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To address the limitations of traditional one-dimensional longitudinal vibration transducers in terms of single-directional acoustic radiation and limited radiation area, this study proposes a novel longitudinal-bending orthogonal coupled piezoelectric ultrasonic vibration system (The vibration schematic diagram of the vibration system is shown in Fig.(a)). By synergistically integrating the orthogonal longitudinal vibration of a sandwich-type piezoelectric transducer, displacement amplification via conical horns, and flexural vibration of metal disks, the system achieves two-dimensional four-directional large-area ultrasonic radiation. A combination of theoretical modeling, finite element simulation, and experimental validation is adopted to investigate the dynamic characteristics the system. First, an electromechanical equivalent circuit model is established based on coupled vibration theory and electro-mechanical analogy principles, from which resonance frequency equation and anti-resonance frequency equation are both derived. Subsequently, finite element simulations are conducted using COMSOL multiphysics to analyze the impedance responses, vibration modes, and acoustic radiation characteristics in air. Finally, prototype fabrication and performance verification are performed through impedance-analyzer measurements, laser vibrometry, and ultrasonic de-misting experiments. Compared with experimental results (22086 Hz and 22196 Hz), the theoretical predictions of anti-phase (22871 Hz) and in-phase (23016 Hz) resonance frequencies show relative errors below 3.7%. Finite element simulations combined with experimental validation confirm the excitation mechanism of 5th-order flexural vibration in the disks. Acoustic directivity patterns reveal a multi-beam radiation pattern with coexistence of main lobes and side lobes (The directional patterns under anti-phase and in-phase vibration modes is shown in Fig.(b)), while in-phase vibration mode demonstrates higher ultrasonic radiation intensity in the near-field region. Furthermore, under 200-W input power, the system reduces smoke concentration within 70 s, demonstrating its feasibility for gas treatment applications. By leveraging the synergistic effect of orthogonal longitudinal coupling and flexural vibration, this design overcomes the limitations of traditional transducers and provides theoretical and technical support for high-power multi-directional acoustic radiation. The research outcomes provide the promising solutions for applications in ultrasonic smoke removal, ultrasonic dust removal, and other gas-phase processing fields. 
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Keywords:
- piezoelectric ultrasonic transducer /
- 2D coupled vibration /
- electro-mechanical equivalent circuit /
- vibration modal
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Cheng J C, Li X D, Yang J 2021 The Current State and Future Development Trends of the Acoustics Discipline (Beijing: Science Press) pp1–30
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[7] Liang Z F, Mo X P, Zhou G P 2017 Acta Acust. 42 7
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[9] 梁召峰, 周光平, 莫喜平 2009 压电与声光 31 760
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Liang Z F, Zhou G P, Mo X P 2009 Piezoelectr. Acoustoopt. 31 760
Google Scholar
[10] 贺西平, 张海岛 2016 中国科学: 物理学 力学 天文学 3 17
He X P, Zhang H D 2016 Sci. Sin. Phys. Mech. Astron. 3 17
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Xu L, Chang Y, Guo L W, Wang Y B, Xu F Q 2016 Acta Acust. 41 105
[12] 许龙, 林书玉 2012 声学学报 37 408
Xu J, Lin S Y 2012 Acta Acust. 37 408
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Liang Z F, Mo X P, Zhou G P 2011 Acta Acust. 36 369
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Li F M, Liu S Q, Xu L, Zhang H D, Zeng X M, Chen Z J 2023 Sci. Sin. Phys. Mech. Astron. 53 194
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Google Scholar
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Google Scholar
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Google Scholar
Zhao F L, Feng D J, Guo D M, Fang Y Y 2002 Acta Acust. 27 554
Google Scholar
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Google Scholar
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图 1 纵弯正交耦合压电超声振动系统的结构(a)以及振动示意图(b)
Figure 1. Schematic diagrams of the structure (a) and vibration (b) of the longitudinal-bending orthogonal coupled piezoelectric ultrasonic vibration system.
图 2 纵弯正交耦合压电超声振动系统整体机电等效电路
Figure 2. Integrated electromechanical equivalent circuit of the longitudinal-bending orthogonal coupled piezoelectric ultrasonic vibration system.
