On the interaction between a quartz crystal resonator and an array of micro-beams in thickness-shear vibrations

We studied the coupled dynamic behavior of a quartz-crystal-resonator (QCR)/microbeams system in the thickness-shear motions. Through taking into account the couple stress in the dynamic equations of the quartz plate, both continuous conditions of shear force and bending moment at the resonator/micro-beams interface are realized. Frequency shift of the compound QCR system induced by micro-beams is studied in detail. The obtained results are useful in device design and frequency-stability analysis of quartz crystal resonators.