Electrically driven flexural resonant modes in symmetrically electroded X-cut and Z-cut quartz discs

While it is well known that flexural mechanical resonant modes can be electrically driven in specimens of quartz and other piezoelectric materials by the judicious choice of electrode patterns, specific experimental data, based on simultaneous interferometric observations of opposite surface points, are presented to show that symmetrically electroded X-cut and Z-cut quartz discs exhibit flexural resonant modes of quite large amplitudes. These resonances are not accompanied by detectable electrical disturbances in the AC-drive circuits. The existence of these modes is demonstrated for an X-cut quartz disc, and specific resonant modes of a Z-cut quartz disc are characterized in detail.