图 3 纵弯正交耦合压电超声振动系统简化等效电路
Figure 3. Simplified equivalent circuit of the longitudinal-bending orthogonal coupled piezoelectric ultrasonic vibration system.
图 4 振动系统谐响应曲线 (a)等效电路法测得结果; (b)有限元法测得结果
Figure 4. Harmonic response curves of the vibration system: (a) Results obtained by the equivalent circuit method; (b) results obtained by the finite element method.
图 5 振动系统的耦合共振模态 (a)反相共振模态; (b)同相共振模态
Figure 5. Coupled resonance modes of the vibration system: (a) Anti-phase resonance mode; (b) in-phase resonance mode.
图 6 振动系统在不同振动模式下的声压分布云图 (a)反相振动; (b) 同相振动
Figure 6. Sound pressure distribution contour maps of the vibration system under: (a) Anti-phase vibration; (b) in-phase vibration.
图 7 反相以及同相振动模式下的指向性图
Figure 7. Directional patterns under anti-phase and in-phase vibration modes.
图 8 轴向声压随距离的变化 (a)反相振动模式; (b)同相振动模式
Figure 8. Variation of axial sound pressure with distance: (a) Anti-phase vibration mode; (b) in-phase vibration mode.
图 9 实验样品
Figure 9. Experimental sample.
图 10 实验法测得振动系统谐响应曲线
Figure 10. Harmonic response curve of the vibration system measured by the experimental method.
图 11 有限元仿真计算所得X方向和Y方向输出圆盘的纵向振动位移分布关系 (a)反相位移振幅; (b)同相位移振幅
Figure 11. Longitudinal vibration displacement distribution relationship of the output disks along the X and Y axes obtained from finite element simulation calculations: (a) Anti-phase displacement amplitude; (b) in-phase displacement amplitude.
图 13 实验法测得X和Y轴向输出圆盘的纵向振动位移分布关系 (a)反相位移振幅; (b)同相位移振幅
Figure 13. Longitudinal vibration displacement distribution relationship of the output disks along the X and Y axes measured by the experimental method: (a) Anti-phase displacement amplitude; (b) in-phase displacement amplitude.
图 12 LV-S01激光测振仪
Figure 12. LV-S01 laser vibrometer.
图 14 超声除雾实验装置
Figure 14. Experimental setup for ultrasonic de-misting.
图 15 超声除雾实验结果图 (a)未开启超声烟雾变化; (b)开启超声后的烟雾变化
Figure 15. Results of the ultrasonic de-misting experiment: (a) Smoke variation without ultrasonic activation; (b) smoke variation after ultrasonic activation.
表 1 反相和同相二维正交纵弯耦合振动共振频率及相对误差
Table 1. Resonance frequencies and relative errors of in-phase and out-of-phase two-dimensional orthogonal longitudinal-bending coupled vibrations.
共振频率/Hz 误差/% ${f_{{\text{M}} - }}$ ${f_{{\text{M + }}}}$ ${f_{{\text{C}} - }}$ ${f_{{\text{C + }}}}$ ${f_{{\text{E}} - }}$ ${f_{{\text{E + }}}}$ ${\Delta _{{\text{ME}} - }}$ ${\Delta _{{\text{ME + }}}}$ ${\Delta _{{\text{CE}} - }}$ ${\Delta _{{\text{CE + }}}}$ 22871 23016 22351 22650 22086 22196 3.6 3.7 1.2 2.0 
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[1] Gallego-Juárez J A 2010 Phys. Procedia 3 35
Google Scholar
[2] Ensminger D, Bond L J 2024 Ultrasonics: Fundamentals, Technologies, and Applications (London: CRC Press) pp1–22
[3] Nie G, Kang J, Hu Y, You R, Ma J, Hu Y, Huang T 2016 Mater. Process. Fundam. 1 125
