An Analysis of Nonlinear Thickness-shear Vibrations of Quartz Crystal Plates by Two-Dimensional Finite Element Method
Abstract
A nonlinear analysis of high-frequency thickness-shear vibrations of AT-cut quartz crystal plates is presented with the two-dimensional finite element method. We expanded both kinematic and constitutive nonlinear Mindlin plate equations and then truncated them to the first-order equations as an approximation, which is used later for the formulation of nonlinear finite element analysis with all zeroth- and first-order displacements and electric potentials. The matrix equation of motion is established with the first-order harmonic approximation and the generalized nonlinear eigensystem is solved by a direct iterative procedure. A backbone curve and corresponding mode shapes are obtained and analyzed. The nonlinear finite element program is developed based on earlier linear edition and can be utilized to predict nonlinear characteristics of miniaturized quartz crystal resonators in the design process.
Keywords
Cite
@article{arxiv.1402.4753,
title = {An Analysis of Nonlinear Thickness-shear Vibrations of Quartz Crystal Plates by Two-Dimensional Finite Element Method},
author = {Ji Wang and Yangyang Chen and Rongxing Wu and Lihong Wang and Huimin Jing and Jianke Du and Yuantai Hu and Guoqing Li},
journal= {arXiv preprint arXiv:1402.4753},
year = {2014}
}
Comments
25 pages, 4 figs