# Mathematical Modelling of Disk Piezoelectric Transducers for Acoustoelectronic Devices

## DOI:

https://doi.org/10.20535/RADAP.2023.91.37-45## Keywords:

piezoelectric transducer, acoustoelectronics, mathematical model, impedance, disc element## Abstract

This study has presented an algorithm for assembling, solving, and analyzing the results obtained by mathematical modeling of the disc piezoelectric transducers, which are widely used in hydroacoustics, microelectronics, microcircuit engineering (for example, as components of receiving antennas of hydroacoustic communication devices). The models developed in this study enable us to establish dependencies, which represent a mathematical description of the electroacoustic connection between the wave fields in different sections of the disc piezoelectric transducers.

Analytical dependences obtained by mathematical modelling make it possible to establish the electrical impedance and quality factor together with the amplitude values of the electric charge and current on the electroded surfaces of the piezoelectric disk, subject to the inverse piezoelectric effect conditions. A complete calculation of the problem of harmonic radial oscillations of disc piezoelectric transducers allowed the authors to significantly expand the list of physical and mechanical parameters of the piezoelectric material, which had been previously determined experimentally.

The research has revealed the dependence of the change in electrical impedance on the values of the electromechanical coupling coefficient, the wave number of elastic oscillations, and the Voigt indices. The study has also determined a high agreement between the electric impedance modules of discs made of lead zirconate titanate PZT piezoelectric ceramics with and without the piezoelectric effect (the difference between the impedance values in these cases did not exceed 18%).

## References

**References**

Jim Tran. These Piezo Technologies are Transforming 2022. *ElectronicDesign*, date of access: 08.04.2022.

Aldahiry D. A., Bajaba D. A., Basalamah N. M., Ahmed M. M. (2022). Piezoelectric Transducer as an Energy Harvester: A Review. *YJES*, Vol. 19, Iss. 1, pp. 30–35. DOI:10.53370/001c.33771.

Compamed and Electronica 2022: PI Ceramic Presents Piezo Elements for Medical Technology and the Electronics Industry. *PI Ceramic – Piezo Technology, Actuators & Components*, date of access: 24.10.2022.

Piezoelectric Ceramics Manufacturing Technology. *Ferroperm Piezoceramics*, date of access: 18.10.2022.

Lupeiko T. G., Lopatin S. S. (2004). Old and New Problems in Piezoelectric Materials Research and Materials with High Hydrostatic Sensitivity. *Inorganic Materials*, Vol. 40, Iss. 1, pp. 19–32. DOI:10.1023/B:INMA.0000036326.98414.3c.

Sharapov V., Sotula Z., Kunickaya L. (2014). Piezo-Electric Electro-Acoustic Transducers. *Springer Cham*, 230 p. DOI:10.1007/978-3-319-01198-1.

Huang Y. H., Yen C. Y. (2017). Holographic determination of solid-liquid coupled vibration on development of circular piezoelectric hydrodevices. *15th Asia Pacific Conference for Non-Destructive Testing (APCNDT2017)*, Singapore, ID138.

Mieczkowski G., Borawski A., Szpica D. (2020). Static Electromechanical Characteristic of a Three-Layer Circular Piezoelectric Transducer. *Sensors*, Vol. 20, Iss. 1, 222. DOI:10.3390/s20010222.

Abidin N. A. K. Z., Nayan N. M., Azizan M. M., et al. (2020). The simulation analysis of piezoelectric transducer with multi-array configuration. *Journal of Physics: Conference Series*, Vol. 1432, 012042. DOI:10.1088/1742-6596/1432/1/012042.

Bazilo C., Zagorskis A., Petrishchev O., Bondarenko Y., Zaika V., Petrushko Y. (2017). Modelling of Piezoelectric Transducers for Environmental Monitoring. *10th International Conference “Environmental Engineering”*, Vilnius Gediminas Technical University, Lithuania. DOI:10.3846/enviro.2017.008.

Bazilo C. V. (2017). Principles of electrical impedance calculating of oscillating piezoceramic disk in the area of medium frequencies. *Radio Electronics, Computer Science, Control*, No. 4, pp. 15–25. DOI:10.15588/1607-3274-2017-4-2.

Yanchevskiy I. V. (2011). Minimizing deflections of round electroelastic bimorph plate under impulsive loading. *Problems of computational mechanics and strength of structures*, Iss. 16. pp. 303–313.

Buchacz A., Placzek M., Wrobel A. (2014). Modelling of passive vibration damping using piezoelectric transducers – the mathematical model. *Eksploatacja i Niezawodnosc — Maintenance and reliability*, Vol. 16, Iss. 2, pp. 301–306.

Bazilo C. (2020). Modelling of Bimorph Piezoelectric Elements for Biomedical Devices. In: Hu Z., Petoukhov S., He M. (eds). Advances in Artificial Systems for Medicine and Education III. Advances in Intelligent Systems and Computing. *Springer, Cham*, Vol. 1126, pp. 151–160. DOI:10.1007/978-3-030-39162-1_14.

Wang, Q., Zhao, L., Yang, T., et al. (2021). A Mathematical Model of a Piezoelectric Micro- Machined Hydrophone With Simulation and Experimental Validation. *IEEE Sensors Journal*, Vol. 21, Iss. 12, pp. 13364-13372. DOI:10.1109/JSEN.2021.3070396.

Imperiale S., Joly P. (2012). Mathematical and numerical modelling of piezoelectric sensors. *ESAIM: Mathematical Modelling and Numerical Analysis*, Vol. 46, Iss. 4, pp. 875–909. DOI:10.1051/m2an/2011070.

Jawaid H., Qureshi W. A., Pasha R. A., Malik R. A. (2019). Characterization and Mathematical Modelling of Geometric Effects on Piezoelectric Actuators. * Integrated Ferroelectrics*, Vol. 201, Iss. 1, pp. 201–217, DOI:10.1080/10584587.2019.1668704.

Sofonea M. and Matea A. (2012). *Mathematical Models in Contact Mechanics*. Cambridge University Press, 280 p.

Antonyuk V. S., Bondarenko M. O., Bondarenko Y. Y. (2012). Studies of thin wear-resistant carbon coatings and structures formed by thermal evaporation in a vacuum on piezoceramic materials. *Journal of Superhard Materials*, Vol. 34, pp. 248–255. DOI:10.3103/S1063457612040065.

Sanchez-Rojas J. L. (Ed.). (2020). *Piezoelectric Transducers: Materials, Devices and Applications*. MDPI, University of Castilla-La Mancha, 524 p. doi:10.3390/books978-3-03936-857-0.

Paltanea V., Paltanea G., Popovici D. (2014). Analysis of the Stress-Strain State in Single Overlap Joints Using Piezo-Ceramic Actuators. *7th International Conference on Times of Polymers and Composites (TOP)*, Vol. 1599, pp. 370-373. DOI: 10.1063/1.4876855.

Lin Shuyu, Jie Xu. (2017). Effect of the Matching Circuit on the Electromechanical Characteristics of Sandwiched Piezoelectric Transducers. *Sensors*, Vol. 17, Iss. 2, pp. 329–343. DOI:10.3390/s17020329.

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, (91), pp. 37-45. doi: 10.20535/RADAP.2023.91.37-45.

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Copyright (c) 2023 Костянтин Базіло, Юрій Коваленко; Людмила Усик; Еміль Фауре, Максим Олексійович Бондаренко

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