Abstract
The experimentally measured resonance frequencies of a thin annular plate with a small ratio of inner to outer radii and clamped on the inner boundary are compared to the predictions of classical thin-plate (CTP) theory and a finite-element (FE) model. The results indicate that, contrary to the conclusions presented in a number of publications, CTP theory does not accurately predict the frequencies of a relatively small number of resonant modes at lower frequencies. It is shown that these inaccuracies are attributable to shear deformations, which are thought to be negligible in thin plates and are neglected in CTP theory. Of particular interest is the failure of CTP theory to accurately predict the resonance frequency of the lowest vibrational mode, which was shifted approximately 30% by shear motion at the inner boundary.
Highlights
The vibrations of circular flat plates have been of intrinsic interest for over a century.[1,2,3,4,5] The interest in such a seemingly simple physical system is due to the widespread application of this geometry, as well as the inherent ability to study it in detail both theoretically and experimentally
We demonstrate that the differences between the predictions of classical thin-plate (CTP) theory and the experimental results for some of the lower modes are due to the effects of transverse shear motion at the inner boundary.we conclude that transverse shear motion can be important even in very thin plates, contrary to what is commonly stated in the literature
The work reported here shows that CTP theory is widely accepted as sufficient for analyzing the lowest normal modes of thin annular plates, there are important cases where the approximations involved in developing the theory are not valid
Summary
The vibrations of circular flat plates have been of intrinsic interest for over a century.[1,2,3,4,5] The interest in such a seemingly simple physical system is due to the widespread application of this geometry, as well as the inherent ability to study it in detail both theoretically and experimentally. CTP theory is especially useful when an understanding of the physics of plate motion is important and merely predicting an accurate result using a finite element program is not sufficient. CTP theory does not include shear deformations and is only applicable for plates having a ratio of thickness to diameter of less than approximately 0.05. When plates are this thin, shear motion is believed to be negligible and can be neglected in the analysis. It is widely accepted that CTP theory is adequate only for predicting the lowest modes of vibration even for very thin plates.[7,8,9] earlier studies indicate that CTP theory “underestimates deflections and overestimates frequencies” of higher modes.[10]
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