Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (1): 29-38.doi: https://doi.org/10.1007/s10483-017-2154-6

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Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams

Jiemin XIE, Yuantai HU   

  1. School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
  • 收稿日期:2016-03-14 修回日期:2016-06-12 出版日期:2017-01-01 发布日期:2017-01-01
  • 通讯作者: Yuantai HU,E-mail:hudeng@263.net E-mail:hudeng@263.net
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Nos. 11272127 and 51435006) and the Research Fund for the Doctoral Program of Higher Education of China (No. 20130142110022)

Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams

Jiemin XIE, Yuantai HU   

  1. School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2016-03-14 Revised:2016-06-12 Online:2017-01-01 Published:2017-01-01
  • Contact: Yuantai HU E-mail:hudeng@263.net
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos. 11272127 and 51435006) and the Research Fund for the Doctoral Program of Higher Education of China (No. 20130142110022)

摘要:

The electric admittance of a compound system composed of a thicknessshear mode (TSM) quartz crystal resonator (QCR) and an array of surface viscoelastic micro-beams (MBs) is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin (SU-8) MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak(s) and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.

关键词: electrical admittance, shear deformation, thickness-shear mode (TSM), quartz crystal resonator (QCR)

Abstract:

The electric admittance of a compound system composed of a thicknessshear mode (TSM) quartz crystal resonator (QCR) and an array of surface viscoelastic micro-beams (MBs) is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin (SU-8) MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak(s) and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.

Key words: thickness-shear mode (TSM), quartz crystal resonator (QCR), shear deformation, electrical admittance

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