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基于声黑洞结构在对弯曲波调控中的能量聚焦与位移放大方面的优势, 提出了一种新型声黑洞夹心式弯曲振动换能器, 该换能器由夹心式弯曲振动换能器与声黑洞探头组成. 基于Timoshenko梁理论, 采用传输矩阵法建立了换能器整体弯曲振动的理论模型, 理论运算得出的解析解与仿真得出的数值解相吻合. 通过有限元方法对该换能器的电阻抗频率响应特性、振动模态、辐射声场和振动位移进行模拟仿真研究, 并与悬链线型换能器进行对比分析, 结果显示, 在相同振动模态下, 声黑洞型换能器的最大声压和振动位移均优于悬链线型换能器, 表明声黑洞结构能够有效提升弯曲振动位移和换能器的侧向辐射性能. 最后加工出了该换能器样机并对其电阻抗特性以及振动模态进行实验测量, 实验结果与仿真结果吻合良好.Based on the advantages of the acoustic black hole (ABH) structure in energy focusing and displacement amplification during the regulation of flexural waves, a new type of ABH sandwich-shaped flexural vibration transducer is proposed in this work. This transducer consists of a sandwich-shaped flexural vibration transducer and an ABH probe. Based on the Timoshenko beam theory, the theoretical model of the overall flexural vibration of the transducer is established by the transfer matrix method, and the calculated results are consistent with the finite element simulation results. The impedance frequency response characteristics, vibration modes, radiation acoustic field and vibration displacement of this transducer are discussed by the finite element method, and a comparative analysis is conducted with the catenary-shaped transducer. The results show that the maximum sound pressure and vibration displacement of the ABH transducer under the same mode are greater than those of the catenary-shaped transducer, indicating that the ABH structure can efficiently enhance the displacement of flexural vibration and the radiation performance of the transducer, and is expected to be utilized as a small-scale acoustic chemical reactor. Finally, a prototype of this transducer is fabricated, then its impedance characteristics and vibration modes are experimentally measured. The experimental results are in agreement with the simulation results.
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Keywords:
- acoustic black hole structure /
- ultrasonic transducer /
- flexural vibration /
- transfer matrix method
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图 1 换能器结构与尺寸参数示意图
Fig. 1. Schematic diagram of the structure and size parameters of the transducer.
图 2 传输矩阵法示意图 (a)模型简化图; (b)梁的振动单元划分
Fig. 2. Schematic diagram of the transfer matrix method: (a) Model simplification diagram; (b) the vibration element division of variable cross-section beam.
图 3 离散振动单元边界力学量
Fig. 3. Mechanical quantities at the boundary of discrete vibration elements.
图 4 理论模型计算结果与收敛性验证 (a) 理论模型计算结果; (b) 收敛性验证
Fig. 4. Theoretical model computation results and convergence verification: (a) The theoretical model calculation results; (b) the convergence verification.
图 5 换能器第六阶弯曲振动模态 (a) 声黑洞型换能器第六阶弯曲振动模态; (b) 悬链线型换能器第六阶弯曲振动模态
Fig. 5. The sixth-order flexural vibration mode of the transducers: (a) The sixth-order flexural vibration mode of the acoustic black hole structure transducer; (b) the sixth-order flexural vibration mode of the catenary-shaped structure transducer.
图 6 探头振动位移对比 (a) 空气中的探头振动位移对比; (b) 水中的探头振动位移对比
Fig. 6. Comparison of probe vibration displacement: (a) Comparison of probe vibration displacements in the air; (b) comparison of probe vibration displacements in the water.
图 7 换能器水中声压 (a) 声黑洞型换能器水中声压; (b) 悬链线型换能器水中声压
Fig. 7. The sound pressure of the transducers in water: (a) The underwater sound pressure of the acoustic black hole structure transducer; (b) the underwater sound pressure of the catenary-shaped structure transducer.
图 10 换能器阻抗分析实验装置以及阻抗测量结果 (a) WK6500B阻抗分析仪及换能器; (b) 阻抗测量结果
Fig. 10. Impedance analyzer experimental equipment of transducer and impedance measurement result: (a) WK6500B impedance analyzer and transducer; (b) the impedance measurement result.
图 11 PSV-400全场扫描式激光振动测量系统及换能器振动模态测量结果 (a) 激光测振实验装置; (b) 换能器弯曲振动模态测量结果; (c) 振动位移分布测量结果
Fig. 11. PSV-400 laser vibrometer measurement system and transducer vibration mode measurement result: (a) Laser vibrometer experimental equipment; (b) measured flexural vibration mode of the transducer; (c) measurement results of vibration displacement distribution.
表 1 m与共振频率的关系
Table 1. Relationship between m and resonant frequency.
悬链线共振
频率/kHz声黑洞共振频率/ kHz m =1.8 m = 2.1 m = 2.4 m = 2.7 m = 3 一阶 2.5 3.1 2.3 1.8 1.5 1.2 二阶 5.9 6.4 5.8 5.3 4.8 4.4 三阶 10.1 10.9 10.0 9.4 8.9 8.4 四阶 15.0 16.1 15.0 14.1 13.5 13.0 五阶 20.8 22.4 20.8 19.6 18.8 17.9 六阶 27.7 29.9 27.7 26.1 24.7 23.7 
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表 2 换能器材料参数
Table 2. Material parameters of the transducer.
材料 钢 PZT-4 铝 密度/
(kg·m–3)7850 7500 2700 泊松比 0.28 — 0.33 杨氏模量
/GPa或
弹性矩阵
/GPa205 ${\left[ {\begin{array}{*{20}{c}} {139}&{77.8}&{74.3}&0&0&0 \\ {77.8}&{139}&{74.3}&0&0&0 \\ {74.3}&{74.3}&{115}&0&0&0 \\ 0&0&0&{25.6}&0&0 \\ 0&0&0&0&{25.6}&0 \\ 0&0&0&0&0&{30.6} \end{array}} \right]}$ 70
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表 3 换能器弯曲振动频率计算结果对比
Table 3. Comparison of calculation results for the flexural vibration frequency of the transducer.
振动频率/kHz 误差/% 理论 仿真 一阶 1.293 1.289 0.31 二阶 4.448 4.432 0.36 三阶 8.518 8.649 1.51 四阶 13.161 13.045 0.88 五阶 18.202 17.979 1.24 六阶 23.948 23.645 1.28
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表 4 两种结构的探头不同入水深度对共振频率与最大声压的关系
Table 4. Relationship between the resonant frequency and the maximum sound pressure of two types of probes with different water entry depths.
入水深度/mm 声黑洞结构 悬链线结构 共振频率/kHz 最大声压/Pa 共振频率/kHz 最大声压/Pa 25 22.815 9.57×105 26.680 3.01×105 50 22.211 4.22×105 26.035 3.42×104 75 21.719 4.96×104 25.476 6.54×103
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