Information Technology, Shaanxi Normal University, Xi’an 710062, China

Corresponding author: Lin Shu-Yu, sylin@snnu.du.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11674206, 11874253)

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参考文献

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[22]	陈海霞, 林书玉 2020 69 134301 Google Scholar Chen H X, Lin S Y 2020 Acta Phys. Sin. 69 134301 Google Scholar
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施引文献

图 1 各阶谐波的声压分布曲线

Fig. 1. The harmonic curve of acoustics.

下载: 全尺寸图片幻灯片

图 2 二次谐波曲线　(a)不同声压下的二次谐波; (b)不同频率下的二次谐波

Fig. 2. The distribution of second harmonic: (a) Different acoustic pressure; (b) different acoustic frequency.

下载: 全尺寸图片幻灯片

图 3 谐波声能与总能量比分布

Fig. 3. Distributions of the ratio of the hamonic and total energies.

下载: 全尺寸图片幻灯片

图 4 和频波声压分布曲线

Fig. 4. The acoustic pressure curves of sum frequency.

下载: 全尺寸图片幻灯片

图 5 差频波声压分布曲线

Fig. 5. The acoustic pressure curves of difference frequency.

下载: 全尺寸图片幻灯片

图 6 谐波声能与总能量比分布

Fig. 6. The ratio of the hamonic and total energies.

下载: 全尺寸图片幻灯片

图 7 基频声能量的分布

Fig. 7. The distribution of fundamental energy.

下载: 全尺寸图片幻灯片

图 8 基频声能量与总声能量比分布

Fig. 8. The ratio of the fundamental and total energies.

下载: 全尺寸图片幻灯片

map

[1]	Westervelt P J 1957 J. Acoust. Soc. Am. 29 199 Google Scholar
[2]	Westervelt P J 1957 J. Acoust. Soc. Am. 29 934 Google Scholar
[3]	Ingard U, Pridmo-Brown D C 1955 J. Acoust. Soc. Am. 27 1002
[4]	Ingard U, Pridmo-Brown D C 1956 J. Acoust. Soc. Am. 28 367 Google Scholar
[5]	钱祖文 1981 30 1479 Google Scholar Qian Z W 1981 Acta Phys. Sin. 30 1479 Google Scholar
[6]	钱祖文 1981 30 1559 Google Scholar Qian Z W 1981 Acta Phys. Sin. 30 1559 Google Scholar
[7]	钱祖文 1988 37 221 Google Scholar Qian Z W 1988 Acta Phys. Sin. 37 221 Google Scholar
[8]	Westervelt P J 1963 J. Acoust. Soc. Am. 35 535 Google Scholar
[9]	钱祖文 1976 25 472 Google Scholar Qian Z W 1976 Acta Phys. Sin. 25 472 Google Scholar
[10]	钱祖文 1999 物理 28 593 Google Scholar Qian Z W 1999 J. Phys. 28 593 Google Scholar
[11]	Wang X, Chen W Z, Liang S D, Zhao T Y, Liang J F 2017 Phys. Rev. E 95 033118 Google Scholar
[12]	Wang X, Chen W Z, Yang J, Liang S D 2018 J. Appl. Phys. 123 214904 Google Scholar
[13]	陈伟中 2018 应用声学 37 675 Google Scholar Chen W Z 2018 Appl. Acoust. 37 675 Google Scholar
[14]	Ashokumar M 2011 Ultrason. Sonochem. 18 864 Google Scholar
[15]	Wijngaarden L V 1972 Ann. Rev. Fluid Mech. 4 369 Google Scholar
[16]	Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732 Google Scholar
[17]	Vanhille C, Cleofé C P 2011 Ultrason. Sonochem. 18 679 Google Scholar
[18]	Thiessen R J, Cheviakov A F 2019 Commun. Nonliear Sci. Numer. Simul. 73 244 Google Scholar
[19]	Zhang H H 2020 J. Acoustic Soc. Am. 147 399 Google Scholar
[20]	王勇, 林书玉, 张小丽 2014 63 034301 Google Scholar Wang Y, Lin S Y, Zhang X L 2014 Acta Phys. Sin. 63 034301 Google Scholar
[21]	钱祖文 2009 非线性声学(北京: 科学出版社) 第14页 Qian Z W 2009 Nonliear Acoustics (Beijing: Science Press) p14 (in Chinese)
[22]	陈海霞, 林书玉 2020 69 134301 Google Scholar Chen H X, Lin S Y 2020 Acta Phys. Sin. 69 134301 Google Scholar
[23]	杜功焕, 朱哲民, 龚秀芬 2001 声学基础 (南京: 南京大学出版社) 第495页 Du G H, Zhu Z M, Gong X F 2001 Fundamentals of Sound (Nanjing: Nanjing University Press) p495 (in Chinese)

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非线性声场中的参量激发