Thickness-shear vibration of a rectangular quartz plate with partial electrodes

Abstract

We study free vibration of a thickness-shear mode crystal resonator of AT-cut quartz. The resonator is a rectangular plate partially and symmetrically electroded at the center with rectangular electrodes. A single-mode, three-dimensional equation governing the thickness-shear displacement is used. A Fourier series solution is obtained. Numerical results calculated from the series show that there exist trapped thickness-shear modes whose vibration is mainly under the electrodes and decays rapidly outside the electrodes. The effects of the electrode size and thickness on the trapped modes are examined.

Thickness-shear vibration analysis of circular quartz crystal plates by a differential quadrature hierarchical finite element method

“…Piezoelectric crystals are widely used to make acoustic wave resonators as a frequency standard for time-keeping, frequency generation and operation, telecommunication, and sensing [2]. Quartz is the most widely used crystal for resonators.…”

The investigation of trapped thickness shear modes in a contoured AT-cut quartz plate using the power series expansion technique

“…When using thickness shear vibration modes in quartz crystal devices, a crucial phenomenon, energy trapping, is a primary task for the design and manufacturing. It is mainly caused by an inertia effect [10,11], thus usually being introduced by plating electrodes [12,13] or an additional mass layer on the partial region of plate surfaces. Based on the design scheme, the shear vibration is confined to the local region with partial electrodes or mass layers essentially, and there is almost no vibration in the rest of the plate.…”

“…When mounting and installing the quartz devices, some auxiliary elements must locate outside the trapping region, so that these auxiliary elements can not affect the central vibration. To address this issue, much effort, including theoretical analysis, numerical simulations and experimental attempts about energy trapping, has been carried out [12][13][14][15][16][17][18][19][20]. The aim mainly contains two aspects.…”

“…The aim mainly contains two aspects. One is to design a proper and practical structure which can excite trapped modes easily and efficiently, including material selection [14], plating electrodes [12][13]15] and optimization of structure [16]. The other is how to exactly calculate the resonant frequencies and reasonably describe the properties of the trapped thickness shear modes, e.g.…”