Correction Factors of the Mindlin Plate Equations with the Consideration of Electrodes

Du Jianke; CHEN Guijia; WANG Wenjun; WU Rongxing; MA Tingfeng; WANG Ji

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Correction Factors of the Mindlin Plate Equations with the Consideration of Electrodes

Du Jianke 1,CHEN Guijia 2,WANG Wenjun 2,WU Rongxing 2,MA Tingfeng 2,WANG Ji 2 *

1.Piezoelectric Device Laboratory, School of Mechanical Engineering and Mexhanics, Ningbo University, ZheJiang NingBo 315211

2.Piezoelectric Device Laboratory, School of Mechanical Engineering and Mexhanics, Ningbo University, 315211

*Correspondence author

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Funding: the Ministry of Education of China（No.No.20093305110003）, National Natural Science Foundation of China （No.Nos.10932004&11072116）

Opened online:16 April 2012

Accepted by: none

Citation: Du Jianke,CHEN Guijia,WANG Wenjun.Correction Factors of the Mindlin Plate Equations with the Consideration of Electrodes[OL]. [16 April 2012] http://en.paper.edu.cn/en_releasepaper/content/4474774

The Mindlin plate theory has been playing a role vital in the analysis of high frequency vibrations of quartz crystal resonators at the thickness-shear mode. The coupled equations with infinite number of vibration modes have been truncated to retain essential ones with strong couplings for simplified analysis, and correction factors have been introduced to ensure exact solutions at cut-off frequencies as part of the validation procedure. Starting form plates without complications, correction factors have also been modified to include electrodes for their mass effect. Such results have been important to higher-order correction factors to ensure accurate consideration of electrodes in the AT-cut quartz crystal plates. The findings in factors systematic study are readily available for the analytical equations with selected modes with strong couplings, and equally convenient for the implementation of the finite element analysis with the Mindlin plate equations.

Keywords:Mindlin; plate; vibration; shear; correction; crystal; resonator

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