FORCED ELECTRO-ELASTIC VIBRATIONS OF THE PIEZOCERAMIC PLATES AND RODS WITH DIVIDED ELECTRODES. PART I: ANALYTICAL RELATIONS FOR COUPLING COEFFICIENTS AND ADMITTANCE’S COMPONENTS

Main Article Content

Velerii Leonidovych Karlash
Oleksandr Ihorovych Bezverkhyi
Luibov Pavlivna Zinchuk

Abstract

This article analyses the forced vibrations of the non-uniform loaded piezoceramic transducers, such as plates-rods with thickness polarization and one or two bilateral electrode coating divisions, thin disks and circular rings with full or concentric and diameter divided electrodes, as well as partly electroded plates. The analytical relations for thin piezoceramic discs’ with partial electrodes radial vibrations and for rods’ with no uniform electric loading longitudinal vibrations are represented in a first part. The experimental data for rods with divided or partial electrodes are represented in a second part.

Ref. 74, fig. 1.

Article Details

How to Cite
Karlash, V. L., Bezverkhyi, O. I., & Zinchuk, L. P. (2017). FORCED ELECTRO-ELASTIC VIBRATIONS OF THE PIEZOCERAMIC PLATES AND RODS WITH DIVIDED ELECTRODES. PART I: ANALYTICAL RELATIONS FOR COUPLING COEFFICIENTS AND ADMITTANCE’S COMPONENTS. Electronics and Communications, 22(2), 43–55. https://doi.org/10.20535/2312-1807.2017.22.2.93918
Section
Acoustical devices and systems

References

I. A. Glozman, Pezokeramika [Piezoceramics]. Moscow: Energiya, 1972.

H. W. Katz, Ed., Magnitnye i dielektricheskie pribory. Ch. І. [Magnetic and dielectric devices. Part I]. Moscow: Energiya, 1964.

N. A. Shul’ga and A. M. Bolkisev, Kolebaniya pezoelektricheskikh tel [Vibrations of piezoelectric bodies]. Kiev: Naukova dumka, 1990.

M. О. Shul’ga and V. L. Karlash, Rezonansni elektromekhanichni kolyvannia piezoelektrychnykh plastyn [Resonant electromechanic vibrations of piezoelectric plates]. Kyiv: Naukova dumka, 2008.

V. L. Karlash, “Resonant electromechanical vibrations of piezoelectric plates,” Int. Appl. Mech, vol. 41, no. 7, pp. 709 – 747, 2005. DOI: 10.1007/s10778-005-0140-2.

V. M. Sharapov, I. G. Minaev, Yu. Yu. Bondarenko et al., Pezoelektricheskie preobrazovateli. Spravochnoe posobie [Piezoelectric transducers. Handbook]. Cherkassy: ChGTU, 2004.

V. L. Karlash, “Metody vyznachennia koefitsiientiv zviazku i vtrat enerhii pry kolyvanniakh rezonatoriv iz piezokeramiky [Methods of determination of coupling factors and energy losses at piezoceramics resonator’s vibrations],” Acoustic bulletin, vol. 15, no. 4, pp. 24–38, 2012.

K. Uchino, J. H. Zheng, Y. H. Chen et al, “Loss mechanisms and high power piezoelectrics,” J. Mat. Sci., vol. 41, pp. 217 – 228, 2006. DOI: 10.1007/s10853-005-7201-0

K. Uchino, Yu. Zhuang, and S. O. Ural, “Loss detertmination methodology for a piezoelectric ceramic: new phenomenological theory and experimental proposals,” J. Advanced Dielectrics, vol. 1, no. 1, pp. 17 – 31, 2011. DOI: 10.1142/S2010135X11000033.

B. Jaffe, W. R. Cook, and H.Jaffe, P'ezoelektricheskaya keramika [Piezoelectric ceramics]. Moscow: Mir, 1974.

V. L. Karlash, “Energy losses in piezoceramic resonators and its influence on vibrations’ characteristics,” Electronics and communication, vol. 19, no. 2(79), pp. 82 – 94, 2014.

V. L. Karlash, “Modeling of energy-loss piezoceramic resonators by electric equivalent networks with passive elements,” Mathematical modeling and computing, vol. 1, no. 2, pp.163 – 177, 2014.

