Перегляд за Автор "Usyk, L. M."

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    Mathematical Modeling of Piezoelectric Ceramic Ring Transducers for Functional Instrumentation
    (КПІ ім. Ігоря Сікорського, 2023) Bazilo, C. V.; Anriienko, V. O.; Tuz, V. V.; Usyk, L. M.; Bondarenko, Yu. Yu.
    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 quasiwave 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%).
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    Mathematical modeling the electrical impedance of the piezoceramic disk oscillating in a wide frequency range (Part 1. Low frequencies)
    (КПІ ім. Ігоря Сікорського, 2023) Bazilo, C. V.; Trembovetska, R. V.; Usyk, L. M.; Faure, E. V.; Chorniy, A. M.
    The article presents the results of mathematical modeling and analysis of the electrical impedance of a piezoceramic disk that undergoes oscillations at low frequencies, i.e., when the length of the elastic wave significantly (by an order of magnitude or more) exceeds the radial size of the disk. Thus, the proposed mathematical model of disk-shaped ceramic elements of piezoelectric transducers, which are an important component of modern communication devices, environmental sensors, precision equipment, medical devices, etc. A key characteristic of the mathematical model described in the article is its ability to determine analytical dependencies that allow estimating such fundamental electrical properties of the piezoceramic disk element as electrical impedance and quasi-static electrical capacitance, thereby significantly simplifying the calculation of such an element already at the design stage. The static dielectric permittivity of a piezoceramic disk vibrating at low frequencies has been investigated. The calculated value of this parameter, based on the physical constants’ characteristic of the piezoceramic of the PZT (lead zirconate titanate) type, is 1.844 times higher compared to the high-frequency (dynamic) dielectric permittivity. It has been found that in the low-frequency range, when the mechanical stresses in the vibrating piezoceramic disk approach zero and the direct piezoelectric effect is almost negligible, the electrical impedance of such a disk can be described as the reactive resistance of a capacitor with electrical capacitance equivalent to the quasi-stationary capacitance of the disk. This is confirmed by a high degree of convergence between theoretical data and experimental results, with discrepancies not exceeding 6%. The results obtained in the article can be valuable for scientific research in the fields of precision instrument engineering and radio equipment manufacturing. Additionally, they have practical applications in the development and production of high-tech equipment.
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    Mathematical Modelling of Cylindrical Piezoelectric Transducers for Electroacoustic Devices
    (КПІ ім. Ігоря Сікорського, 2022) Bazilo, C. V.; Bondarenko, M. O.; Usyk, L. M.; Andriienko, O. I.; Antonyuk, V. S.
    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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    Mathematical Modelling of Disk Piezoelectric Transducers for Acoustoelectronic Devices
    (КПІ ім. Ігоря Сікорського, 2023) Bazilo, C. V.; Bondarenko, M. O.; Usyk, L. M.; Faure, E. V.; Kovalenko, Yu. I.
    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%).