Mathematical Modelling of Cylindrical Piezoelectric Transducers for Electroacoustic Devices
Keywords:piezoelectric transducer, acoustoelectronics, mathematical model, impedance, cylindrical shell
This paper will review the procedure and the results of the research conducted on developing mathematical models of cylindrical piezoelectric transducers that are extensively applied in electrical acoustics and hydro acoustics (for example, in devices designed for radiating and receiving acoustic oscillations in air or water medium). The distinctive feature of the developed models lies in the fact that the dependences established are a mathematical description of the electroacoustic connection between the wave fields located in different parts of a hollow piezoceramic cylindrical transducer. The analytical dependences obtained in the result of a simulation allow us to establish the electrical impedance and amplitude values of the electric current and electric charge on the electroded surface of a piezoelectric transducer (cylindrical piezoelectric shell of finite height) under the inverse piezoelectric effect, thus obtaining a complete solution for the problem of harmonic axisymmetric oscillations of a transducer of this type. In order to assess the results, the developed mathematical model was used in cylindrical shell transducers made of PZT-type (plumbum zirconate titanate) piezoelectric ceramics. Strong evidence of a frequency-dependent change of electric impedance and components of the displacement vector for material particles in the oscillating piezoelectric transducer was found with frequencies of electromechanical resonances within the range of 33-35 kHz and 82 kHz, when a sharp impedance decrease was observed (2.6-5 times). A comparative analysis of mathematically calculated and experimentally obtained values of the electrical impedance of the oscillating cylindrical piezoceramic shell revealed high convergence between them (the discrepancy between the simulation results and experimentally obtained data at the same values of operating frequency within the range up to 100 kHz did not exceed 17%).
Sanchez-Rojas J. L. (2020). Piezoelectric Transducers: Materials, Devices and Applications, Micromachines. MDPI, 524 p. DOI: 10.3390/books978-3-03936-857-0.
Zheng T., Ardolino M., Bacchetti A. & Perona M. (2020). The applications of Industry 4.0 technologies in manufacturing context: a systematic literature review. International Journal of Production Research, Vol. 59, Iss. 6, pp. 1922-1954. DOI: 10.1080/00207543.2020.1824085.
Butler J. L., Sherman Ch. H. (2016). Transducers and Arrays for Underwater Sound. Springer, 716 p.
Sharapov V., Sotula Zh., Kunickaya L. (2014). Piezo-Electric Electro-Acoustic Transducers. Springer, 230 p. DOI: 10.1007/978-3-319-01198-1.
Piezoelectric Sensor Market Report with In-Depth Analysis 2021 // Growth, Latest Trends, Size and Stocks, Opportunities, Country Data and Forecast to 2026 with Prominent Key Players, SKU ID: Maia-19372652. 2021. MarketWatch. Date of access: 18.11.2021.
Sharapov V. M., Minaev I. G., Sotula Zh. V., Kunitskaya L. G. (2013). Electroacoustic transducers [Elektroakusticheskie preobrazovateli]. Technosphere, Moskow, 280 p. [In Russian].
Bazilo C. V., Bondarenko M. O., Khlivnyi V. V., Tomenko M. H. and Tomenko V. I. (2021). Mathematical Modelling of Rod-Type Piezo-Electric Transducers for Acoustoelectronic Devices. Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, Vol. 86, pp. 58-67. DOI: 10.20535/RADAP.2021.86.58-67.
Petrishchev O. N. (2012). Harmonic vibrations of piezoceramic elements. Part 1. Harmonic vibrations of piezoceramic elements in vacuum and the method of resonance – antiresonance [Garmonicheskie kolebaniya piezokeramicheskikh elementov. Chast’ 1. Garmonicheskie kolebaniya piezokeramicheskikh elementov v vakuume i metod rezonansa – antirezonansa]. Kyiv, Avers Publ., 300 p. [In Russian].
Soloviev A. N., Chebanenko V. A., Parinov I. A. (2018). Mathematical Modelling of Piezoelectric Generators on the Base of the Kantorovich Method. In: Altenbach H., Carrera E., Kulikov G. (eds) Analysis and Modelling of Advanced Structures and Smart Systems. Advanced Structured Materials. Springer, Singapore, Vol 81. doi: 10.1007/978-981-10-6895-9_11.
