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Gauss声束对离轴椭圆柱的声辐射力矩

## Gauss声束对离轴椭圆柱的声辐射力矩

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• #### 摘要

利用部分波展开法求解得到了Gauss声束入射下刚性和非刚性椭圆柱的声散射系数, 推导了一般情况下的声辐射力矩表达式. 在此基础上, 通过一系列数值仿真详细分析了离轴距离、入射角度和束腰半径对声辐射力矩的影响. 结果表明: 正向与负向声辐射力矩均可以在一定条件下存在; 低频情况下刚性椭圆柱比非刚性椭圆柱更容易产生较强的声辐射力矩; 特定频率的入射声场可以激发出非刚性椭圆柱不同阶的共振散射模式, 因而非刚性椭圆柱的声辐射力矩峰值与频率的关系更密切; 增加束腰半径有利于扩大散射截面, 进而增加椭圆柱的声辐射力矩. 该研究结果预期可以为利用声辐射力矩实现粒子的可控旋转和流体黏度的反演提供一定的理论指导.

#### 施引文献

• 图 1  Gauss声束斜入射到无限长椭圆柱上

Fig. 1.  Description for the interaction of a Gauss beam with an infinitely long elliptical cylinder.

图 2  柱的声辐射力矩函数随kbky0的变化关系(kx0 = 0, kW0 = 3)　(a) a/b = 1/2, 刚性; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, 刚性; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, 刚性; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, 刚性; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, 刚性; (j) a/b = 2, PDMS-TBE

Fig. 2.  The acoustic radiation torque function plots for an elliptical cylinder versus kb and ky0 (kx0 = 0, kW0 = 3): (a) a/b = 1/2, rigid; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, rigid; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, rigid; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, rigid; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, rigid; (j) a/b = 2, PDMS-TBE.

图 3  PDMS椭圆柱的共振散射函数幅值$\left| {{f^{{\rm{res}}}}} \right|$随角度θ的变化关系 (kx0 = 0, ky0 = 6, α = π/4, kW0 = 3)　(a) kb = 5.5; (b) kb = 6.1

Fig. 3.  The resonance scattering function modulus $\left| {{f^{{\rm{res}}}}} \right|$ for a PDMS-TBE elliptical cylinder versus the angle θ (kx0 = 0, ky0 = 6, α = π/4, kW0 = 3): (a) kb = 5.5; (b) kb = 6.1.

图 4  椭圆柱的声辐射力矩函数随kbkx0的变化关系(ky0 = –3, kW0 = 3)　(a) a/b = 1/2, 刚性; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, 刚性; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, 刚性; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, 刚性; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, 刚性; (j) a/b = 2, PDMS-TBE

Fig. 4.  The acoustic radiation torque function plots for an elliptical cylinder versus kb and kx0 (ky0 = –3, kW0 = 3): (a) a/b = 1/2, rigid; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, rigid; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, rigid; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, rigid; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, rigid; (j) a/b = 2, PDMS-TBE.

图 5  椭圆柱的声辐射力矩函数随kbα的变化关系(kx0 = –3, ky0 = –3, kW0 = 3)　(a) a/b = 1/2, 刚性; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, 刚性; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, 刚性; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, 刚性; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, 刚性; (j) a/b = 2, PDMS-TBE

Fig. 5.  The acoustic radiation torque function plots for an elliptical cylinder versus kb and α (kx0 = –3, ky0 = –3, kW0 = 3): (a) a/b = 1/2, rigid; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, rigid; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, rigid; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, rigid; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, rigid; (j) a/b = 2, PDMS-TBE.

图 6  椭圆柱的声辐射力矩函数随kbkW0的变化关系(kx0 = –3, ky0 = –3, α = π/4)　(a) a/b = 1/2, 刚性; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, 刚性; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, 刚性; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, 刚性; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, 刚性; (j) a/b = 2, PDMS-TBE

Fig. 6.  The acoustic radiation torque function plots for an elliptical cylinder versus kb and kW0 (kx0 = –3, ky0 = –3, α = π/4): (a) a/b = 1/2, rigid; (b) a/b = 1/2, PDMS-TBE; (c) a/b = 2/3, rigid; (d) a/b = 2/3, PDMS-TBE; (e) a/b = 1, rigid; (f) a/b = 1, PDMS-TBE; (g) a/b = 3/2, rigid; (h) a/b = 3/2, PDMS-TBE; (i) a/b = 2, rigid; (j) a/b = 2, PDMS-TBE.

图 7  PDMS-TBE椭圆柱的声辐射力矩函数随kb的变化关系(kx0 = 0, ky0 = 6, kW0 = 3, α = π/4)

Fig. 7.  The acoustic radiation torque function plots for a PDMS-TBE elliptical cylinder versus kb (kx0 = 0, ky0 = 6, kW0 = 3, α = π/4).

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##### 出版历程
• 收稿日期:  2020-10-03
• 修回日期:  2020-12-04
• 上网日期:  2021-04-05

## Gauss声束对离轴椭圆柱的声辐射力矩

• 1. 中国科学院声学研究所, 北京　100190
• 2. 中国科学院大学, 北京　100049
• 3. 北京市海洋深部钻探测量工程技术研究中心, 北京　100190
基金项目: 国家自然科学基金 (批准号: 11604361, 11904384)、国家重点研发计划 (批准号: 2018YFC0114900)和中国科学院青年创新促进会(批准号: 2019024)资助的课题

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