Title :
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
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;
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
DOI :
10.1109/FREQ.1993.367430
