Abstract
The scientific results on the resonant electromechanical vibrations of piezoceramic plates in the form of disks, rings, and polygons obtained over the last 30 years are analyzed, systematized, and generalized. Emphasis is on experimental methods. It is shown that all piezoceramic plates have vibration modes at which deformations are in-phase over the entire volume of the body
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REFERENCES
G. Alenkovich, “A note on the calculation of vibrations of a loaded thin piezoceramic plate poled across the thickness,” Nauchn. Tr. VUZov LitSSR, Ul'trazvuk, 20, 27–37 (1988).
D. Berlinkur, D. Kerran, and G. Jaffe, “Piezoceramic electric and piezomagnetic materials and their application in transducers,” in: W. P. Mason (ed.), Physical Acoustics, Principles and Methods, Vol. 1, Part A, Methods and Devices, Academic Press, New York-London (1964).
S. A. Boidek, “A set-up for recording impedance diagrams of electroacoustic transducers,” in: 6th All-Union Acoust. Conf. GP-7 [in Russian], Akin, Moscow (1968), pp. 1–4.
A. M. Bolkisev, V. L. Karlash, and N. A. Shul'ga, “Temperature dependence of the properties of piezoelectric ceramics,” Int. Appl. Mech., 20, No.7, 650–653 (1984).
A. A. Bondarenko, N. I. Karas', and A. F. Ulitko, “Methods for determining the vibrational dissipation characteristics of piezoceramic structural elements,” Int. Appl. Mech., 18, No.2, 175–179 (1982).
I. A. Vekovishcheva, “Simple cases of bending of thin piezoelectric plates,” Int. Appl. Mech., 13, No.12, 1275–1277 (1977).
I. P. Vovkodav and A. T. Ulitko, “Radial vibrations of a thin piezoceramic plate,” DAN URSR, Ser. A, No. 9, 830–833 (1973).
V. G. Gavrilyachenko, A. Ya. Dantsiger, V. A. Doroshenko, et al., “Increasing the cyclic strength of piezoceramic materials,” in: Proc. 2nd All-Union Semin. on Strength of Materials and Structural Members at Acoustic and Ultrasonic Frequencies of Loading [in Russian], Naukova Dumka, Kiev (1980), pp. 194–198.
I. A. Glozman, Piezoceramics [in Russian], Energia, Moscow (1972).
GOST 12370-72. Piezoceramic Materials: Test Methods [in Russian], Izd. Stand., Moscow (1973).
V. T. Grinchenko, V. L. Karlash, V. V. Meleshko, and A. F. Ulitko, “Investigation of planar vibrations of rectangular piezoceramic plates,” Int. Appl. Mech., 12, No.5, 483–488 (1976).
V. T. Grinchenko, A. F. Ulitko, and N. A. Shul'ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kiev (1989).
A. N. Guz, V. A. Zarutskii, I. Ya. Amiro, et al., Experimental Investigations into Thin-Walled Structures [in Russian], Naukova Dumka, Kiev (1984).
V. Domarkas, A. Mazhonas, and A. Pyatrauskas, “Bending vibrations of compound rectangular piezoelectric transducers,” Nauchn. Tr. VUZov LitSSR, Ul'trazvuk, 21, 43–49 (1989).
A. A. Erofeev, G. A. Danov, and V. N. Frolov, Piezoceramic Transformers and Their Application in Radio Electronics [in Russian], Radio i Svyaz', Moscow (1988).
V. L. Karlash, “Nonsymmetric vibrations of piezoelectric ceramic rings polarized along the thickness, ” Int. Appl. Mech., 14, No.12, 1303–1308 (1978).
V. L. Karlash, “Radial modes of piezoceramic disks with open circuit electrodes,” Int. Appl. Mech., 17, No.9, 836–839 (1981).
V. L. Karlash, “Theory of asymmetric vibrations of piezoceramic circular plates with separated electrodes,” Izv AN ArmSSR, Mekh., 34, No.6, 60–65 (1981).
