# Mathematical Modelling of Cylindrical Piezoelectric Transducers for Electroacoustic Devices

## DOI:

https://doi.org/10.20535/RADAP.2022.88.24-34## Keywords:

piezoelectric transducer, acoustoelectronics, mathematical model, impedance, cylindrical shell## Abstract

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%).

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, (88), pp. 24-34. doi: 10.20535/RADAP.2022.88.24-34.

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Copyright (c) 2022 Максим Олексійович Бондаренко

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