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Applied Mathematics and Mechanics

, Volume 38, Issue 1, pp 29–38 | Cite as

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

  • Jiemin Xie
  • Yuantai HuEmail author
Article

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.

Keywords

quartz crystal resonator (QCR) thickness-shear mode (TSM) electrical admittance shear deformation 

Chinese Library Classification

O441.3 

2010 Mathematics Subject Classification

74F15 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Civil Engineering and MechanicsHuazhong University of Science and TechnologyWuhanChina

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