V. L. Karlash, “Amplitude-phase relationships in the piezotransformer sensor method,” Int. Appl. Mech., 19, No.10, 911–916 (1983).
V. L. Karlash, “Influence of energy dissipation on the frequency response of the admittance of a thin piezoceramic disk,” Elektrichestvo, No. 4, 59–61 (1984).
V. L. Karlash, “Energy dissipation during vibrations of thin circular piezoceramic plates,” Int. Appl. Mech., 20, No.5, 460–464 (1984).
V. L. Karlash, “Resonant vibrations of thin piezoceramic plates with curved boundaries,” Prikl. Mekh., 23, No.7, 105–109 (1987).
V. L. Karlash, “Peculiarities of planar vibrations of piezoelectric round plates,” Int. Appl. Mech., 23, No.11, 1059–1063 (1987).
V. L. Karlash, “Nonaxisymmetric vibrations of circular piezoceramic rings with an electrode coating having two-sided diametrical slits,” Int. Appl. Mech., 24, No.8, 798–803 (1988).
V. L. Karlash, Experimental Study of the Stress-Strain State of Structural Members by the Method of Piezoceramic Models [in Russian], Manuscript No. 5001-V88, dep VINITI 06.23.88, Kiev (1988).
V. L. Karlash, “Theory of planar vibrations of thin piezoceramic plates,” in: Proc. 4th Symp. on Theoretical Fundamentals of Magnetoelasticity [in Russian], Yerevan (1989), pp. 106–112.
V. L. Karlash, “Nonaxisymmetric vibrations of circular piezoceramic multielectrode rings with thickness polarization,” Int. Appl. Mech., 26, No.4, 374–378 (1990).
V. L. Karlash, “Forced high-frequency vibrations of thin circular piezoceramic disks,” Int. Appl. Mech., 31, No.5, 394–398 (1995).
V. L. Karlash, “Planar thickness vibrations of piezoceramic rings and disks,” Prikl. Mekh., 33, No.7, 72–78 (1997).
V. L. Karlash, “The forced electroelastic vibrations of a planar piezoelectric transformer of longitudinal-transverse type,” Int. Appl. Mech., 36, No 7, 923–930 (2000).
V. L. Karlash, “Frequency properties of a planar piezoelectric transformer of longitudinal-transverse type,” Int. Appl. Mech., 36, No.8, 1103–1111 (2000).
V. L. Karlash, “The stress state of a rectangular piezoceramic plate with transverse-longitudinal polarization,” Int. Appl. Mech., 37, No.3, 386–392 (2001).
V. L. Karlash, “Transformation ratio and vibration modes of a Rosen-type piezoelectric transformer, ” Elektrichestvo, No. 1, 51–55 (2002).
V. L. Karlash, “Longitudinal vibrations and input admittance of a compound piezoceramic rectangular plate with cross polarization,” Int. Appl. Mech., 38, No.5, 617–622 (2002).
V. L. Karlash, “Electroelastic vibrations and a refined formula for the transformation ratio of a piezotransformer plate,” Visn. Donetsk. Univ., Ser. A, Pryrod. Nauky, 1, 98–102 (2003).
V. L. Karlash, “Influence of energy losses on the performance of a piezoelectric transformer plate, ” Int. Appl. Mech., 39, No.8, 987–992 (2003).
V. L. Karlash, Experimental and Theoretical Analysis of Electromechanical Resonant Vibrations and Efficiency of Energy Conversion in Piezoceramic Thin-Walled Elements [in Ukrainian], DSci Thesis, Inst. Mekh. NAN Ukrainy, Kiev (2004).
V. L. Karlash and A. T. Ulitko, “A method for studying the radial vibrations of a thin piezoceramic plate,” DAN URSR, Ser. A, No. 9, 804–807 (1974).
