Affiliations: [a] Department of Engineering Mechanics and Materials
Science, School of Engineering, Ningbo University, Ningbo, Zhejiang 315211,
China | [b] Epson Palo Alto Laboratory, 3145 Porter Drive, Suite
104, Palo Alto, CA 94304-1224, USA | [c] Department of Civil and Environmental Engineering,
Rutgers University, 623 Bowser Road, Piscataway, NJ 08854, USA
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.
