Frequency shifts in plate crystal resonators induced by electric, magnetic, or mechanical fields in surface films

We study frequency shifts in plate crystal resonators with surface films. The films are multiphysical, including the effects of inertia, stiffness, intrinsic stress, piezoelectric coupling, and piezomagnetic coupling. Mindlin´s two-dimensional equations for a crystal plate with two elastic surface films are generalized to include the multiphysical effects of the films. They are used to study thickness-shear vibrations of a rotated Y-cut quartz plate with initial fields resulting from the mechanical, electric, and magnetic fields in the surface films. Frequency shifts caused by the initial fields are calculated and examined. Results show that plate crystal resonators with multiphysical surface films may be used for electric/magnetic field sensing.