Applied Mathematics and Mechanics >
Temperature-induced frequency activity dips in AT-cut quartz crystal resonators
Received date: 2025-07-24
Revised date: 2026-01-12
Online published: 2026-03-02
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)
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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.
Nian LI , Chao GAO , Feng CHEN , Zhenghua QIAN , I. KUZNETSOVA . Temperature-induced frequency activity dips in AT-cut quartz crystal resonators[J]. Applied Mathematics and Mechanics, 2026 , 47(3) : 639 -652 . DOI: 10.1007/s10483-026-3360-9
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