Resonant mode calculations of contoured doubly-rotated quartz crystals using a variational approach

Author

EerNisse, Errol P.

Author_Institution

Quartzdyne, Inc., Salt Lake, UT, USA

Volume

2

fYear

2003

fDate

5-8 Oct. 2003

Firstpage

1432

Abstract

A technique has been developed using variational calculus for calculating resonant modes in doubly-rotated contoured quartz crystal. Basis functions used are similar to past analytical solutions for the slow-shear, fast-shear, and extensional thickness modes. Flexural motion is included in the analysis to ensure rotational balance. Calculated frequencies and mode shapes are consistent with past analytical results for trapped modes. However the present approach includes coupling between the different mode families. In addition, mode shapes are available for weakly trapped modes that are not predicted by past analytical methods. The present approach offers the future opportunity to analyze the impact of loss of symmetry of the crystal from electrode patterns and imperfect contouring processes.

Keywords

modal analysis; quartz; variational techniques; basis functions; contoured doubly-rotated quartz crystal; crystal symmetry; electrode patterns; extensional thickness modes; fast-shear modes; flexural motion; frequencies calculation; imperfect contouring; mode coupling; mode shapes; resonant mode calculations; rotational balance; slow-shear modes; variational approach; variational calculus; weakly trapped modes; Capacitance; Cities and towns; Crystals; Electrodes; Finite element methods; Frequency; Perturbation methods; Resonance; Shape; Temperature sensors;

fLanguage

English

Publisher

ieee

Conference_Titel

Ultrasonics, 2003 IEEE Symposium on

Print_ISBN

0-7803-7922-5

Type

conf

DOI

10.1109/ULTSYM.2003.1293173

Filename

1293173