Membrane analogy of the Stevens-Tiersten equation for essentially thickness modes in plate quartz resonators

Author

Zhang, Weiping ; Yang, Zengtao ; Yang, Jiashi

Author_Institution

Mobile Device Bus. Unit, Libertyville, IL

Volume

55

Issue

7

fYear

2008

fDate

7/1/2008 12:00:00 AM

Firstpage

1665

Lastpage

1668

Abstract

We show that the well-known Stevens- Tiersten equation for essentially thickness modes in doubly rotated quartz resonators is mathematically analogous to the equation governing the transverse motion of a pre- stretched elastic membrane resting on an elastic foundation. The implication of this analogy is that commercial finite element software for structural analysis can be used to solve the Stevens-Tiersten equation for resonators.

Keywords

crystal resonators; finite element analysis; membranes; Stevens-Tiersten equation; doubly rotated quartz resonators; elastic membrane; finite element software; membrane analogy; plate quartz resonators; thickness modes; Anisotropic magnetoresistance; Biomembranes; Business; Educational products; Elasticity; Equations; Finite element methods; Geometry; Scholarships; Vibrations; Acoustics; Computer Simulation; Computer-Aided Design; Electronics; Equipment Design; Equipment Failure Analysis; Models, Theoretical; Quartz; Scattering, Radiation; Transducers; Vibration;

fLanguage

English

Journal_Title

Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on

Publisher

ieee

ISSN

0885-3010

Type

jour

DOI

10.1109/TUFFC.2008.843

Filename

4559665