Google Scholar
[4] 程建春, 李晓东, 杨军 2021 声学学科现状以及未来发展趋势(北京: 科学出版社) 第1—30页
Cheng J C, Li X D, Yang J 2021 The Current State and Future Development Trends of the Acoustics Discipline (Beijing: Science Press) pp1–30
[5] 王莎, 林书玉 2019 物理学报 68 024303
Google Scholar
Wang S, Lin S Y 2019 Acta Phys. Sin. 68 024303
Google Scholar
[6] Fu Z Q, Xian X J, Lin S Y, Wang C H, Hu W X, Li G Z 2012 Ultrasonics 52 578
Google Scholar
[7] Liang Z F, Mo X P, Zhou G P 2017 Acta Acust. 42 7
[8] Rodríguez G, Riera E, Gallego-Juárez J A, Gallego-Juárez V M A, Pinto A, Martínez I, Blanco A 2010 Phys. Procedia 3 135
Google Scholar
[9] 梁召峰, 周光平, 莫喜平 2009 压电与声光 31 760
Google Scholar
Liang Z F, Zhou G P, Mo X P 2009 Piezoelectr. Acoustoopt. 31 760
Google Scholar
[10] 贺西平, 张海岛 2016 中国科学: 物理学 力学 天文学 3 17
He X P, Zhang H D 2016 Sci. Sin. Phys. Mech. Astron. 3 17
[11] 许龙, 常燕, 郭林伟, 王月兵, 徐方迁 2016 声学学报 41 105
Xu L, Chang Y, Guo L W, Wang Y B, Xu F Q 2016 Acta Acust. 41 105
[12] 许龙, 林书玉 2012 声学学报 37 408
Xu J, Lin S Y 2012 Acta Acust. 37 408
[13] Xu J, Lin S Y, Ma Y, Tang Y F 2017 Sensors-Basel 17 2850
Google Scholar
[14] 梁召峰, 莫喜平, 周光平 2011 声学学报 36 369
Liang Z F, Mo X P, Zhou G P 2011 Acta Acust. 36 369
[15] Itoh K, Mori E 1972 J. Acoust. Soc. Jpn. 28 127
Google Scholar
[16] Itoh K, Mori E 1973 J. Acoust. Soc. Jpn. 29 28
Google Scholar
[17] Xu L, Qiu X J, Zhou J C, Li F M, Zhang H D, Wang Y B 2019 Smart Mater. Struct. 28 025017
Google Scholar
[18] 杜耀东, 许龙, 周光平 2021 中国科学: 物理学 力学 天文学 51 10
Du Y D, Xu L, Zhou G P 2021 Sci. Sin. Phys. Mech. Astron. 51 10
[19] 李凤鸣, 刘世清, 许龙, 张海岛, 曾小梅, 陈赵江 2023 中国科学: 物理学 力学 天文学 53 194
Li F M, Liu S Q, Xu L, Zhang H D, Zeng X M, Chen Z J 2023 Sci. Sin. Phys. Mech. Astron. 53 194
[20] 许龙, 周锦程, 常燕, 李凤鸣, 李伟东 2018 声学学报 43 786
Xu L, Zhou J C, Chang Y, Li F M, Li W D 2018 Acta Acust. 43 786
[21] Khmelev V N, Shalunov A V, Nesterov V A 2021 Ultrasonics 114 106413
Google Scholar
[22] 桑永杰, 蓝宇, 丁玥文 2016 物理学报 65 1
Google Scholar
Sang Y J, Lan Y, Ding Y W 2016 Acta Phys. Sin. 65 1
Google Scholar
[23] 刘世清, 许龙, 张志良, 陈赵江, 沈建国 2014 声学学报 39 104
Liu S Q, Xu L, Zhang Z L, Chen Z J, Shen J G 2014 Acta Acust. 39 104
[24] Martin G E 1964 J. Acoust. Soc. Am. 36 1496
Google Scholar
[25] Kalthoff J F, Winkler S 1988 Impact Load. Dyn. Behav. Mater. 1 185
[26] 潘瑞, 莫喜平, 柴勇, 张秀侦, 田芝凤 2024 物理学报 73 194301
Google Scholar
Pan R, Mo X P, Chai Y, Zhang X Z, Tian Z F 2024 Acta Phys. Sin. 73 194301
Google Scholar
[27] Chen C, Dong Y L, Wang S, Hu L Q, Lin S Y 2022 J. Acoust. Soc. Am. 151 2712
Google Scholar
[28] 赵福令, 冯冬菊, 郭东明, 方亚英 2002 声学学报 27 554
Google Scholar
Zhao F L, Feng D J, Guo D M, Fang Y Y 2002 Acta Acust. 27 554
Google Scholar
[29] Zhang X L, Liang B 2018 Appl. Acoust. 129 284
Google Scholar
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