Thickness-shear vibration of a quartz plate connected to piezoelectric plates and electric field sensing

We study thickness-shear vibration of a quartz plate connected to two piezoelectric ceramic plates with initial deformations caused by a biasing electric field. The theory for small deformations superposed on finite biasing deformations in an electroelastic body is used. It is shown that the resonant frequencies of the incremental thickness-shear vibration of the quartz plate vary with the biasing electric field. The biasing electric field induced frequency shift depends linearly on the field. Therefore this effect may be used for electric field sensing. The dependence of the electric field induced frequency shift on various material and geometric parameters is examined. When the electric field is of the order of 100 V/mm, the relative frequency shift is of the order of 10−5. The case when the piezoelectric plates are replaced by piezomagnetic plates is also investigated for magnetic field sensing, and similar results are obtained.