On the correction of the higher-order Mindlin plate theory

Ji Wang, Jiun Der Yu, Yook Kong Yong

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

The Mindlin plate theory was developed to provide accurate solutions of vibrations in the vicinity of the fundamental thickness-shear mode, which has a very high frequency compared to flexural vibrations. The most important application of the theory is the high frequency vibrations of crystal plates although it has been applied to many problems beyond the original purpose. Recent studies found that, to improve the frequency solutions for plates with larger aspect ratios, the third-order plate based on Mindlin's power series expansion has to be used. It was shown through comparisons with three-dimensional elasticity solutions that the fundamental thickness-shear frequency is almost exact. The third-order theory was applied to frequency, mode shape, and other related analyses. In this study, we reconfirm that the third-order plate theory is very accurate because it has an almost exact cut-off frequency for the fundamental thickness-shear mode. By adopting a procedure developed by Mindlin, we find the inaccuracies in cut-off frequencies of the fundamental thickness modes and their overtones can be improved through the introduction of new correction factors. Corrections can be made with either the natural or symmetric procedure. Correction factors for natural and symmetric procedures based on stresses will be given.

Original languageEnglish (US)
Pages (from-to)83-96
Number of pages14
JournalInternational Journal of Applied Electromagnetics and Mechanics
Volume22
Issue number1-2
DOIs
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Electrical and Electronic Engineering

Keywords

  • Correction
  • Crystal
  • Factors
  • Frequency
  • Mindlin
  • Plate
  • Resonator
  • Thickness-shear
  • Vibration

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