Analysis On The Coupled Vibrations And Frequency Shift Of A Compound System Consisting Of A Quartz Crystal Plate And Surface Structures In Liquid Environment

Quartz crystal resonator(QCR)is a kind of electronic component which is composed of a quartz crystal plate that has the function of electromechanical conversion.It is widely used to provide frequency standards and perform the function of frequency,such as timing,communication and control,etc.On the other hand,QCR is also very sensitive to surface changes.The physical and geometric properties of the surface materials or structures can be identified and characterized by detecting the change of dynamic and electrical parameters of the loaded QCR.Compared with the traditional QCR sensor based on Sauerbrey equation and one-dimensional transmission line model,the new compound QCR system presents many new features,such as non-uniform mass distribution,specific geometries,specific mechanical properties and vibrational states of surface materials or structures,fluid-solid coupling,size effect,and environmental bias,etc.To solve these problems,the coupling dynamic model of a compound system consisting of a QCR and surface structures in liquid environment is established in this paper.The influence of fluid-solid coupling vibration,size effect of the materials and internal stratification of materials/structures on the resonant frequency of the compound QCR system are studied.The main research achievements are as follows:(1)The fluid-solid coupling vibration model of the immersed micro-beam(s)subjected to QCR excitation is established.The fluid-solid coupling vibration equations of single micro-beam and double micro-beams are derived and solved respectively.The hydrodynamic pressure and velocity distribution of the liquid around the single beam and double beams are compared and analyzed.The results show that for a sparse array of micro-beams,the results of a single beam can be applied to all beams if the vibration states of each beam are assumed to be consistent.(2)The coupling dynamic model of a compound system consisting of a QCR and surface micro-beams in liquid environment is established.The influence of different liquid level on the vibration of micro-beams and the resonance frequency of compound QCR system is analyzed.The maximum liquid level which has the greatest impact on the vibration of micro-beams and the resonance frequency of compound QCR system has been found.(3)The coupling dynamic model of a compound system consisting of a QCR and surface micro-beams in liquid environment is established based on the modified couple stress theory.The governing equations and boundary conditions of the compound QCR system are deduced by Hamiltonian principle.The influence of size effect of quartz crystal plate and micro-beams on the resonance frequency of compound QCR system is studied.(4)The coupling dynamic model of a compound system consisting of a QCR and surface hemispherical units in liquid environment is established.The effect of the fluid-solid coupling vibration of the hemispherical units on the resonant frequency of the compound QCR system is studied.(5)The coupling dynamic model of a compound system consisting of a QCR and surface core-shell hemispherical units is established.The influence of the internal stratification of the material/structure on the resonant frequency of the compound QCR system is studied.In this paper,the coupling dynamic model of a quartz crystal plate and surface microstructure array in the liquid environment is established,and the coupled vibration and frequency characteristics of the compound system are analyzed theoretically.The research results have important guiding significance for the application expansion,precision improvement and scientific design of the QCR sensor.