C. E. Land, G. W. Smith, and C. R. Westgate, “The dependence of small-signal parameters of the ferroelectric ceramic resonators upon state of polarization,” IEEE Trans. Sonics and Ultrasonics, SU-11, pp. 8 – 19, 1964. DOI: 10.1109/T-SU.1964.29327.

J. A. Lewis, “The effect of driving electrode shape on the electrical properties of piezoelectric crystals,” Bell System Techn. J., vol. 40, pp. 1259 – 1280, 1961.

M. Redwood, “Coupling between two modes of vibrations in piezoelectric resonator,” J. Acoust. Soc. Am., vol. 38, pp. 568 – 582, 1965. DOI: 10.1121/1.1909748.

A. F. Ulitko, “K teorii elektromekhanicheskogo preobrazovatelya ehnergii v neravnomerno deformiruemykh pezokeramicheskikh telakh [On the theory of the electro-mechanical energy transform in non-uniform deformed piezoceramic bodies],” Prikladnaya mekhanika, vol. 13, no. 10, pp. 115 – 123, 1977.

W. Cady, Pezoelektrichestvo i ego prakticheskoe primenenie [Piezoelectricity and its practical application]. Moscow: Izdatelstvo inostrannoy literatury, 1949.

D. E. Dye, “The piezoelectric quartz resonator and its equivalent circuit,” in 1926 Proc. Phys. Soc., vol. 38, pp. 399 – 453.

C. A. Rosen, U.S. Patent 439 992, June 29, 1954.

S. Butterworth, “On electrically maintained vibrations,” in 1915 Proc. Phys. Soc., vol. 27, pp. 410 – 424.

J. Valasek, “Piezoelectric activity of Rochelle salt under various conditions,” Phys. Rev., vol. 19, pp. 478-491, 1922.

W. G. Cady, “Piezoelectric etalons of high frequency,” J. Opt. Soc. Am., vol. 10, pp. 475 – 489, 1925.

W. G. Cady, “Theory of longitudinal vibrations of viscous rods,” Phys. Rev., vol. 19, no. 1, pp. 1 – 6, 1922.

S. Ya. Sokolov, “Kolebaniya pezoelektricheskikh kvarcevykh sterzhnej v neodnorodnom pole [Vibrations of the piezoelectric quartz rods in non-uniform field],” Uspiekhy fizicheskykh nauk, vol. 50, pp. 385 – 394, 1928.

J. Erhart and S. Tutu,“Effective electromechanical coupling for the partially electroded ceramic resonators of different geometries,” The Annals “Dunarea de Jos” University of Galati, Fascicle IX. Metallurgy and Material Science, no 2, pp. 7 – 16, 2015.

P. Pulpan and J. Erhart, “Experimental verification of an analytical model for the ring shaped piezoelectric transformer,” Journal of Electrical and Electronics Engineering. Vol. 8, no. 2, pp. 23 – 28, 2015.

K. Nadal, F. Pigache and J. Erhart, “Modeling of a ring Rosen-type piezoelectric transformer by Hamilton's principle,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 62, no. 4, pp. 709 – 720, 2015. DOI: 10.1109/TUFFC.2014.006719

J. Erhart, “Parameters and design optimization of the ring piezoelectric ceramic transformer,” J. Adv. Dielect., vol. 5, no. 3, Art no. 1550022, 2015. DOI: 10.1142/S2010135X15500228

S. Tutu and J. Erhart, “Bar piezoelectric ceramic transformers working in longitudinal mode,” Ferroelectrics, vol. 486, no. 1, pp. 13 – 24, 2015. DOI: 10.1080/00150193.2015.1099413

J. Erhart, “Bulk piezoelectric ceramic transformers,” Adv. Appl. Ceram., vol. 112, no. 2, pp. 91 – 96, 2013. DOI: 10.1179/1743676112Y.0000000028

N. F. Ivina,“Analysis of the natural vibrations with partial electrodes,” Acoustical physics, vol. 47, no. 6, pp. 714 – 720, 2001. DOI: 10.1134/1.1418899

N. N. Rogacheva,“The dependence of the electromechanical coupling coefficient of piezoelectric elements on the position and size of the electrodes,” J. Appl. Math. Mech., vol. 65, no. 2, pp. 317 – 326, 2001. DOI: 10.1016/S0021-8928(01)00036-3

V. O. Andrushchenko, O. V. Boryseyko, D. S. Nemchenko, and I. A. Ulitko, “Eksperymentalne vyvchennia efektyvnosti peretvorennia enerhii na rezonansnykh kolyvanniakh piezokeramichnoho sterzhnia z rozriznymy elektrodamy pry kerovanomu elektrychnomu zbudzhenni [Experimental investigation of the energy transducing affectivity at piezoceramic bar with divided electrodes and control electric exiting resonant vibrations],” in Proc. Acoustic symposium “Konsonans-2009”, Kyiv, pp. 38 – 43.