Ivanov I., Kolev S., Nenova B., Kossev V. (2020). Investigation of characteristics of cylindrical piezoceramic transducers used in systems for underwater monitoring and management. Security & Future, Vol. 4, Issue 2, pp. 75-77.
Didkovskyi V. S., Korzhyk O. V., Leiko O. H., Naida S. A., Poroshyn S .M., Petrishchev O. M. (2012). Orientation of interference and focused acoustic antennas [Napravlenist interferentsiinykh ta fokusovanykh akustychnykh anten]. NTUU «KPI», Kyiv, 150 p. [In Ukrainian].
Kudzinovska I. P. (2014). Mathematical modelling of vibrations of round piezoceramic plate taking into account viscoelasticity of material. Bulletin of Zaporizhzhia National University [Visnyk Zaporiz’kogo nacional’nogo universytetu], No 1, pp. 59–66. [In Ukrainian].
Mouhanned Brahim (2017). Modeling and Position Control of Piezoelectric Motors. Automatic. Université Paris Saclay (COmUE), English. NNT : 2017SACLS296.
Halchenko V. Y., Filimonov S. A., Batrachenko A. V. and Filimonova N. V. (2018). Increase the Efficiency of the Linear Piezoelectric Motor. Journal of Nano- and Electronic Physics, Vol. 10, Iss. 4, pp. 04025-1. DOI: 10.21272/jnep.10(4).04025.
Khutornenko S. V., Voeikov A. N., Vasilchuk D. P. (2011). Mathematical model of a piezoelectric resonator in the presence of a gradient field in the plane of the crystal element [Matematicheskaya model’ piezoelektricheskogo rezonatora pri nalichii gradientnogo polya v ploskosti kristallicheskogo elementa]. Scientific works of DonNTU. Series: ''Mining and electromechanical'' [Naukovi praci DonNTU. Seriya: ''Girny’choelektromexanichna''], Vol. 21(189), pp. 168–172. [In Russian].
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.
Yuanmao Ye et al. (2012). A Novel Method for Connecting Multiple Piezoelectric Transformer Converters and its Circuit Application. IEEE Transactions on Power Electronics, Vol. 27, Iss. 4, pp. 1926-1935. DOI: 10.1109/TPEL.2011.2171007.
Yanchevskiy I. V. (2011). Minimizing deflections of round electroelastic bimorph plate under impulsive loading. Problems of computational mechanics and strength of structures, Vol. 16, pp. 303–313. [In Russian].
Lineykin S., Ben-Yaakov S. (2004). Feedback isolation by piezoelectric transformers: comparison of amplitude to frequency modulation. IEEE 35th Annual IEEE Power Electronics Specialists Conference, Aachen, Germany, pp. 1834–1840. DOI: 10.1109/PESC.2004.1355395.
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, No. 2, pp. 301–306.
Ajitsaria J., et al. (2007). Modeling and analysis of a bimorph piezoelectric cantilever beam for voltage generation. Smart Materials and Structures, Vol. 16, No. 2, pp. 447-454. doi: 10.1088/0964-1726/16/2/024.
Kanan A., Kaliske M. (2021). On the computational modelling of nonlinear electro-elasticity in heterogeneous bodies at finite deformations. Mechanics of Soft Materials, Vol. 3, No. 4. doi: 10.1007/s42558-020-00031-6.
Hyun-Gwon Kil, Chan Lee (2018). Analysis of Characteristics of Elastic Waves Propagating on a Vibrating Cylindrical Shell at Frequencies around a Ring Frequency. Proccedings of Euronoise 2018, pp. 2631-2636.
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, Issue 3, pp. 03022-1–03022-6. DOI: 10.21272/jnep.9(3).03022.
Bazilo C., Zagorskis A., Petrishchev O., Bondarenko Y., Zaika V., Petrushko Y. (2017). Modelling of Piezoelectric Transducers for Environmental Monitoring. Proccedings of 10th International Conference ''Environmental Engineering'', Vilnius Gediminas Technical University, Lithuania. DOI: 10.3846/enviro.2017.008.
How to Cite
Copyright (c) 2022 Максим Олексійович Бондаренко
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).