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

Abstract

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.

P1F-2 Effects of Electromagnetic Radiation on the Q of Quartz Resonators

“…[1], and [2]. The equations for viscopiezoelectricity [1] will be used for determining the resonator Q due to acoustic, viscoelastic energy loss in the resonator structure; while the equations for viscopiezoelectromagneticism [2] will be used for determining the resonator Q due to both viscoelastic energy loss and electromagnetic radiation loss in the resonator structure.…”

“…In order to include the electromagnetism in the 3-D equations of viscopiezoelectricity, the following equations of viscopiezoelectromagnetism [2] were employed in our finite element models:…”

“…The electromagnetic radiation loss was compared with viscoelastic energy loss for quartz resonators at various operating frequencies. Equations of viscopiezoelectricity [1] and visco-piezoelectromagneticism [2] were solved two-dimensionally using COMSOL for straight crested waves in quartz resonators.…”

Spatial Behavior and Continuous Dependence Results in the Linear Dynamic Theory of Magnetoelectroelasticity

“…For many applications, the quasi-static theory is sufficient, but there are C. Galeş ( ) Faculty of Mathematics, University of Iaşi, 700506 Iaşi, Romania e-mail: cgales@uaic.ro situations, relevant in the calculation of radiated electromagnetic power from a vibrating piezoelectric device [27,29,31], in which full electromagnetic coupling needs to be considered. Such a fully dynamic theory is called piezoelectromagnetism [17,28,32,38].…”

Piezoelectromagnetic waves in a ceramic plate between two ceramic half-spaces

“…Therefore it does not describe the wave behavior of electromagnetic fields. Electromagnetic waves generated by mechanical fields need to be studied in the calculation of radiated electromagnetic power from a vibrating piezoelectric device (Mindlin, 1972;Lee, 1989;Lee et al, 1990), and are also relevant in electromechanical devices in which acoustic waves produce electromagnetic waves or vise versa (Oliner, 1978;Scholl et al, 1998). When electromagnetic waves need to be considered, the complete set of Maxwell's equations should be used, coupled to the mechanical equations of motion.…”