Applied Mathematics and Mechanics >
A semi-analytical model and mechanism analysis for force-frequency effect and coefficient of square quartz
Received date: 2024-11-07
Revised date: 2025-03-27
Online published: 2025-06-06
Supported by
Project supported by the Ningbo Youth Science and Technology Innovation Leading Talents Project of China (No. 2023QL020), the Ningbo Science and Technology Major Project of China (No. 2022Z015), and the K. C. Wong Magana Fund through Ningbo University
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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 force-frequency 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
Lixia MA, Qiang ZHOU, Lijun YI, Ji WANG . A semi-analytical model and mechanism analysis for force-frequency effect and coefficient of square quartz[J]. Applied Mathematics and Mechanics, 2025 , 46(6) : 1089 -1106 . DOI: 10.1007/s10483-025-3255-6
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