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

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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.

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Authors and Affiliations

  1. School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jiemin Xie & Yuantai Hu

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  1. Jiemin Xie
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  2. Yuantai Hu
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Correspondence to Yuantai Hu.

Additional information

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)

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Xie, J., Hu, Y. Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams. Appl. Math. Mech.-Engl. Ed. 38, 29–38 (2017). https://doi.org/10.1007/s10483-017-2154-6

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  • DOI: https://doi.org/10.1007/s10483-017-2154-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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