The influence of an asymmetric air gap on the vibration characteristics of quartz trapped energy resonators

Author

Tiersten, H.F.

Author_Institution

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

fYear

1995

fDate

31 May-2 Jun 1995

Firstpage

740

Lastpage

745

Abstract

An analysis of the influence of an asymmetric air gap on transversely varying thickness modes in quartz trapped energy resonators is performed. The thickness-dependent coupled electrostatic-piezoelectric problem that transforms the inhomogeneities from the electrodes into the equation for transversely varying thickness modes is identified and solved. It turns out that the asymmetry of the gap has no influence on any of the coefficients in the thickness solution that influence either the resonant frequencies or motional and static capacitances and only the mean value of the gap does. The equation for transversely varying thickness modes modified to account for the gap is presented. The solution for the harmonics and anharmonics of a contoured resonator when a gap is present is given along with the expression for the associated resonant frequencies

Keywords

air gaps; crystal resonators; quartz; vibrations; SiO₂; anharmonics; asymmetric air gap; contoured resonators; coupled electrostatic-piezoelectric analysis; electrode inhomogeneities; harmonics; motional capacitances; quartz trapped energy resonators; resonant frequencies; static capacitances; transversely varying thickness modes; vibration characteristics; Aerospace engineering; Capacitance; Differential equations; Electrodes; Mechanical engineering; Performance analysis; Resonant frequency; Transforms; Vibrations; Voltage;

fLanguage

English

Publisher

ieee

Conference_Titel

Frequency Control Symposium, 1995. 49th., Proceedings of the 1995 IEEE International

Conference_Location

San Francisco, CA

Print_ISBN

0-7803-2500-1

Type

conf

DOI

10.1109/FREQ.1995.484078

Filename

484078