An analysis of nonlinear thickness-shear vibrations of quartz crystal plates using the two-dimensional finite element method. Issue 5 (4th April 2018)

• Record Type: Journal Article
• Authors: Chen, Yangyang; Wu, Rongxing; Wang, Lihong; Jing, Huimin; Du, Jianke; Hu, Yuantai; Li, Guoqing; Wang, Ji
• Is Part Of: Mechanics of advanced materials and structures. Volume 25:Issue 5(2018)
• Page Start: 395
• Page End: 406
• Publication Date: 2018-04-04
• Subjects: Nonlinear -- Mindlin plate theory -- finite element method -- quartz -- resonators -- vibration; Composite materials -- Mechanical properties -- Periodicals; Composite construction -- Periodicals; 620.118
• DOI: 10.1080/15376494.2017.1285454
• Languages: English
• ISSNs: 1537-6494

Abstract

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. The Mindlin plate equations are truncated to the first-order ones as an approximation, and then they are used for the formulation of nonlinear finite element analysis with all zero- and first-order displacements. 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 displacement amplitude versus frequency curve and corresponding mode shapes are obtained and examined. The nonlinear finite element program is developed based on the earlier linear edition and can be utilized to predict nonlinear characteristics of miniaturized quartz crystal resonators in the design process.