Email Alert    RSS

Applied Mathematics and Mechanics (English Edition) ›› 2026, Vol. 47 ›› Issue (3): 639-652.doi: https://doi.org/10.1007/s10483-026-3360-9

Previous Articles    

Temperature-induced frequency activity dips in AT-cut quartz crystal resonators

Nian LI1, Chao GAO1, Feng CHEN2, Zhenghua QIAN3,4,†(), I. KUZNETSOVA5   

  1. 1.School of Mechanical Engineering, Suzhou University of Technology, Suzhou 215500, Jiangsu Province, China
    2.School of Mechanical and Electrical Engineering, Soochow University, Suzhou 215021, Jiangsu Province, China
    3.State Key Laboratory of Mechanics and Control for Aerospace Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    4.Shenzhen Research Institute, Nanjing University of Aeronautics and Astronautics, Shenzhen 518057, Guangdong Province, China
    5.Kotelnikov Institute of Radio Engineering and Electronics of RAS, Moscow 125009, Russia
  • Received:2025-07-24 Revised:2026-01-12 Published:2026-03-02
  • Contact: Zhenghua QIAN, E-mail: qianzh@nuaa.edu.cn
  • Supported by:
    Project supported by the National Key Research and Development Program of China (No. 2023YFE0111000), the National Natural Science Foundation of China (Nos. 12102183, 12172171, and U24A2005), and the Shenzhen Science and Technology Program of China (No. JCYJ20230807142004009)

PDF

1

Abstract:

This study investigates the frequency-temperature behaviors in AT-cut quartz crystal resonators (QCRs). First, the dispersion relations of an infinite quartz plate are obtained through a semi-analytical finite element (SAFE) analysis, which explicitly reveals the intrinsic frequency-temperature dependence of different vibration modes. Subsequently, we address practical resonator configurations by examining finite quartz plates, where numerical simulations uncover critical interactions between the operational thickness-shear (TS) mode and coupling modes, i.e., the flexure (F), face-shear (FS), and extension (E) modes. Through the frequency spectra analysis, we demonstrate that both the plate aspect ratio and thermal variations affect mode-coupling behaviors. Unstable frequency-temperature variations (activity dips) are observed at critical resonator dimensions. Validation through the free-vibration eigen-frequency analysis and forced-vibration admittance characterization confirms the stable or unstable states predicted by the frequency spectra. The established framework not only reveals the origin of temperature-induced activity dips but also provides the crucial design criteria for suppressing the mode-coupling interference in high-stability resonators.

Key words: quartz crystal resonator (QCR), frequency spectrum, admittance, activity dip

2010 MSC Number: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals
Total visitors:
Copyright © Applied Mathematics and Mechanics (English Edition)
Address：P. O. Box 122, Shanghai University, 99 Shangda Road, Shanghai 200444, China
E-mail： amm@department.shu.edu.cn
Technical support: Beijing Magtech Co.ltd support@magtech.com.cn