Abstract
Electrically forced thickness-shear vibrations of a Y-cut quartz plate resonator under time-dependent extensional biasing vibrations are studied using the two-dimensional equations for small deformations superposed on finite biasing deformations in electroelastic plates. It is shown that the thickness-shear vibration is governed by the well know Mathieu equation with a time-dependent coefficient and a driving term. Two approximate analytical solutions are obtained. One may be called a quasi-static solution which is valid when the frequency of the biasing extensional deformation is much lower than the frequency of the thickness-shear vibration. The other is a first-order perturbation solution valid when the biasing deformations are infinitesimal. Both solutions show that the static and motional capacitances of the resonator become time-dependent with a frequency the same as that of the biasing deformation.
Original language | English |
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Pages (from-to) | 96-102 |
Number of pages | 7 |
Journal | Proceedings of the Annual IEEE International Frequency Control Symposium |
State | Published - 2002 |
Event | Proceedings of the 2002 IEEE International Frequency Control Symposium and PDA Exhibition - New Orleans, LA, United States Duration: 29 May 2002 → 31 May 2002 |