Abstract
A computer algorithm proposed for the numerical solution of the problem of natural vibrations of axisymmetric variable-thickness piezoelectric elements can determine the complete spectrum of thickness-shear vibrations of a given class of piezoelectric elements and their displacements distribution. Examples are given of the calculation of the spectrum of piezoelectric elements with the corresponding vibration topograms and the temperature—frequency characteristics and anharmonic vibrations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. F. Kolpakov, Yu. S. Shmalii, and V. A. Shevelev, Inventor's Certificate 900126 (USSR). “Two-parameter frequency-meter transducer,” Byull. Izobret., No. 3 (1983).
F. F. Kolpakov, “Use of multiparameter sensitivity of piezoelectric resonators in measuring devices,” Élektron. Tekh. Ser. Radiodet. Radiokomp., No. 2, 62 (1985).
V. Ya. Barzhin, F. F. Kolpakov, and V. A. Shevelev, Inventor's Certificate 1232964 (USSR). “Differential piezo-electric transducer,” Byull. Izobret., No. 19 (1983).
I. I. Postnikov, “Computer analysis of the characteristics of radio-frequency quartz resonators,” Radiotekhnika, No. 12, 85 (1989).
I. I. Postnikov, “Determination of the frequency interval to the extraneous vibrations in lens-type piezoelectric elements,” Radiotekh. Élektron.,32, No. 12, 2678 (1987).
I. I. Postnikov, “Natural vibrations of lens-type piezoelectric elements,” Izv. Vyssh. Uchebn. Zaved., Radiofiz.,29, No. 6, 740 (1986).
I. I. Postnikov, “Eigenfunctions of anharmonic vibrations n15, n33, n51 of lens-type piezoelectric elements,” Izv. Vyssh. Uchebn. Zaved., Radiofiz.,33, No. 10, 1176 (1990).
I. I. Postnikov, “Dynamic inductance of rf quartz resonators under anharmonic vibrations,” Radiotekhnika, No. 5, 34 (1986).
G. I. Veselov, I. I. Postnikov, and V. S. Samoilov, “Stable algorithms for computer simulation of the vibrations of rf quartz resonators,” Izv. Vyssh. Uchebn. Zaved., Radioélektron.,36, No. 6, 27 (1983).
V. G. Androsova, E. G. Bronnikova, A. M. Vasil'ev, et al., in: P. E. Kandyba and P. G. Poznyakov (eds.), Handbook of Piezoelectric Resonators [in Russian], Radio Svyaz', Moscow (1992).
V. I. Smirnov, A Course of Higher Mathematics. Vol. 2. Advanced Calculus, Pergamon Press, Oxford (1964).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
N. S. Bakhvalov, Numerical Methods [in Russian], Nauka, Moscow (1973).
N. N. Kalitkin, Numerical Methods [in Russian], Nauka, Moscow (1978).
G. Hall and J. M. Watt (eds.), Modern Numerical Methods for Ordinary Differential Equations, Oxford Univ. Press (1976).
C. J. Witson, “Vibration modes of AT-cut convex quartz resonators,” J. Phys. D.,7, No. 18, 2449 (1974).
Additional information
Mytishchi Scientific-Research Institute of Radio-Measuring Instruments. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1519–1531, December, 1994.
Rights and permissions
About this article
Cite this article
Postnikov, I.I. Thickness-shear vibrations in round variable-thickness piezoelectric crystal plates. Radiophys Quantum Electron 37, 984–992 (1994). https://doi.org/10.1007/BF01056152
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01056152