Bechmann's Number for Harmonic Overtones of Thickness/Twist Vibrations of Rotated-Y-Cut Quartz Plates

Two methods are described for calculating Bechmann's number for harmonic overtones of thickness/twist modes in rotated Y-cut quartz plates: one based on an exact solution of the equations of elasticity and the other based on an asymptotic form of the exact solution. The latter leads to an explicit formula for Bechmann's number and it is shown to give results very close to the former—which requires extensive computations.