The general solution to the problem of the nonaxisymmetric electromechanical vibrations of a piezoceramic ring plate is found. The effect of boundary conditions (clamped edge–free edge, free edge–clamped edge, free edge–free edge) on the natural frequency spectra (for the first circumferential harmonics) of plates with radially cut electrode coating is numerically analyzed
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References
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics, Dover, New York (1990).
N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).
M. O. Shul’ga, ”Revisiting the theory of nonaxisymmetric electromechanical vibrations of piezoceramic plates polarized across the thickness,” Sist. Tekhnol., No. 7, 63–68 (2007).
M. O. Shul’ga and V. V. Levchenko, “Revisiting the theory of nonaxisymmetric electroelastic vibrations of piezoceramic plates,” Dop. NAN Ukrainy, No. 6, 6168 (2012).
E. Dieulesant and D. Royer, Ondes elastiques dans les solides. Application au raiment du signal, Masson et C, Paris (1974).
T. S. Krasnopolskaya and A. Yu. Shvets, “Deterministic chaos in a system generator–piezoceramic transducer,” Nonlin. Dynam. Syst. Theor., 6, No. 4, 367–387 (2006).
C. H. Huang, C. C. Ma, and Y. C. Lin, “Theoretical, numerical, and experimental investigation on resonant vibrations of piezoceramic annular disks,” IEEE Trans. on Ultrasonics, Ferroelectrics and Frequency Control, 52, No. 8, 1204–1216 (2005).
C. H. Huang, “Resonant vibration investigations for piezoceramic disks and annuli by using the equivalent constant method,” IEEE Trans. on Ultrasonics, Ferroelectrics and Frequency Control, 52, No. 8, 1217–1228 (2005).
W. P. Mason, “Piezoelectricity, its history and applications,” J. Acoust. Soc. Am., 70, No. 6, 1561–1566 (1981).
N. A. Shul’ga, “Mixed systems of equations in Kirchhoff’s theory of the transverse vibrations of plates,” Int. Appl. Mech., 49, No. 2, 194–202 (2013).
N. A. Shul’ga and V. V. Levchenko, “Natural modes of piezoelectric circural plates with radially cut electrodes,” Int. Appl. Mech., 50, No. 5, 582–592 (2014).
N. A. Shul’ga, L. O. Grigor’eva, and N. O. Babkova, “Electrically excited nonstationary vibrations of thin circular piezoelectric plates,” Int. Appl. Mech., 50, No. 4, 406–411 (2014).
H. F. Tiersten, Linear Theory of Piezoelectric Plate Vibrations, Plenum Press, New York (1969).
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Translated from Prikladnaya Mekhanika, Vol. 51, No. 2, pp. 78–87, March–April 2015.
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Levchenko, V.V. Effect of Boundary Conditions on the Natural Frequencies and Vibration Modes of Piezoelectric Plates with Radially Cut Electrodes. Int Appl Mech 51, 187–195 (2015). https://doi.org/10.1007/s10778-015-0684-8
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DOI: https://doi.org/10.1007/s10778-015-0684-8