Finite element analysis of the piezoelectric vibrations of quartz plate resonators with higher-order plate theory

Ji Wang, Yook Kong Yong, Tsutomu Imai

Research output: Contribution to journalArticlepeer-review

89 Scopus citations

Abstract

A finite element formulation of the piezoelectric vibrations of quartz resonators based on Mindlin plate theory is derived. The higher-order plate theory is employed for the development of a collection of successively higher-order plate elements which can be effective for a broad frequency range including the fundamental and overtone modes of thickness-shear vibrations. The presence of electrodes is also considered for their mechanical effects. The mechanical displacements and electric potential are combined into a generalized displacement field, and the subsequent derivations are carried out with all the generalized equations. Through the standard finite element procedure, the vibration frequency, the vibration mode shapes and the electric potential distribution are obtained. The frequency spectra are compared with some well-known experimental results with good agreement. Our previous experience with finite element analysis of high-frequency quartz plate vibrations leads us to believe that memory and computing time will always remain as key issues despite the advances in computers. Hence, the use of sparse matrix techniques, efficient eigenvalue solvers, and other reduction procedures are explored.

Original languageEnglish (US)
Pages (from-to)2303-2319
Number of pages17
JournalInternational Journal of Solids and Structures
Volume36
Issue number15
DOIs
StatePublished - Jan 6 1999

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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