V. L. Karlash,“Forced electromechanical vibrations of rectangular piezoceramic bars with sectionalized electrodes,” Int. Appl. Mech., vol. 49, no. 3, pp. 360 – 368, 2013. DOI: 10.1007/s10778-013-0574-x

B. Van der Veen, “The equivalent network of a piezoelectric crystal with divided electrodes,” Phillips. Res. Rep., vol. 11, pp. 66 – 79, 1956.

A. F. Ulitko, “Ob opredelenii koeffitsienta elektromekhanicheskoy svyazi v zadachakh ustanovivshikhsya kolebaniy pezokeramicheskikh tel [On electromechanical coupling factor determine in problem of the piezoceramic bodies’ fixed vibrations],” Math. methods and physicomech. fields, issue 7, pp. 77 – 81, 1978.

V. L. Karlash, “Formy kolebaniy i effektivnost preobrazovaniya energii sostavnymi pezokeramicheskimi sterzhnyami [Vibration forms and efficiency of the energy transform by composed piezoceramic bars],” Prikladnaya mekhanika, vol. 23, no. 2, pp. 72 – 78, 1987.

M. Onoe, “Frequency of edge mode of isotropic thin rectangular plate, circular disk and rod,” J. Acoust. Soc. Am., vol. 33, p. 1627L, 1961.

E. C. Munk,“The equivalent electrical circuit for radial modes of a piezoelectric ceramic disk with concentric electrodes,” Phillips Res. Rep., vol. 20, pp. 170 – 189, 1965.

K. Okadzakhi and M. Umino, “Analysis of vibrations in thin piezoceramic resonators with annular electrodes,” Nippon Onkyo Gakkaishi (J. Acoust. Soc. Jpn), vol. 25, no. 6, pp. 325 – 334, 1969.

V. N. Lazutkin, Yu. V. Tsyganov, V. A. Klyushnichenko, “Radialnye kolebaniya i elektricheskiy impedans pezokeramicheskikh kolets s polyarizatsiey po vysote [Radial vibrations and electrical impedance of piezoceramic rings with height polarization],” in Piezoelectric materials and transducers. Rostov-on-Don: Izdatelstvo RGU, pp. 4 – 9, 1971.

I. F. Vovkodav, “Radialnye kolebaniya tonkoy pezokeramicheskoy plastinki s razreznymi elektrodami [Radial vibrations of the thin piezoceramic plate with divided electrodes],” Teplovye naprtyuazheniya v elementakh konstruktziy, vol. 15, pp. 99–103, 1975.

V. A. Andrushchenko, I. F. Vovkodav, V. L. Karlash, and A. F. Ulitko, “Issledovanie koeffitsienta elektromekhanicheskoy svyazi v kruglykh pezokeramicheskikh plastinakh [Coefficient of electromechanical coupling in piezoceramic disks],” Prikladnaya mekhanika, vol. 11, no. 4, pp. 42 – 48, 1975.

V. L. Karlash, V. A. Klyushnichenko, Yu. A. Kramarov, and A. F. Ulitko, “Issledovanie radialnykh kolebaniy tonkih pezokeramicheskikh diskov pri neravnomernom elektricheskom nagruzhenii [Investigation of the radial vibrations of the thin piezoceramic disks with non-uniform electric loading],” Prikladnaya mekhanika, vol. 13, no. 3, pp. 56 – 62, 1977.

V. L. Karlash, “K teorii nesimmetrichnyh kolebanij pezokeramicheskih kruglyh plastin s razdelennymi elektrodami [On the theory of the circular piezoceramic plates’ with divided electrodes asymmetric vibrations],” Izvestiya AN ArmSSR, mekhanika, vol. 34, no. 6, pp. 60 – 65, 1981.

