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

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. A generalized Poynting's theorem is derived for general media in which electromagnetic and mechanical fields interact with each other. For linear piezoelectric crystals it is shown that the generalized theorem may still be interpreted as an energy theorem, and hence densities of energy stored in the electric, magnetic, and elastic strain fields can be identified. Radiated power, per unit surface area and averaged over the period, and induced strain and electric fields in the middle plane of the plate are calculated for doubly rotated quartz plates whose cut orientations follow the upper and lower loci of zeros of the first-order temperature coefficient of frequency of the x₁ -thickness-shear mode. Quality factors and partition of stored energies are also examined.