An analysis of thickness-shear vibrations of an annular plate with the Mindlin plate equations

Ji Wang, Hui Chen, Tingfeng Ma, Jianke Du, Lijun Yi, Yook Kong Yong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

The Mindlin plate equations with the consideration of thickness-shear deformation as an independent variable have been used for the analysis of vibrations of quartz crystal resonators of both rectangular and circular types. The Mindlin or Lee plate theories that treat thickness-shear deformation as an independent higher-order vibration mode in a coupled system of two-dimensional variables are the choice of theory for analysis. For circular plates, we derived the Mindlin plate equations in a systematic manner as demonstrated by Mindlin and others and obtained the truncated two-dimensional equations of closely coupled modes in polar coordinates. We simplified the equations for vibration modes in the vicinity of fundamental thickness-shear frequency and validated the equations and method. To explore newer structures of quartz crystal resonators, we utilized the Mindlin plate equations for the analysis of annular plates with fixed inner and free outer edges for frequency spectra. The detailed analysis of vibrations of circular plates for the normalized frequency versus dimensional parameters provide references for optimal selection of parameters based on the principle of strong thickness-shear mode and minimal presence of other modes to enhance energy trapping through maintaining the strong and pure thickness-shear vibrations insensitive to some complication factors such as thermal and initial stresses.

Original languageEnglish (US)
Title of host publication2015 Joint Conference of the IEEE International Frequency Control Symposium and the European Frequency and Time Forum, FCS 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages402-405
Number of pages4
ISBN (Electronic)9781479988662
DOIs
StatePublished - Jun 29 2015
Event2015 Joint Conference of the IEEE International Frequency Control Symposium and the European Frequency and Time Forum, FCS 2015 - Denver, United States
Duration: Apr 12 2015Apr 16 2015

Publication series

Name2015 Joint Conference of the IEEE International Frequency Control Symposium and the European Frequency and Time Forum, FCS 2015 - Proceedings

Other

Other2015 Joint Conference of the IEEE International Frequency Control Symposium and the European Frequency and Time Forum, FCS 2015
Country/TerritoryUnited States
CityDenver
Period4/12/154/16/15

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Signal Processing

Keywords

  • annular plate
  • frequency
  • resonator
  • shear
  • vibration

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