Mathematical Modeling of Piezoelectric Ceramic Ring Transducers for Functional Instrumentation
Keywords:piezoelectric transducer, functional instrumentation, mathematical model, ring element, impedance
The article reviews a mathematical model of piezoelectric ceramic ring transducers which are functional, highly effective, and applicable as components of functional instrumentation devices, such as sensors, automatic control devices, measuring devices, data collection devices, electronic control systems, etc. The main distinctive characteristic of the mathematical model developed in this study is the ability to establish analytical dependencies for determining such electromechanical characteristics of a piezoceramic ring as: electrical impedance, quality factor, elastic modulus, piezo modulus, dielectric constant, as well as the amplitude values of the electric charge and electric current on the electroded surfaces of the piezoceramic ring, thus significantly expanding the range of these products and determine their operational characteristics at the design stage.
The key research question of this study is frequency dependence of the change in electrical impedance for a ring made of PZT-type (plumbum zirconate titanate) piezoelectric ceramics, which significantly depends on the values of mechanical and geometric parameters, the wave number of elastic oscillations, as well as the corresponding Bessel and Neumann functions of the first order, according to which a sharp decrease in the electrical impedance from 4900 to 10 Ohms is observed when the quasi-wave number increases from 0 to 2. Also, this study has established a high degree of convergence between the theoretically obtained and experimentally determined electrical impedance modules for ring transducers made of PZT-type piezoelectric ceramics (the discrepancy between the impedance values in these cases did not exceed 16%).
Dunn W. C. (2018). Fundamentals of Industrial Instrumentation and Process Control, 2nd ed. McGraw-Hill Education, 336 p.
Piezoelectric Devices: From Bulk to Thin-Film 2019. Yolegroup, date of access: May 2023.
Prokic M. (2004). Piezoelectric Transducers Modelling and Characterization. MP Interconsulting, 266 p.
Campisi M. A. (2017). Tools and Modeling of Piezoelectric Sensor Structural Health Monitoring for Space Applications. ProQuest, 10622754.
Kozlov V. I., Zinchuk L. P., Karnaukhova T. V. (2021). Nonlinear Vibrations and Dissipative Heating of Laminated Shells of Piezoelectric Viscoelastic Materials with Shear Strains*. International Applied Mechanics, Vol. 57, pp. 669–686. DOI: 10.1007/s10778-022-01117-6.
Karlash V. L. (2018). Analysis of forced vibration of piezoceramic transducers at a non-uniformelectric loading. Hydrodynamics and Acoustics, Vol. 1(91), Iss. 2, pp. 160-190. DOI: 10.15407/jha2018.02.160.
Polyakov M. V., Okovityy S. I. (Eds.) (2018). Scientific and technical developments of the Dnipro National University: Scientific and informational edition. Dnipro, LIRA, 230 p.
Liu J., O'Connor W. J., Ahearne E., Byrne G. (2014). Electromechanical modelling for piezoelectric flextensional actuators. Smart Materials and Structures, Vol. 23, Iss. 2, 17 p. DOI:10.1088/0964-1726/23/2/025005.
Nikta Amiri, et al (2021). Experimentally verified finite element modeling and analysis of a conformable piezoelectric sensor. Smart Materials and Structures, Vol. 30, Iss. 8, pp. 085017. DOI: 10.1088/1361-665X/ac08ae.
Lašová Z., Zemčík R. (2012). Comparison of Finite Element Models for Piezoelectric Materials. Procedia Engineering, Vol. 48, pp. 375-380. DOI: 10.1016/j.proeng.2012.09.528.
Haldkar R. K., Cherpakov A. V., Parinov I. A., Yakovlev V. E. (2022). Comprehensive Numerical Analysis of a Porous Piezoelectric Ceramic for Axial Load Energy Harvesting. Applied Sciences, Vol. 12(19), pp. 10047. DOI: 10.3390/app121910047.
Petrishchev O. N., Bazilo C. V. (2017). Methodology of Determination of Physical and Mechanical Parameters of Piezoelectric Ceramics. Journal of Nano- and Electronic Physics, Vol. 9, Iss. 3, pp. 03022-1–03022-6. DOI: 10.21272/jnep.9(3).03022.
Petrakov E. V., Balandin D. V. (2023). Active Damping of Transverse Vibrations of Console Beam by Piezoelectric Layer with Different Electrode Shapes. In: Deformation and Destruction of Materials and Structures Under Quasi-static and Impulse Loading. Cham: Springer International Publishing, pp. 201-213.
Do T. B., Nasedkin A., Oganesyan P., Soloviev A. (2023). Multilevel Modeling of 1-3 Piezoelectric Energy Harvester Based on Porous Piezoceramics. Journal of Applied and Computational Mechanics, Vol. 9(3), pp. 763-774. DOI: 10.22055/JACM.2023.42264.3900.
Liu W., Jin H., Yao J. (2022). Vibration performance an alysis of a self-energized damper composed of electrorheological fluid and piezoelectric ceramics. Mechanics Based Design of Structures and Machines, Vol. 51, Iss. 10, pp. 5968-5982. DOI: 10.1080/15397734.2022.2027781.
Wang G., Zhao Z., Tan J., Cui S., Wu H. (2020). A novel multifunctional piezoelectric composite device for mechatronics systems by using one single PZT ring. Smart Materials and Structures, Vol. 29(5), pp. 055027. DOI:10.1088/1361-665X/ab710b.
Livingston F., Grant E. (2022). A Design and Modeling Software Tool for Prototyping for Ultrasonic Transceivers. 2022 IEEE Sensors, pp. 1-4. DOI: 10.1109/SENSORS52175.2022.9967042.
Chen J., Peng G., Hu H., Ning J. (2020). Dynamic Hysteresis Model and Control Methodology for Force Output Using Piezoelectric Actuator Driving. IEEE Access, Vol. 8, pp. 205136-205147. DOI: 10.1109/ACCESS.2020.3037216.
Petrishchev O. N. (2019). Principles and methods of mathematical modeling of oscillating piezoelectric elements. Cherkasy, Ye. Gordiienko Publ., 408 p.
Bazilo C. V., Bondarenko M. O., Usyk L. M., Faure E. V., Kovalenko Yu. I. (2023). Mathematical Modelling of Disk Piezoelectric Transducers for Acoustoelectronic Devices. Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, Vol. 91, pp. 37–45. DOI: 10.20535/RADAP.2023.91.37-45.
Lahmer T., Kaltenbacher M., Kaltenbacher B., Lerch R., Leder E. (2008). FEM-based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 55(2), pp. 465–475. DOI: 10.1109/TUFFC.2008.664.
Tytarenko V., Tychkov D., Bilokin S., Bondarenko M., Andriienko V. (2020). Development of a simulation model of an information-measuring system of electrical characteristics of the functional coatings of electronic devices. Mathematical modeling, Vol. 4, Iss. 2, pp. 68–71.
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.
How to Cite
Copyright (c) 2023 Костянтин Базіло, Андрієнко Володимир, Вячеслав Туз; Людмила Усик; Iuliia Bondarenko
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).