TY - JOUR
T1 - Thickness-shear vibrations of a quartz plate under time-dependent biasing deformations
AU - Yang, Jiashi
AU - Zhang, Xuesong
AU - Kosinski, John A.
AU - Pastore, Robert A.
PY - 2003/9
Y1 - 2003/9
N2 - 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.
AB - 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.
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U2 - 10.1109/TUFFC.2003.1235323
DO - 10.1109/TUFFC.2003.1235323
M3 - Article
AN - SCOPUS:0141904120
SN - 0885-3010
VL - 50
SP - 1114
EP - 1123
JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
IS - 9
ER -