Affiliations: [a] School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou, Henan, China | [b] School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan, China | [c] Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA
Correspondence:
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Corresponding author: Jiashi Yang, School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450001, Henan, China. E-mail:jyang1@unl.edu
Abstract: We study thickness-shear vibrations of a piezoelectric
plate of AT-cut quartz with two pairs of electrodes. The plate represents a
monolithic, two-pole acoustic wave filter. The scalar differential equations
by Tiersten and Smythe for thickness-shear vibrations of electroded and
unelectroded quartz plates are employed. Based on the variational
formulation of the scalar differential equations established in a previous
paper and the Ritz method with trigonometric functions as basis functions,
free vibration resonant frequencies and thickness-shear modes of the plate
are obtained. For a structurally symmetric filter, the modes can be
separated into symmetric and antisymmetric ones. Trapped modes with
vibrations mainly under the electrodes are presented. The effects of the
electrode inertia and the distance between the two pairs of electrodes are
examined. It is also found that the classical frequency prediction given by
Tiersten from an approximate analysis has an inaccuracy of tens of parts per
million, significant in filter design and application.