V. L. Karlash and A. F. Ulitko, “A method for studying mechanical stresses in vibrating piezoceramic bodies,” Elektrichestvo, No. 11, 82–83 (1976).
V. L. Karlash and A. F. Ulitko, “Investigating the vibrations of piezoceramic elements by the piezotransformer-transducer method,” in: A. N. Guz and V. A. Zarutskii (eds.), Experimental Investigations of Thin-Walled Structures [in Russian], Naukova Dumka, Kiev (1984), pp. 178–196.
V. L. Karlash, V. A. Klyushnichenko, Yu. A. Kramarov, and A. F. Ulitko, “Radial vibrations of thin piezoceramic disks under a nonuniform electric load,” Int. Appl. Mech., 13, No.8, 784–789 (1977).
V. L. Karlash, R. F. Kubyak, E. Ya. Filatov, and N. A. Shul'ga, “A possibility of using piezoceramic transducers to control the level of loading in fatigue tests,” Zavod. Labor., 53, No.12, 64–65 (1987).
V. G. Karnaukhov, I. F. Kirichok, and V. I. Kozlov, “Electromechanical vibrations and dissipative heating of viscoelastic thin-walled piezoelements,” Int. Appl. Mech., 37, No.2, 182–212 (2001).
V. G. Karnaukhov, V. I. Kozlov, V. V. Mikhailenko, and S. V. Mikhailenko, “Planar vibrations of piezoceramic plates with account for material depolarization caused by vibratory heating,” Int. Appl. Mech., 30, No.3, 222–227 (1994).
W. G. Cady, Piezoelectricity, McGraw-Hill, New York (1946).
H. W. Katz (ed.), Solid State Magnetic and Dielectric Devices, Wiley, New York (1959).
V. N. Lazutkin, Yu. V. Tsyganov, and V. A. Klyushnichenko, “Radial vibrations and impedance of piezoceramic rings polarized along the height,” in: Piezoelectric Materials and Transducers [in Russian], Izd. RGU, Rostov-on-Don (1971), pp. 4–9.
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge Univ. Press (1959).
W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, Van Nostrand, New York (1950).
K. Okazaki and M. Umino, “Analysis of vibrations in thin piezoceramic resonators with annular electrodes,” Nippon Onkyo Gakkaishi (J. Acoust. Soc. Japan), 25, No.6, 325–334 (1969).
O. P. Petin, Yu. A. Kramarov, and G. P. Petin, “A set-up for measuring the admittance-frequency characteristics of piezoelectric transducers,” in: Piezoelectric Materials and Transducers [in Russian], Izd. RGU, Rostov-on-Don (1977), pp. 22–25.
A. Pyatrauskas, C. Prialgauskas, and A. Mazhonas, “Investigation of vibrations of compound circular piezoelectric transducers,” Nauchn. Tr. VUZov LitSSR, Ul'trazvuk, 19, 107–113 (1987).
Y. Ramanauskas, “Experimental investigation of disk bimorph elements under flexural vibrations,” Nauchn. Tr. VUZov LitSSR, Ul'trazvuk, 20, 158–163 (1990).
S. I. Rudnitskii, V. M. Sharapov, and N. A. Shul'ga, “Vibrations of a bimorphic disk transducer of the metal-piezoceramic type,” Int. Appl. Mech., 26, No.10, 973–980 (1990).
K. Shibayama, “Piezoceramic transducers as short rods,” in: Y. Kikuchi (ed.), Ultrasonic Transducers, Corona, Tokyo (1969).
E. G. Smazhevskaya and N. B. Fel'dman, Piezoelectric Ceramics [in Russian], Sov. Radio, Moscow (1971).
E. G. Smazhevskaya, R. F. Zhuchina, and N. A. Podol'ner, “Influence of the basic parameters of a piezoceramic material on the characteristics of resonant piezoelectric transformers,” in: Ultrasonic Transmitters and Receivers [in Russian], Pt. 2, LDNTP, Leningrad (1966), pp. 22–35.
