TY - JOUR
T1 - Thickness-shear vibration of crystal plates under time-dependent biasing deformations
AU - Kosinski, John A.
AU - Pastore, Robert A.
AU - Yang, Jiashi
AU - Zhang, Xuesong
PY - 2001
Y1 - 2001
N2 - Incremental vibration of a crystal plate raider time-harmonic biasing deformations is studied using the equations for small fields superposed on finite biasing fields. It is shown that the incremental thickness-shear vibration of certain crystal plates, including Y-cut quartz and langasite plates, is governed by an equation with time dependent coefficients. The equation is reduced to the well known Mathieu equation. Approximate analytical solutions are obtained. In particular, the case when the frequency of the biasing deformations is much lower than the frequency of the incremental thickness-shear vibration is examined in detail. The thickness-shear vibration 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 results are of fundamental importance to the study of the vibration sensitivity of crystal resonators.
AB - Incremental vibration of a crystal plate raider time-harmonic biasing deformations is studied using the equations for small fields superposed on finite biasing fields. It is shown that the incremental thickness-shear vibration of certain crystal plates, including Y-cut quartz and langasite plates, is governed by an equation with time dependent coefficients. The equation is reduced to the well known Mathieu equation. Approximate analytical solutions are obtained. In particular, the case when the frequency of the biasing deformations is much lower than the frequency of the incremental thickness-shear vibration is examined in detail. The thickness-shear vibration 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 results are of fundamental importance to the study of the vibration sensitivity of crystal resonators.
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U2 - 10.1109/FREQ.2001.956346
DO - 10.1109/FREQ.2001.956346
M3 - Article
AN - SCOPUS:0035169790
SN - 0161-6404
SP - 597
EP - 604
JO - Proceedings of the Annual IEEE International Frequency Control Symposium
JF - Proceedings of the Annual IEEE International Frequency Control Symposium
ER -