This study presents a closed-form solution for central stress,a semi-analytical model,and a modified anisotropic semi-analytical model to efficiently calculate the forcefrequency coefficients(FFCs)of square quartz cry...This study presents a closed-form solution for central stress,a semi-analytical model,and a modified anisotropic semi-analytical model to efficiently calculate the forcefrequency coefficients(FFCs)of square quartz crystal resonators(QCRs)with different side lengths and azimuth angles under eccentrically concentrated and distributed loads.The semi-analytical model is validated by comparisons between the experimental results and the nonlinear finite element method(FEM)simulation results.Based on the semi-analytical model for the FFC and nonlinear FEM simulations,the FFC variations of square QCRs under external loads and the related mechanisms are investigated.Among the initial stresses caused by external loads,the central stress parallel to the xcrystallographic axis is the primary factor influencing the FFC of quartz.Our findings can provide practical tools for calculating the FFC,and help the design and development of square quartz force sensors.展开更多
基金supported by the Ningbo Youth Science and Technology Innovation Leading Talents of China(No.2023QL020)the Ningbo Science and Technology Major of China(No.2022Z015)the K.C.Wong Magana Fund through Ningbo University。
文摘This study presents a closed-form solution for central stress,a semi-analytical model,and a modified anisotropic semi-analytical model to efficiently calculate the forcefrequency coefficients(FFCs)of square quartz crystal resonators(QCRs)with different side lengths and azimuth angles under eccentrically concentrated and distributed loads.The semi-analytical model is validated by comparisons between the experimental results and the nonlinear finite element method(FEM)simulation results.Based on the semi-analytical model for the FFC and nonlinear FEM simulations,the FFC variations of square QCRs under external loads and the related mechanisms are investigated.Among the initial stresses caused by external loads,the central stress parallel to the xcrystallographic axis is the primary factor influencing the FFC of quartz.Our findings can provide practical tools for calculating the FFC,and help the design and development of square quartz force sensors.
