Title :
An analysis of contoured quartz resonators with beveled cylindrical edges
Author :
Yang, J.S. ; Tiersten, H.F.
Author_Institution :
Dept. of Mech. Eng., Rensselaer Polytech. Inst., Troy, NY, USA
fDate :
31 May-2 Jun 1995
Abstract :
The equation for transversely varying thickness modes in doubly-rotated quartz resonators is applied in the analysis of contoured resonators with beveled 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 contoured cylindrical beveled 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 some contoured beveled SC-cut quartz resonators
Keywords :
crystal resonators; quartz; SC-cut quartz resonators; SiO2; admittance; anisotropy; asymptotic eigensolutions; beveled cylindrical edges; contoured quartz resonators; doubly-rotated quartz resonators; lumped parameter model; planar differential operator; resonant frequencies; transversely varying thickness modes; Admittance; Aerospace engineering; Anisotropic magnetoresistance; Differential equations; Electrodes; Mechanical engineering; Resonance; Resonant frequency; Steady-state; Vibrations;
Conference_Titel :
Frequency Control Symposium, 1995. 49th., Proceedings of the 1995 IEEE International
Conference_Location :
San Francisco, CA
Print_ISBN :
0-7803-2500-1
DOI :
10.1109/FREQ.1995.484077
