Research On The Dynamic And Electrical Behavior Of A Compound Surface Structure/Quartz Crystal Resonator System In Thickness-shear Modes

Quartz crystal resonator(QCR)can be used to characterize the physical properties(e.g.,density,shear modulus,size,etc.)of the surface loaded structure/material.The QCR system is usually simplified as a multi-layer structure by assuming the oscillation phase to be constant in the surface layers,and analyzed through the one-dimensional transmission line model(TLM)in previous studies.With the rapid development in QCR miniaturization,the characteristic scale of surface attached materials/structures gradually becomes comparable to QCR thickness,and the geometrical configurations effect of surface loadings gradually become evident.Thus,an in-depth analysis is required to describe the effect of geometrical configurations of surface loadings on the dynamic and electric behavior of compound QCR systems.In this dissertation,the free vibration and electrically forced vibration analysis are adopted considering some related coupled surface structure/QCR system,and the influence of the surface materials/structures to the resonator admittance spectra and vibration modes is investigated in detail.The main research achievements are as follows:Firstly,a two-dimensional model on the coupling thickness-shear mode(TSM)vibrations of a QCR carrying an array of spherical-cap viscoelastic material units is established.The electrical admittance of the compound QCR system is described directly in terms of the physical properties of the surface material units.The admittance spectra about the tendon stem cells(TSCs)acquired from our calculation are compared with the existing experiment data and found to be consistent with each other,indicating our model has good veracity and reliability in analyzing the mechanical properties of covered loadings.Furthermore,the admittance spectra of surface Epoxy Resin(SU-8)units with different geometrical configurations and bulk effect are calculated.It is found that both geometrical configuration and bulk effect produce influence on the resonant frequency and admittance of the compound QCR system.Secondly,thickness-shear vibration of an elastic plate carrying an array of rigid microbeams(MBs)with their bottoms attached to the top surface of the plate is studied.The plate is modeled by the couple-stress theory of elasticity to properly take into account both the shear forces and the bending moments at the bottoms of the beams.An equation that determines the resonant frequencies of the structure is derived.Analytical and numerical examinations of a few special cases of the general frequency equation reveal that the frequency of the fundamental thickness-shear mode is less sensitive to the couple stress than the higher-order modes.Due to the small wavelength of the higher-order vibrations,the couple stress effects increase along with the higher-order resonant frequencies.The results indicate that the effects of the couple stress on higher-order resonant frequencies are not negligible.Thirdly,the governing equations of an array of surface viscoelastic MBs coupling with a QCR in TSM are derived from the Timoshenko beam(TB)theory in consideration of shear deformation.The electrical admittance is described directly in terms of the physical properties of the surface SU-8 MBs from an electrically forced vibration analysis.It is found that both the inertia effect and the constraint effect of MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system.By further comparing the numerical results calculated from the Timoshenko beam model with those from the Euler beam(EB)model,some deviations of admittance spectrum are revealed.Fourthly,a coupling dynamic model on an acoustic wave sensor system,consisting of a TSM QCR and an array of surface nanowires(NWs),has been established with including the surface effects of NWs.The governing equations of NWs are derived from the Timoshenko beam theory in consideration of shear deformation and rotary inertia.The electrical admittance is described directly in terms of the physical properties of the surface NWs from an electrically forced vibration analysis.The effects of residual surface tension ?0 and surface elasticity Es of NWs on the admittance spectra and vibration modes of the compound QCR system are examined and some useful results are obtained,which will be helpful to the design of nano-sized beams loaded acoustic wave sensors and some related applications.A two-dimensional vibration model of a compound surface structure/QCR system is developed in this dissertation,and both the influences producing by the vibration mode characteristics and surface effects of the surface spherical-cap and MB array on the resonant frequency and admittance of the compound QCR system are discussed in detail.The achievements of this work have instructional significance to the application of QCR,and have given effective analytic methods to study on QCR.By conducting this kind of work,the crosses and integration between transdisciplinary subjects can be further promoted.