An analysis of transversely varying thickness modes in quartz resonators with bevelled cylindrical edges

Author

Tiersten, H.F. ; Zhou, Y.S.

Author_Institution

Dept. of Mech. Eng., Rensselaer Polytech. Inst., Troy, NY, USA

fYear

1993

fDate

2-4 Jun 1993

Firstpage

431

Lastpage

441

Abstract

The equation for transversely varying thickness modes in doubly rotated quartz resonators is applied in the analysis of trapped energy resonators with bevelled cylindrical edges. The coefficients appearing in the planar differential operator are written as a sum of a mean or isotropic part plus a deviation. Asymptotic eigensolutions for the nearby isotropic case are obtained for the cylindrical bevelled resonator. The resonant frequencies for the actual anisotropic case are obtained from an equation for the perturbation in eigenfrequency from the isotropic solution. A lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained. Calculated results are presented for a few bevelled AT- and SC-cut quartz resonator

Keywords

crystal resonators; eigenvalues and eigenfunctions; partial differential equations; quartz; AT-cut quartz; SC-cut quartz; SiO₂; admittance; asymptotic eigensolution; bevelled cylindrical edges; doubly rotated quartz resonators; eigenfrequency; isotropic solution; lumped parameter representation; perturbation; planar differential operator; resonant frequencies; transversely varying thickness mode equation; trapped energy resonator analysis; Admittance; Aerospace engineering; Anisotropic magnetoresistance; Differential equations; Electrodes; Mechanical engineering; Resonance; Resonant frequency; Shape; Voltage;

fLanguage

English

Publisher

ieee

Conference_Titel

Frequency Control Symposium, 1993. 47th., Proceedings of the 1993 IEEE International

Conference_Location

Salt Lake City, UT

Print_ISBN

0-7803-0905-7

Type

conf

DOI

10.1109/FREQ.1993.367430

Filename

367430