A. Pyatrauskas, A. Prialgauskas, and A. Mazhonas, “Issledovanie kolebanij sostavnyh kruglyh p'ezopreobrazovatelej [Investigation of the vibrations of the composed circular piezoransducers],” Ultrazvuk, vol. 19, pp. 107 – 113, 1987.

Y. Ramanauskas, “Eksperimental'noe issledovanie diskovyh bimorfnyh ehlementov na izgibnyh kolebaniyah [Experimental investigation of the disk bimorph elements on flexural vibrations],” Ultrazvuk, vol. 20, pp. 158 – 163, 1990.

N. A. Shul’ga and L. V. Borisenko, “Elektrouprugie kolebaniya radialno polyarizovannogo pezokeramicheskogo tsilindra s chastichno ehlektrodirovannymi bokovymi poverhnostyami [Electroelastic vibrations of radial polarized piezoceramic cylinder with partly electroded sides],” Prikladnaya mekhanika, vol. 26, no. 1, pp. 43 – 47, 1990.

I. A. Kartashov and N. V. Marchenko, Pezoelektricheskie transformatory toka [Piezoelectric current transformer]. Kiev: Tekhnika, 1978

V. V. Lavrinenko, Pezoelektricheskie transformatory [Piezoelectric Transformers]. Moscow: Energiya, 1975.

Yu. A. Kramarov and V. A. Klyushnichenko, “Neravnomerno–polyarizovannyi pezopreobrazovatel [A non-uniform polarized piezotransducer],” Acusticheskiye metody i sredstva issledovaniya okeana. Collection of scientific works. Part II, Vladivostok, pp. 3 – 6, 1974.

V. G. Karnaukhov, V. I. Kozlov, V. V. Mikhaylenko, and S. V. Mikhaylenko, “Planarnye kolebaniya pezokeramicheskoy plastiny s uchetom depolyarizatsii materiala, vyzvannoy temperaturoy vibrorazogreva [Planar vibrations of the piezoceramic plate with accounting the material depolarization, caused by vibration heating],” Prikladnaya mekhanika, vol. 30, no. 3, pp. 67 – 73, 1994.

S. I. Rudnitskiy, V. M. Sharapov, and N. A. Shu’lga, “Kolebaniya diskovogo bimorfnogo preobrazovatelya tipa metall-p'ezokeramika [Vibrations of the disk bimorph transducer of metal-piezoceramic type],” Prikladnaya mekhanika, vol. 26, no. 10, pp. 64 – 72, 1990.

O. P. Chervinko and Ya. O. Zhuk, “Spivvidnoshennia zviazanoi dynamichnoi zadachi termoviazkoplastychnosti dlia hnuchkykh obolonok z piezoaktyvnymy sharamy [Relations of the coupled dynamic thermoviscoplastic problem for flexible shells with piezoactive layers],” Dopovidi NAN Ukrainy, no. 1, pp. 68 – 74, 2002

V. L. Karlash, “Electroelastic vibrations and transformation ratio of a planar piezoceramic transformer,” J. Sound Vib., vol. 277, pp. 353 – 367, 2004. DOI: 10.1016/j.jsv.2003.03.012.

V. Karlash, “Longitudinal and lateral vibrations of a planar piezoceramic transformer,” Jpn. J. Appl. Phys., vol. 44, part 1, no. 4A, pp. 1852 – 1856, 2005. DOI: 10.1143/JJAP.44.1852.

J. Hu, Y. Fuda, M. Katsuno and T. A. Yoshiba, “Study on the rectangular-bar shaped multilayer piezoelectric transformer using length extensional vibration mode,” Jpn. J. Appl. Phys., vol. 38, pp. 3208 – 3212, 1999. DOI: 10.1143/JJAP.38.3208

H. Xue, J. Yang and Y. Hu, “Analysis of Rosen Piezoelectric Transformers with a Varying Cross-Section,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 55, no. 7, pp. 1632 – 1639, 2008. DOI: 10.1109/TUFFC.2008.837

N. Y. Wong, Y. Zhang, H .L. W. Chan and C.L. Choy, “A bilayer piezoelectric transformer operating in a bending vibration mode,” Mater. Sci. Eng. B, vol. 99, no. 1-3, pp. 164 – 167, 2003. DOI: 10.1016/S0921-5107(02)00472-5

