Thickness-shear vibrations of a quartz plate under time-dependent biasing deformations

Jiashi Yang, Xuesong Zhang, John A. Kosinski, Robert A. Pastore

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Incremental thickness-shear vibrations of Y-cut quartz crystals plate under time-harmonic biasing extensional deformations are studied using the two-dimensional equations for small fields superposed on finite biasing fields in an electroelastic plate. It is shown that the incremental thickness-shear vibrations are governed by the well-known Matheiu's equation with a time-dependent coefficient. Both free and electrically forced vibrations are studied. Approximate analytical solutions are obtained when the frequency of the biasing deformation is much lower than that of the incremental thickness-shear vibration. The incremental thickness-shear free vibration mode is shown to be both frequency and amplitude modulated, with the frequency modulation as a first-order effect and the amplitude modulation a second-order effect. The forced vibration solutions show that both the static and motional capacitances become time-dependent due to the time-harmonic biasing deformation.

Original languageEnglish
Pages (from-to)1114-1123
Number of pages10
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Volume50
Issue number9
DOIs
StatePublished - Sep 2003

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