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The Radial Electric Field Excited Circular Disk Piezoceramic Acoustic Resonator and Its Properties

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The Radial Electric Field Excited Circular Disk Piezoceramic Acoustic Resonator and Its Properties sensors Article The Radial Electric Field Excited Circular Disk Piezoceramic Acoustic Resonator and Its Properties Andrey Teplykh * , Boris Zaitsev , Alexander Semyonov and Irina Borodina Kotel’nikov Institute of Radio Engineering and Electronics of RAS, Saratov Branch, 410019 Saratov, Russia; [email protected] (B.Z.); [email protected] (A.S.); [email protected] (I.B.) * Correspondence: [email protected]; Tel.: +7-8452-272401 Abstract: A new type of piezoceramic acoustic resonator in the form of a circular disk with a radial exciting electric field is presented. The advantage of this type of resonator is the localization of the electrodes at one end of the disk, which leaves the second end free for the contact of the piezoelectric material with the surrounding medium. This makes it possible to use such a resonator as a sensor base for analyzing the properties of this medium. The problem of exciting such a resonator by an electric field of a given frequency is solved using a two-dimensional finite element method. The method for solving the inverse problem for determining the characteristics of a piezomaterial from the broadband frequency dependence of the electrical impedance of a single resonator is proposed. The acoustic and electric field inside the resonator is calculated, and it is shown that this location of electrodes makes it possible to excite radial, flexural, and thickness extensional modes of disk oscillations. The dependences of the frequencies of parallel and series resonances, the quality factor, and the electromechanical coupling coefficient on the size of the electrodes and the gap between them are calculated. Keywords: acoustic resonator; circular piezoceramic disk; finite element method; electrical impedance; acoustic resonance spectroscopy; electromechanical coupling coefficient; Q-factor; Nelder–Mead al- gorithm Citation: Teplykh, A.; Zaitsev, B.; Semyonov, A.; Borodina, I. The Radial Electric Field Excited Circular Disk Piezoceramic Acoustic Resonator and 1. Introduction Its Properties. Sensors 2021, 21, 608. There are many types of piezoelectric transducers and resonators that operate in differ- https://doi.org/10.3390/s21020608 ent acoustic modes and are used in different practical applications. Cylindrical piezoelectric transducers operating on a longitudinal acoustic mode are used for the emission and re- Received: 30 December 2020 ceiving of ultrasound in a liquid [1,2] and piezoelectric energy harvesting solutions [3,4]. Accepted: 14 January 2021 Resonators with a transverse electric field are used for various sensor applications [5–9]. Published: 17 January 2021 Resonators of this type are sensitive to mechanical and electrical properties of the medium, which borders on the free surface of the resonator [7,8]. Publisher’s Note: MDPI stays neu- One of the possible new applications of piezoceramic resonators is the creation of tral with regard to jurisdictional clai- sensors for determining the acoustic and electrical characteristics of the medium in contact ms in published maps and institutio- with the resonator by the method of broadband acoustic resonance spectroscopy (ARS) [9]. nal affiliations. This work is devoted to the study of a new type of piezoelectric resonator with ring electrodes, which can be used to determine the mechanical and electrical properties of thin films or viscous conducting liquids. The study of such a resonator was carried out in Copyright: © 2021 by the authors. Li- two stages. First, the electrical impedance of the unloaded resonator was measured in a censee MDPI, Basel, Switzerland. sufficiently wide frequency range, and all its resonant frequencies were found. At this stage, This article is an open access article a finite element model of the resonator was created, and the characteristics of the material distributed under the terms and con- (elastic, piezoelectric and dielectric constants, density, and viscosity) of the resonator itself ditions of the Creative Commons At- were refined [10,11]. This was done by the method of broadband acoustic resonance tribution (CC BY) license (https:// spectroscopy [10–12]. Then, these measurements were carried out in the same frequency creativecommons.org/licenses/by/ range for the resonator, the free surface of which was in contact with the investigated 4.0/). Sensors 2021, 21, 608. https://doi.org/10.3390/s21020608 https://www.mdpi.com/journal/sensors Sensors 2021, 21, x FOR PEER REVIEW 2 of 16 onance spectroscopy [10–12]. Then, these measurements were carried out in the same fre- quency range for the resonator, the free surface of which was in contact with the investi- gated medium. This medium