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On the vibrations of a plate with a concentrated mass and very small thickness
Author(s) -
Gómez D.,
Lobo M.,
Pérez E.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.342
Subject(s) - eigenfunction , eigenvalues and eigenvectors , mathematics , vibration , order (exchange) , mathematical analysis , value (mathematics) , geometry , physics , statistics , quantum mechanics , finance , economics
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.