Abstract
An approximate dispersion equation describing the mode shape along the surface of a doublyrotated SC-cut quartz plate vibrating in the vicinity of the fundamental and odd overtone essentially thickness-shear frequencies of interest is obtained from the equations of three-dimension al linear piezoelectricity . The influence of piezoelectric stiffening, electrode mass loading and electrical shorting is included in the treatment. The dispersion relations in both the electroded and unelectroded regions of the plate are obtained along with simple approximate edge conditions to be satisfied at a junction between the two regions. The dispersion relations and edge conditions are applied in the analysis of trapped energy resonators with rectangular electrodes on SC-cut quartz plates and a lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained. In addition, the two-dimensional generalization of Bechmann' S number in one dimension is provided.
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