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Acoustic black hole (ABH) structures are renowned for their unique wave-focusing ability and have been widely utilized in the fields of acoustics and vibration. Based on this property, a novel high-sensitivity hydrophone design incorporating a two-dimensional (2D) ABH structure is proposed in this work. According to the principles of geometrical acoustics, the wave-converging behavior of bending waves in ABH structures is compared to the bending of acoustic ray in underwater acoustics. A simplified theoretical model describing the relationship between the bending wave trajectory and the wave speed gradient in polar coordinates is established for two-dimensional (2D) ABH configurations and verified through numerical simulations. Based on this mechanism, a 2D ABH hydrophone is developed by integrating the ABH structure into bending-plate hydrophone, enabling vibration energy concentration and significantly enhancing sensitivity. The comparative studies of hydrophones using uniform-thickness plates and linearly tapered thickness plates as receiving surfaces confirm the superior performance of the ABH hydrophone in a frequency range of 1.7–5.8 kHz. To address the significant undulations observed in the sensitivity response, which is attributed to vibration superposition, a liquid cavity of specific length is introduced. This leads to the development of an ABH-Helmholtz-coupled hydrophone (ABHH hydrophone), wherein the first two bending modes of the ABH structure are coupled with the resonant modes of a single-ended open liquid cavity, resulting in broadband reception capability. The prototypes of both hydrophone designs are fabricated and experimentally tested in an anechoic water tank. The results show that both devices achieve peak receiving sensitivities exceeding –169 dB. Notably, the ABHH hydrophone maintains sensitivity fluctuations within 8 dB in a frequency band of 2.6–5.3 kHz. This study confirms that 2D ABH structures can effectively improve hydrophone sensitivity through bending wave convergence, and can achieve broadband acoustic detection when the structure is coupled with liquid cavity resonators. These findings lay a solid foundation for the application of ABH structures in the design of underwater acoustic transducer.
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Keywords:
- hydrophone /
- two-dimensional acoustic black hole /
- high sensitivity /
- modal coupling
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图 1 (a) 厚度呈幂律形式变化的梁横截面; (b) 二维ABH结构
Figure 1. (a) Cross-section of a beam with power-law thickness variation; (b) 2D ABH structure.
图 2 极坐标系中弯曲波轨迹微元几何关系
Figure 2. Geometric relationship of an infinitesimal element along the bending wave trajectory in the polar coordinate system.
图 3 (a) 嵌入二维ABH凹坑的薄板; (b) 正弦激励信号
Figure 3. (a) Thin plate embedded with a 2D ABH pit; (b) sinusoidal excitation signal.
图 4 1—7 ms时刻两种板的位移响应 (a)均匀板; (b) 嵌入二维ABH凹坑的薄板
Figure 4. Displacement responses of two types of plates at 1–7 ms: (a) Uniform plate; (b) thin plate embedded with a 2D ABH pit.
图 5 (a) 二维ABH水听器结构剖面图; (b) ABH板的一维截面
Figure 5. (a) Cross-sectional view of the 2D ABH hydrophone structure; (b) one-dimensional profile of the ABH plate.
图 6 ABH水听器的有限元模型 (a) 整体图; (b) 局部图
Figure 6. Finite element model of the ABH hydrophone: (a) General view; (b) enlarged view.
图 7 4种厚度板的一维截面 (a) 均匀厚度$ {h_1} $; (b) 均匀厚度$ {h_2} $; (c) 线性变厚度; (d) ABH
Figure 7. One-dimensional profiles of plates with four thickness types: (a) Uniform thickness $ {h_1} $; (b) uniform thickness $ {h_2} $; (c) linear thickness variation; (d) ABH.
图 8 4种厚度形式的板作为声波接收面的水听器接收电压灵敏度级曲线
Figure 8. Receiving voltage sensitivity level curves for hydrophones with plates of four thickness types as the acoustic wave receiving surface.
图 9 4种厚度形式的板作为声波接收面的水听器接收指向性 (a) 2.95 kHz; (b) 5.25 kHz
Figure 9. Receiving directivity of hydrophones with plates of four thickness types as the acoustic wave receiving surface: (a) 2.95 kHz; (b) 5.25 kHz.
图 10 ABH水听器位移场和稳态声压场的整体图和局部放大图 (a) 2.95 kHz; (b) 5.25 kHz
Figure 10. General and enlarged views of displacement fields and steady-state sound pressure fields for the ABH hydrophone: (a) 2.95 kHz; (b) 5.25 kHz.
图 11 ABH水听器衍射常数
Figure 11. Diffraction constant of the ABH hydrophone.
图 12 (a) 面激励等效为无数个同心圆周上线激励叠加; (b) 圆周上线激励近似为无数个线段上线激励叠加
Figure 12. (a) Equivalence of a surface excitation to the superposition of an infinite number of line excitations on concentric circumferences; (b) approximation of a line excitation on a circumference as the superposition of an infinite number of line excitations on line segments.
