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为了实现单个压电超声振动系统的多维超声辐射、有效增大系统的超声辐射面积, 本文提出了一种新型纵弯正交耦合压电超声振动系统. 其由纵向正交复合振动夹心式压电超声换能器、纵向振动圆锥形变幅杆和弯曲振动金属圆盘组成. 基于耦合振动理论和力电类比原理建立了振动系统的机电等效电路模型, 推导了其共振、反共振频率方程. 通过等效电路法、有限元仿真以及实验测试对振动系统的纵弯耦合振动特性进行研究, 结果表明该振动系统可有效实现二维四向超声辐射, 为该类新型超声振动系统的工程设计提供了理论基础. 本文成果有望在超声凝聚、超声除雾等领域获得广泛应用.
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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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)
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 8. Variation of axial sound pressure with distance: (a) Anti-phase vibration mode; (b) in-phase vibration mode.
图 10 实验法测得振动系统谐响应曲线
Fig. 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
Fig. 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
Fig. 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 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
Fig. 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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