Anharmonic, Thickness-Twist Overtones of Thickness-Shear and Flexural Vibrations of Rectangular, AT-Cut Quartz Plates

Abstract

Equations of motion accommodating thickness‐twist overtones of thickness‐shear and flexural vibrations of rectangular, AT‐cut, quartz plates are obtained. The equations are solved in closed form for plates with all four edges free. The predicted frequencies are compared with measured resonances. X‐ray topographs of typical thickness‐twist overtone modes are exhibited which verify that the mode shapes correspond to those predicted.