On the vibrations of a plate with a concentrated mass and very small thickness |
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Authors: | D. G mez,M. Lobo,E. P rez |
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Affiliation: | D. Gómez,M. Lobo,E. Pérez |
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Abstract: | We consider the vibrations of an elastic plate that contains a small region whose size depends on a small parameter ε. The density is of order O(ε–m) in the small region, the concentrated mass, and it is of order O(1) outside; m is a positive parameter. The thickness plate h being fixed, we describe the asymptotic behaviour, as ε→O, of the eigenvalues and eigenfunctions of the corresponding spectral problem, depending on the value of m: Low‐ and high‐frequency vibrations are studied for m>2. We also consider the case where the thickness plate h depends on ε; then, different values of m are singled out. Copyright © 2003 John Wiley & Sons, Ltd. |
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Keywords: | concentrated masses spectral analysis Reissner– Mindlin plate Kirchhoff– Love plate |
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