can be a viscoelastic film with finite conductivity or viscous conducting liquid. By changing the values of the resonance frequencies and the magni- tude of the resonance peaks, one can estimate the properties of the medium under study Sensors 2021, 21, 608 [12]. In order to determine the mechanical and electrical properties of the2 of medium, 15 the electric field that accompanies acoustic oscillations must freely penetrate from the resona- tor into the medium. This means that the medium must be in direct contact with the res- onatormedium. material This and medium not with can be a ametal viscoelastic electro filmde withon its finite surface. conductivity To successfully or viscous apply the methodconducting of broadband liquid. By changingacoustic the resonance values of the spectros resonancecopy, frequencies it is necessary and the magnitude to be able to effec- tivelyof thedetermine resonance the peaks, oscillation one can estimate spectrum the propertiesof the resonator of the medium (its natural under study frequencies) [12]. or the In order to determine the mechanical and electrical properties of the medium, the electric responsefield that of the accompanies resonator acoustic (its electrical oscillations impeda must freelynce) penetrateto excitation from at the a resonator certain frequency into [13]. Ourthe studies medium. revealed This means that the that distribution the medium must of th bee acoustic in direct contactand electric with the fields resonator and the electric impedancematerial andof a not piezoelectric with a metal electrodedisk made on its of surface. a 6 mm To successfully group piezomaterial, apply the method the crystallo- graphicof broadband axis of which acoustic coincides resonance with spectroscopy, the axis of it isthe necessary disk, can to be be calculated able to effectively quite accurately determine the oscillation spectrum of the resonator (its natural frequencies) or the response and ofquickly. the resonator In this (its case, electrical it is impedance)possible mathematically to excitation at a to certain strictly frequency take into [13]. account Our the dif- ferentstudies positions revealed of thatthe theexciting distribution electrodes of the acoustic and the and inhomogeneity electric fields and of the the electric disk material if this impedancedoes not ofviolate a piezoelectric the axial disk symmetry made of a 6 mmof th groupe problem piezomaterial, [14]. In the this crystallographic paper, we propose a designaxis of of such which a coincidesresonator with in thethe axisform of of the a disk, circular can be piezoceramic calculated quite disk accurately with a andradial exciting quickly. In this case, it is possible mathematically to strictly take into account the different electric field. A mathematical model of this resonator based on the finite element method positions of the exciting electrodes and the inhomogeneity of the disk material if this does wasnot created. violate A the comparison axial symmetry of oftheoretical the problem and [14]. ex Inperimental this paper, we results propose for a designradial ofelectric field excitedsuch resonator a resonator made in the form from of Russian a circular commercia piezoceramiclly disk available with a radial piezoelectric exciting electric ceramics with bariumfield. lead A mathematical zirconate titanate model of (BPZT) this resonator was carried based on out, the finiteand the element material method constants was of pie- zoelectriccreated. ceramics A comparison were of theoretical refined. and The experimental dependences results of for radialits electrical electric field impedance excited on fre- resonator made from Russian commercially available piezoelectric ceramics with barium quencylead and zirconate other titanate characteristics (BPZT) was of carried the resona out, andtor the were material calculated constants offor piezoelectric different radii of the electrodesceramics and were the refined. gap Thebetween dependences them. of its electrical impedance on frequency and other characteristics of the resonator were calculated for different radii of the electrodes and the 2. Materialsgap between and them. Methods 2.1. 2.Numerical Materials Model and Methods of a Radial Electric Field Excited Piezoceramic Disk Resonator 2.1.Consider Numerical the Model problem of a Radial of Electricforced Field vibrations Excited Piezoceramic of a circular Disk piezoceramic Resonator disk excited by a pair ofConsider concentric the problemelectrodes of forced located vibrations on one of side a circular of the piezoceramic disk. The diskgeometry excited byof athe problem pair of concentric electrodes located on one side of the disk. The geometry of the problem is shownis shown in inFigure Figure 1.1. (a) (b) Figure 1.Figure The geometry 1. The geometry of the of problem. the problem. (a) (a Side) Side view view ofof the the resonator resonator and and
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