R. Truell, C. Elbaum, and B. Chick, Ultrasonic Methods in Solid State Physics, Acad. Press, New York (1969).
A. F. Ulitko, “The theory of vibrations of piezoceramic bodies,” Tepl. Napr. Elem. Konstr., 15, 90–99 (1975).
G. G. Chernykh, L. S. Soboleva, and V. V. Kharitonov, “Radial vibrations of thin piezoceramic disks and rings,” Electron. Tekhn., No. 1, 67–84 (1972).
N. A. Shul'ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kiev (1990).
B. Jaffe, W. R. Cook, and H. Jaffe, Piezoelectric Ceramics, Academic Press, New York (1971).
W. G. Cady, “Theory of longitudinal vibrations of viscous rods,” Phys. Rev., 19, No.1, 1–6 (1922).
M. C. Dokmeci, “Recent progress in the dynamic applications of piezoelectric crystals,” The Shock and Vibration Digest, 20, No.2, 3–20 (1988).
D. E. Dye, “The piezoelectric quartz resonator and its equivalent circuit,” Proc. Phys. Soc. (London), 38, 399–453 (1926).
H. Ekstein, “Free vibrations of anisotropic bodies,” Phys. Rev., 66, 109–117 (1944).
Y. Fuda, K. Kumasaka, M. Katsumo, H. Sato, and Y. Ino, “Piezoelectric transformer for cold cathode fluorescent lamp inverter,” Jpn. J. Appl. Phys., 1.36, No.5B, 3050–3052 (1997).
S. K. Ha, “Analysis of the asymmetric triple-layered piezoelectric bimorf using equivalent circuit models,” J. Acoust. Soc. Am., 110, 856–864 (2001).
S. K. Ha and Y. H. Kim, “Analysis of an asymmetrical piezoelectric annular bimorf using impedance and admittance matrices,” J. Acoust. Soc. Am., 110, 212–215 (2001).
S. Hirose, N. Magami, and S. Takanashi, “Piezoelectric ceramic transformer using piezoelectric lateral effect on input and on output,” Jpn. J. Appl. Phys., 35, 3038–3041 (1996).
R. Holland, “Representation of dielectric, elastic and piezoelectric losses by complex coefficients, ” IEEE Trans. Sonics and Ultrasonics, SU-14, 18–20 (1967).
R. Holland and E. P. Eer Nisse, Design of Resonant Piezoelectric Devices, M. I. T. Press, Cambridge-London (1969).
J. Hu, Y. Fuda, M. Katsuno, and T. Yoshiba, “A study on the rectangular-bar shaped multilayer piezoelectric transformer using length extensional vibration mode,” Jpn. J. Appl. Phys., 38, 3208–3212 (1999).
H. Ikushima and K. Ohji, “Observation of Chladni figures in piezoelectric ceramic plates of rectangular form,” Jpn. J. Appl. Phys., 13, 20–33 (1974).
T. Inoue, M. Yamamoto, S. Kawashima, and S. Hirose, “Third order longitudinal piezoelectric ceramic transformer for high-voltage power inverter,” IEICE T ELECTRON, E81, No.7, 1128–1135 (1998).
IRE Standards on Piezoelectric Crystals: Measurements of Piezoelectric Ceramics, Proc. IRE, 49, 1161–1169 (1961).
T. Irie, G. Yamada, and K. Yoda, “Free vibration of membranes and plates with four curved edges,” J. Acoust. Soc. Am., 70, 1083–1088 (1981).
V. L. Karlash, “Electroelastic characteristics of a piezoelectric transformer plate,” Int. Appl. Mech., 39, No.7, 870–874 (2003).
V. L. Karlash, “Electroelastic vibrations and transformation ratio of a planar piezoceramic transformer, ” J. Sound Vib., 277, 353–367 (2004).
