[3] [3] Wu R X, Wang W J, Chen G J, et al. Free and forced vibrations of SC-cut quartz crystal rectangular plates with the first-order Mindlin plate equations［J］. Ultrasonics, 2017, 73: 96-106.

[4] [4] Huang Q, Wu R X, Xie L T, et al. Examinations of vibration frequency and mode shape variations of quartz crystal plates in a thermal field with strain and kinetic energies［J］. Journal of Thermal Stresses, 2020, 43(4): 456-472.

[5] [5] Mindlin R D. An introduction to the mathematical theory of vibrations of elastic plates［M］. New Jersey: World Scientific, 2006.

[6] [6] Wang J, Yang J S. Higher-order theories of piezoelectric plates and applications［J］. Applied Mechanics Reviews, 2000, 53(4): 87-99.

[7] [7] Wu R X, Zhang W L, MA T F, et al. Thickness-shear frequencies of an infinite quartz plate with graded material properties across the thickness［J］. Acta Mechanica Solida Sinica, 2020, 33(3): 361-367.

[8] [8] Shi J J, Fan C Y, Zhao M H, et al. Thickness-shear vibration characteristics of an AT-cut quartz resonator with rectangular ring electrodes［J］. International Journal of Applied Mechanics, 2016, 51(1): 1-10.

[9] [9] Wang J, Zhao W H. The determination of the optimal length of crystal blanks in quartz crystal resonators［J］. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2005, 52(11): 2023-2030.

[10] [10] Xu L M, Geng Y L, Hu Y T, et al. Thickness-shear vibration of an AT-cut quartz plate with elliptical electrodes and implications in optimal blank geometry［J］. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2019, 56(4): 875-879.

[12] [12] Wang, J N, Hu Y T, Yang J S. Frequency spectra of AT-cut quartz plates with electrodes of unequal thickness［J］. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2005, 57(5): 1146-1151.

[15] [15] Wang J, Yu J D, Yong Y K. On the correction of the higher-order Mindlin plate theory［J］. International Journal of Applied Electromagnetics and Mechanics, 2005, 22(1-2): 83-96.

[16] [16] Wang J, Shen L J, Yang J S. Effects of electrodes with continuously varying thickness on energy trapping in thickness-shear mode quartz resonators［J］. Ultrasonics, 2018, 48(2): 150-154.