Numerical algorithms and results for SC-cut quartz plates vibrating at the third harmonic overtone of thickness shear

Y. K. Yong, Z. Zhang

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

Abstract

Finite element matrix equations, derived from two-dimensional, piezoelectric high frequency plate theory proposed by Lee, Syngellakis, and Hou, are solved to study the vibrational behavior of the third overtone of thickness shear in square and circular SC-cut quartz resonators. The mass-loading and electric effects of electrodes are included. A perturbation method is employed to calculate the piezoelectric resonant frequencies which reduces the memory requirements and computational time significantly. A new storage scheme is introduced which reduces memory requirements for mass matrix by about 90% over that of the envelope storage scheme. Substructure techniques are used in eigenvalue calculation to save storage. Resonant frequency and the mode shapes of the harmonic third overtone thickness shear vibrations for rectangular and circular plates are calculated. A pure third overtone thickness shear displacement, coupled with the third overtone of thickness stretch and thickness twist, is observed. Weak coupling between the zeroth, first and second order displacements and the third order thickness shear displacement is noted. The magnitudes of the lower order displacements are found to be about two orders smaller than that of the third overtone thickness shear displacement.

Original languageAmerican English
Title of host publicationProceedings of the IEEE Ultrasonics Symposium
EditorsM. Levy, B.R. McAvoy
PublisherPubl by IEEE
Pages553-558
Number of pages6
ISBN (Print)0780312783
StatePublished - 1993
EventProceedings of the IEEE 1993 Ultrasonics Symposium. Part 1 (of 2) - Baltimore, MD, USA
Duration: Oct 31 1993Nov 3 1993

Publication series

NameProceedings of the IEEE Ultrasonics Symposium
Volume1

Other

OtherProceedings of the IEEE 1993 Ultrasonics Symposium. Part 1 (of 2)
CityBaltimore, MD, USA
Period10/31/9311/3/93

ASJC Scopus subject areas

  • Acoustics and Ultrasonics

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