Analysis Of The Nonlinear Deformation Effect Of Surface Beam Structure On Frequency Shift Characteristics Of A Quartz Resonator

Quartz crystal resonator(QCR)is widely used to provide frequency and frequency functions due to their electromechanical coupling characteristics.The material properties and structural dimensions can be detected by measuring the resonant frequency or admittance spectrum of the composite QCR system when the additional material or structure attached to the surface of the QCR system.If the bending stiffness of the surface beam structure is small,it will appear with the bending deformation with the QCR vibration process.The nonlinear effect of the surface micro-beam bending vibration will have an important effect on the resonant frequency of the system.Therefore,this dissertation carries out the nonlinear effect analysis of the surface beam structure in the composite QCR system.In this dissertation,a vibration governing equation considering the nonlinear bending deformation effect of micro-beams is established,and then the perturbation solution of the vibration equation is solved.A series of studies are carried out in detail after the frequency shift equation of the composite QCR system is deduced.The main research achievements are as follows:Firstly,the influence of the nonlinear effect of a uniform section micro-beam array in the first order and second order vibration modes on the frequency shift of the composite system is studied.It is found that the frequency shift exhibits a periodic variation characteristic with the elastic modulus(span to height ratio),there will be a jump point between adjacent cycles,and the frequency shift of the composite system with the elastic modulus(span to height ratio)curve will be a certain right(left)translation when considering the nonlinear effect of the micro-beam,because the nonlinear effect leads to shorten the projection of the micro-beam in the axial direction,and the nonlinear effect of the second order case is more obvious than the first order case.Secondly,the influence of nonlinear effect of a conical micro-beam array on the frequency shift of the composite QCR system is studied.It is found that the nonlinear effect makes the jump point of the QCR frequency shift curve to have a translation in a certain degree.Thirdly,the influence of the nonlinear deformation effect of the micro-beam on the frequency shift of the composite QCR system in the first order vibration mode is studied when the surface structure is a circular shaped micro-beam array.Similarly,it will increase the equivalent stiffness of the surface structure when considering the nonlinear effect of the micro-beam,and the system frequency shift curve translates in result.The influence of the nonlinear deformation effect of the surface beam structure on the frequency shift of the composite quartz resonator system is studied deeply in this dissertation,and the research achievements of this work have great instructional significance to the practical application of QCR.