V. L. Karlash, “Modal analysis of a rectangular piezoceramic plate with cross polarization,” Int. Appl. Mech., 39, No.10, 1215–1220 (2003).
I. F. Kirichok, “Radial vibrations and heating of a ring piezoplate under electric excitation applied to nonuniformly electroded surfaces,” Int. Appl. Mech., 37, No.3, 304–309 (2004).
R. Lakes, “Shape-dependent damping in piezoelectric solids,” IEEE Trans., Sonics and Ultrasonics, SU-27, 208–213 (1980).
P. A. A. Laura, R. H. Gutierrez, and R. E. Rossi, “Transverse vibrations of circular annular plate with free edges and two intermediate concentric supports,” J. Sound Vib., 226, 1043–1047 (1999).
P. A. A. Laura, R. H. Gutierrez, and R. E. Rossi, “Vibrations of a circular annular plates of cylindrical anisotropy and nonuniform thickness,” J. Sound Vib., 231, 246–252 (2000).
K. M. Liew, T. Y. Ng, and B. P. Wang, “Vibration of annular plates from three-dimensional analysis, ” J. Acoust. Soc. Am., 110, 233–242 (2001).
G. E. Martin, “Dielectric, elastic and piezoelectric losses in piezoelectric materials,” in: Ultrasonic Symp. Proc. Milwaukee (1974), pp. 613–617.
K. Maruyama and O. Ichinomiya, “Experimental investigation of free vibrations of clamped sector plates, ” J. Sound Vib., 74, 565–573 (1981).
W. P. Mason, “Electrostrictive effect in barium titanate ceramics,” Phys. Rev., 74, 1134–1147 (1948).
M. A. Medick and Y.-H. Pao, “Extensional vibrations of thin rectangular plates,” J. Acoust. Soc. Am., 37, 59–65 (1965).
E. C. Munk, “The equivalent electrical circuit for radial modes of a piezoelectric ceramic disk with concentric electrodes,” Phillips Res. Rep., 20, 170–189 (1965).
M. Onoe, “Frequency of edge mode of isotropic thin rectangular plate, circular disk and rod,” J. Acoust. Soc. Am., 33, 1627 L (1961).
M. Redwood, “Coupling between two modes of vibrations in piezoelectric resonator,” J. Acoust. Soc. Am., 38, 568–582 (1965).
A. G. Shaw, “On the resonant vibrations of thick barium titanate disks,” J. Acoust. Soc. Am., 28, 38–50 (1956).
O. Stephan, “Electric equivalent circuit of the circular piezoelectric resonators,” Chech. J. Phys., 20, No.4, 432–441 (1970).
C. V. Stephenson, “Higher modes of radial vibrations in short, hollow cylinders of barium titanate, ” J. Acoust. Soc. Am., 28, No.5, 928–929 (1956).
C. A. Rosen, US Patent 439 992 1954, 29.06.54 (1954).
K. S. Van Dyke, “The electric network equivalent of piezoelectric resonators,” Phys. Rev., 25, 895(A) (1925).
M. Yamamoto, Y. Sasaki, A. Ochi, T. Inoue, and S. Hamamura, “Step-down piezoelectric transformer for AC-DC converters,” Jpn. J. Appl. Phys., 1.40, No.5B, 3637–3642 (2001).
J. Yoo, K. Yoon, Y. Lee, S. Suh, J. Kim, and C. Yoo, “Electrical characteristics of the contour-vibration-mode piezoelectric transformer with ring/dot electrode area ratio,” Jpn. J. Appl. Phys., 39, 2680–2684 (2000).
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 3–46, July 2005.
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Karlash, V.L. Resonant Electromechanical Vibrations of Piezoelectric Plates. Int Appl Mech 41, 709–747 (2005). https://doi.org/10.1007/s10778-005-0140-2
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DOI: https://doi.org/10.1007/s10778-005-0140-2