图 13 不同位置不同频率激励信号下的位移响应 (a) 圆周1处施加5.86 kHz信号激励; (b) 圆周2处施加5.86 kHz信号激励; (c) 圆周1和2处共同施加5.86 kHz信号激励; (d) 圆周1处施加6.53 kHz信号激励; (e) 圆周2处施加6.53 kHz信号激励; (f) 圆周1和2处共同施加6.53 kHz信号激励
Figure 13. Displacement responses under excitation at different positions and frequencies: (a) Excitation on circumference 1 with a 5.86 kHz signal; (b) excitation on circumference 2 with a 5.86 kHz signal; (c) simultaneous excitation on circumferences 1 and 2 with a 5.86 kHz signal; (d) excitation on circumference 1 with a 6.53 kHz signal; (e) excitation on circumference 2 with a 6.53 kHz signal; (f) simultaneous excitation on circumferences 1 and 2 with a 6.53 kHz signal.
图 14 ABHH水听器结构剖面图
Figure 14. Cross-sectional view of the ABHH hydrophone structure.
图 15 ABH水听器和ABHH水听器仿真接收电压灵敏度级曲线对比
Figure 15. Comparison of simulated receiving voltage sensitivity level curves between the ABH hydrophone and the ABHH hydrophone.
图 16 ABHH水听器改变液腔腔体长度接收电压灵敏度级曲线对比
Figure 16. Comparison of receiving voltage sensitivity level curves for the ABHH hydrophone with variation in the liquid cavity length.
图 17 ABHH水听器仿真指向性图
Figure 17. Simulated directivity pattern of the ABHH hydrophone.
图 18 ABHH水听器位移场和稳态声压场的整体图和局部放大图 (a) 2.75 kHz; (b) 3.85 kHz; (c) 5.3 kHz
Figure 18. General and enlarged views of displacement fields and steady-state sound pressure fields for the ABHH hydrophone: (a) 2.75 kHz; (b) 3.85 kHz; (c) 5.3 kHz.
图 19 ABHH水听器衍射常数
Figure 19. Diffraction constant of the ABHH hydrophone.
图 20 水听器零件及水密灌封后样机 (a) 水听器金属零件; (b) PZT-5 A压电陶瓷; (c) ABH水听器样机; (d) ABHH水听器样机
Figure 20. Hydrophone components and prototypes after waterproof potting: (a) Metal components; (b) PZT-5 A piezoelectric ceramic; (c) ABH hydrophone prototype; (d) ABHH hydrophone prototype.
图 21 (a) 水听器接收灵敏度和指向性的实验测量装置; (b) ABH水听器入水姿态; (c) ABHH水听器入水姿态
Figure 21. (a) Experimental setup for measuring hydrophone receiving sensitivity using the comparative method; (b) immersion posture of the ABH hydrophone; (c) immersion posture of the ABHH hydrophone.
图 22 ABH水听器和ABHH水听器实测接收电压灵敏度级曲线
Figure 22. Measured receiving voltage sensitivity level curves for the ABH hydrophone and ABHH hydrophone.
图 23 ABH水听器和ABHH水听器实测指向性图
Figure 23. Measured directivity patterns of the ABH hydrophone and ABHH hydrophone.
表 1 4种厚度形式的板作为声波接收面的水听器性能对比
Table 1. Performance comparison of hydrophones with plates of four thickness types as the acoustic wave receiving surface.
水听器接收面模型 接收灵敏度/dB 指向性–3 dB开角/(°) 最大值 最大起伏 2.95 kHz 5.25 kHz 均匀板$ h = {h_1} $ –178.7 21.35 121.6 91.8 均匀板$ h = {h_2} $ –176.3 33.2 144.8 139.2 线性变厚度板 –180.6 23.1 153.7 116.6 ABH板 –167.3 20.7 156.0 99.0 
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表 2 ABH水听器的仿真与实测性能对比
Table 2. Comparison of simulated and measured performance for the ABH hydrophone.
模态
阶数仿真 实测 频率
/kHz灵敏度
/dB–3 dB开
角/(°)频率
/kHz灵敏度
/dB–3 dB开
角/(°)1阶 2.95 –167.3 156 2.9 –168.8 120 2阶 5.25 –168.5 99 5.0 –168.6 85
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表 3 ABHH水听器的仿真与实测性能对比
Table 3. Comparison of simulated and measured performance for the ABHH hydrophone.
模态
阶数仿真 实测 频率
/kHz灵敏度
/dB–3 dB开
角/(°)频率
/kHz灵敏度
/dB–3 dB开
角/(°)1阶 2.75 –167.0 160 2.8 –170.4 135 2阶 3.85 –168.4 96 3.6 –173.9 95 3阶 5.30 –167.8 64 5.0 –169.0 69
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