Tuesday, 12 October 2004 - 2:40 PM

This presentation is part of : Active Materials

On the Correction of Higher-Order Mindlin Plate Theory

Ji Wang, School of Engineering, Ningbo University, 1211 Zhenning Xilu Road, Ningbo, Zhejiang, 315211, China and Jiun-Der Yu, Epson Palo Alto Laboratory, 3145 Porter Dr, Ste 104, Palo Alto, CA 94304.

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 the flexural vibrations. The most important application of this theory is the high-frequency vibrations of crystal plates although it has been applied to many problems beyond the original purpose. Recent studies have found that, to improve the frequency solutions of plates with larger aspect ratios, the third-order plate theory 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. With this belief, the third-order plate theory was applied to frequency, mode shape, and other related analyses. In this study, we re-confirm 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-shear mode and their overtones can be corrected with the introduction of new correction factors. Corrections can be made with either the natural or symmetric procedure with values of the correction factors given in this paper.

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