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Документ Відкритий доступ Mathematical Modeling the Electrical Impedance of Piezoceramic Disk Oscillating in Wide Frequency Range (Part 2. Medium Frequencies)(КПІ ім. Ігоря Сікорського, 2024) Bazilo, C. V.; Faure, E. V.; Usyk, L. M.; Tuz, V. V.; Chorniy, A. M.This paper presents further developments in mathematical modeling of the electrical impedance of a piezoceramic disk in a wide frequency range, specifically focusing on the mid-frequency range, i.e., when the elastic wavelength becomes commensurate with the radius of the piezoceramic disk, which is important for numerous modern applications. A mathematical model was developed for disk piezoelectric transducers made of piezoceramics to estimate their electrical impedance and quasi-static electrical capacity in the medium frequency range basing on their geometrical, physical, and mechanical characteristics. The research has found that a piezoceramic disc attains electromechanical anti-resonance in the medium frequency range at frequency, at which its electrical impedance follows to infinity. This effect is due to the polarization charges being completely compensated by the electric charge, when the electric current vanishes and energy consumption from the generator is absent. The calculations proved that at frequencies close to the first thickness resonance (corresponding to the dimensionless wave number from 40 to 60), the radial displacements of material particles of the disk vanish. A very rapid decrease in the levels of radial shifts with a simultaneous increase in the electromechanical resonance number was noted. The evaluation of the mechanical quality factor of piezoceramic disk elements, obtained with the developed mathematical model, closely correlates with real values, which is confirmed by the high agreement between theoretical and experimental results.Документ Відкритий доступ 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.Документ Відкритий доступ Сomparative Analysis of Polynomial Maximization and Maximum Likelihood Estimates for Data with Exponential Power Distribution(КПІ ім. Ігоря Сікорського, 2020) Zabolotnii, S. V.; Chepynoha, A. V.; Chorniy, A. M.; Honcharov, A. V.