C. M. Leung, S. W. Or, F. Wang, S.L. Ho, H. Luo, “Enhanced magnetoelectric effect in heterostructure of magnetostrictive alloy bars and piezoelectric single-crystal transformer,” Rev. Sci. Instrum, vol. 82, issue 1, Art no. 013903, 2011. DOI: 10.1063/1.3529439

Sh. Dong, “Review on piezoelectric, ultrasonic and magnetoelectric actuators,” J. Adv. Dielect., vol. 2, no. 1, Art no. 1230001, 2012. DOI: 10.1142/S2010135X12300010

V.H. Dubenets, O.V. Savchenko and O.L. Derkach, “Nonstationary vibrations of a beam with electro-viscoelastic dissipative patches,” Visnyk of Chernihiv state technological university, no. 3 (67), pp. 53 – 61, 2013.

V. Dubenets, O. Savchenko and O. Derkach, “Active damping of nonstationary vibrations in a beam with electro-viscoelastic dissipative patches,” Visnyk of Chernihiv state technological university, no. 1 (71), pp. 43 – 50, 2014.

O. I. Bezverkhyi, L. P. Zinchuk, and V. L. Karlash, “Vplyv elektrychnoho navantazhennia na vymusheni kolyvannia poperechno poliaryzovanykh piezokeramichnykh sterzhniv [Effect of the electrical loading on forced vibrations of transversely polarized piezoceramic bars],” Electronics and communication, vol. 20, no. 4 (87), pp. 77 – 88, 2015. DOI: 10.20535/2312-1807.2015.20.4.69911

V. T. Grinchenko, V. L. Karlash, V. V. Meleshko, and A. F. Ulitko, “Issledovanie planarnykh kolebaniy pryamougolnykh pezokeramicheskikh plastin [Investigation of the planar vibrations of the rectangular piezoceramic plates],” Prikladnaya mekhanika, vol. 12, no. 5, pp. 71 – 78, 1976.

O. N. Petrishchev, Garmonicheskie kolebaniya pezokeramicheskikh elementov. CH. І. Garmonicheskie kolebaniya pezokeramicheskikh elementov v vakuume i metod rezonansa-antirezonansa [Harmonic vibrations of the piezoceramic elements. Part I. Harmonic vibrations of the piezoceramic elements in vacuum and resonance-anti-resonance method]. Kiev: Avers, 2012.

O. N. Petrishchev, A. V. Korzhik, and A. V. Bogdanov, ”Raschet chastotnoy kharakteristiki nesimmetrichnogo pezoelektricheskogo akselerometra [The calculation of the frequency characteristics of asymmetric piezoelectric accelerometer],” Acoustic bulletin, vol. 16, no. 2, pp. 47 – 55, 2013 – 2014.

R. Holland, “The equivalent circuit of an N-electrode piezoelectric bar,” in Proc. IEEE, vol. 54, no. 7, pp. 968 – 975, 1966. DOI: 10.1109/PROC.1966.4942

R. Holland, “The equivalent circuit of a symmetric N-electrode piezoelectric disk,” IEEE Trans. Sonics and Ultrasonics, vol. 14, no. 1, pp. 21–32, 1967. DOI: 10.1109/T-SU.1967.29406

R. Holland and E.P. EerNisse, Design of resonant piezoelectric devices. Cambridge and London: M.I.T. Press, 1969. ISBN: 9780262080330

V. M. Sharapov, Yu. Yu. Bondarenko, M. P. Musiyenko, and T. Yu. Kisil, “About the methods of a linearization of a peak-frequency characteristics of piezoceramic transducers,” Visnyk ChDTU, no. 3, pp. 51 – 53, 2005.

V. M. Sharapov, M. P. Musiyenko, and S. A. Filimonov, “The investigation of frequency characteristics of piezotransducers with double circuit negative feedback,” Visnyk ChDTU. Spetsvypusk, pp. 262 – 264, 2006.

IRE Standards on Piezoelectric Crystals: Measurements of Piezoelectric Ceramics, in Proс. IRE, vol. 49, iss. 7, pp. 1161 – 1169, 1961. DOI: 10.1109/JRPROC.1961.287860

V. A. Akopyan, A.N Soloviev, and S. N. Shevtsov, Metody i algoritm opredeleniya polnogo nabora sovmestimykh materialnykh konstant pezokeramicheskikh materialov [Methods and algorithm to determine the complete set of compatible material constants of piezoelectric materials]. Rostov-on-Don: Publishing House of the SFU, 2008.