Electrical Impedance Mathematical Modeling of Piezoceramic Disc Oscillating in Wide Frequency Range (Part 3. High Frequencies)
DOI:
https://doi.org/10.20535/RADAP.2025.99.15-23Keywords:
electrical impedance, piezoceramic disk, high frequencies, mathematical modeling, mechanical quality factor, electromechanical resonanceAbstract
This paper discusses the results of mathematical modelling the electrical impedance of a piezoceramic disk oscillating in a wide range of high frequencies. The study aimed to create a mathematical model that would incorporate geometric, physical, and mechanical characteristics of the material to assess the behavior of the disk under conditions of electromechanical resonance and antiresonance. The research particularly focused on the influence of radial and axial displacements of material particles on the frequency dependence of the mechanical quality factor and electrical impedance of the disk. Even more closely, this research scrutinizes specific effects characteristic of the high-frequency mode, in order to increase the accuracy of modeling and ensure optimal technical characteristics of the devices. The mathematical model developed in this paper serves as a tool to obtain estimates for the frequency dependence of the mechanical quality factor and the dynamic electrical capacitance in real conditions, in particular, by including energy losses due to viscous friction into the calculations. Numerical calculations confirm the high correlation between theoretical and experimental data (with the discrepancy lower than 3.10-3), which proves the model usable for designing piezoelectric devices. In particular, it was found that the frequencies of electromechanical resonance and antiresonance are virtually independent of the radial displacements of material particles and are determined by the axial components solely. In addition, the calculation model provides the ability to assess the electrical impedance in the high-frequency range with an accuracy that meets modern requirements for the design of functional piezoelectric devices. The results obtained have practical significance for developing precision elements for military equipment, high-precision sensors, ultrasonic generators, medical diagnostic devices, and other technological systems that function with piezoelectric materials.
References
References
1. Dong H., Zhu Z., Li Z. et al. (2024). Piezoelectric Composites: State-of-the-Art and Future Prospects. JOM, Vol. 76, pp. 340–352. DOI: 10.1007/s11837-023-06202-w.
2. Stankiewicz G., Dev C., Weichelt M. et al. (2024). Towards advanced piezoelectric metamaterial design via combined topology and shape optimization. Struct Multidisc Optim., Vol. 67, article number 26. DOI: 10.1007/s00158-024-03742-w.
3. Shung K. K. (2015). Diagnostic Ultrasound: Imaging and Blood Flow Measurements, Second Edition (2nd ed). CRC Press, Washington, D.C. DOI: 10.1201/b18323.
4. Antonio Arnau Vives (2008). Piezoelectric transducers and applications. Springer Berlin, Heidelberg. DOI: 10.1007/978-3-540-77508-9.
5. Ammari H., Garnier J., & Jing W. (2012). Resolution and stability analysis in acoustoelectric imaging. Inverse Problems, Vol. 28, No. 8, 084005. DOI: 10.1088/0266-5611/28/8/084005.
6. Ammari H., Grasland-Mongrain P., Millien P., Seppecher L., & Seo J. K. (2015). A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography. Journal de Mathématiques Pures et Appliquées, Vol. 103, Iss. 6, pp. 1390-1409. DOI: 10.48550/arXiv.1401.2337.
7. Gebauer B. & Scherzer O. (2008). Impedance-Acoustic Tomography. SIAM J. Appl. Math., Vol. 69, Iss. 2, pp. 565–576. DOI: 10.1137/080715123.
8. Poplavko Y. M., Yakymenko Y. I. (2020). Large Parameters and Giant Effects in Electronic Materials. Radioelectron. Commun. Syst., Vol. 63, pp. 289–298. DOI: 10.3103/S0735272720060023.
9. Oleynyk G. S. (2018). Structure formation of ceramic materials. Naukova dumka, Kyiv, Ukraine.
10. Antonyuk V. S., Bondarenko M. O., Bondarenko Yu. Yu. (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, No. 4, pp. 248–255. DOI: 10.3103/ S1063457612040065.
11. Aladwan I. M., Bazilo C., Faure E. (2022). Modelling and Development of Multisectional Disk Piezoelectric Transducers for Critical Application Systems. Jordan Journal of Mechanical and Industrial Engineering, Vol. 16, No. 2, pp. 275–282.
12. Petrishchev O. N. (2012). Harmonic vibrations of piezoceramic elements. Part 1. Harmonic vibrations of piezoceramic elements in vacuum and the method of resonance-antiresonance. Avers, Kiev, Ukraine.
13. Bazilo C. V. (2018). Principles and methods of the calculation of transfer characteristics of disk piezoelectric transformers. Radio Electronics, Computer Science, Control, No. 4, pp. 7-22. DOI: 10.15588/1607-3274-2018-4-1.
14. 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, Vol. 1126, Springer, Cham, pp. 151–160. DOI: 10.1007/978-3-030-39162-1_14.
15. Nithya G., Sthuthi A., Chandrashekar N., et al. (2024). Modeling, Simulation, and Optimization of Piezoelectrically Actuated Dual-Axis MEMS Accelerometer for Seismic Sensing. J. Vib. Eng. Technol., Vol. 12, pp. 5383–5395. DOI: 10.1007/s42417-023-01169-z.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Костянтин Базіло, Людмила Усик, Євген Хижняк, Дмитро Жуйков, Андрій Ярославський
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
