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<p>This study tries to address the limitations of conventional one-dimensional models in analyzing the complex vibration behaviours of Langevin piezoelectric transducers by developing a three-dimensional vibration framework based on the apparent elasticity method. At first, theoretical equations for coupled longitudinal-radial vibrations were developed to integrate established mechanical coupling coefficients, equivalent elastic moduli, and wave numbers into multidimensional dynamics. Then, the transducer model was constructed in SOLIDWORKS, and the respective finite element analysis was performed with COMSOL Multiphysics for working frequency, amplitude, and electrical conductance. Following that, the key structural dimensions were designed using a multi-objective genetic algorithm to achieve the target operating frequency and vibration velocity ratio. At last, the optimized frequency was compared with the original for accuracy. It is found that the established model might be capable of describing the dynamic characteristics of the transducer and offering the necessary parameters to the further analysis. The improved design achieved nearly precise frequency alignment with the target 20&#xa0;kHz, significantly reducing the initial frequency deviation. Experimental validation confirmed a resonant frequency of 20.302&#xa0;kHz with a deviation of 1.51% from the target and a head displacement amplitude of 29.23&#xa0;µm.</p>

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3D Vibration Modeling and Performance Design of Langevin Piezoelectric Transducer Based on Apparent Elasticity Method

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Zongyu Bai,
  • Jingtao Zhao,
  • Jiaxin Liu,
  • Xiaolei Dong,
  • Aiyun Zheng,
  • Martin Kreschel

摘要

This study tries to address the limitations of conventional one-dimensional models in analyzing the complex vibration behaviours of Langevin piezoelectric transducers by developing a three-dimensional vibration framework based on the apparent elasticity method. At first, theoretical equations for coupled longitudinal-radial vibrations were developed to integrate established mechanical coupling coefficients, equivalent elastic moduli, and wave numbers into multidimensional dynamics. Then, the transducer model was constructed in SOLIDWORKS, and the respective finite element analysis was performed with COMSOL Multiphysics for working frequency, amplitude, and electrical conductance. Following that, the key structural dimensions were designed using a multi-objective genetic algorithm to achieve the target operating frequency and vibration velocity ratio. At last, the optimized frequency was compared with the original for accuracy. It is found that the established model might be capable of describing the dynamic characteristics of the transducer and offering the necessary parameters to the further analysis. The improved design achieved nearly precise frequency alignment with the target 20 kHz, significantly reducing the initial frequency deviation. Experimental validation confirmed a resonant frequency of 20.302 kHz with a deviation of 1.51% from the target and a head displacement amplitude of 29.23 µm.