Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

Abstract

We study the dynamic behavior of a quartz crystal resonator (QCR) in thickness-shear vibrations with the upper surface covered by an array of micro-beams (MBs) under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right (left) translation for increasing elastic modulus (length/radius ratio) of MBs. Moreover, the frequency right (left) translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one.