Electromagnetic radiation from doubly rotated piezoelectric crystal plates vibrating at thickness frequencies

The exact solution of the three-dimensional linear equations of piezoelectromagnetism is obtained for doubly rotated piezoelectric crystal plates surrounded by vacuum and excited by face traction. Radiated power and induced electric field in the middle plane of the plate are obtained for doubly rotated quartz plates for which the cut orientations follow the upper and lower loci of zeros of the first-order temperature coefficient of frequency of the x₁-thickness-shear mode. Variations of these quantities are computed for either constant magnitude of face traction for constant shearing strain component and at the mechanical resonance frequencies of the x₁-thickness-shear, x ₃-thickness-shear, and thickness-stretch modes. Radiated power is also computed as a function of cut angle for rotated Y-cuts of quartz at x₁-thickness-shear frequency for S°₁₂=10^-5