On the vibrations of a plate with a concentrated mass and very small thickness

✍ Scribed by D. Gómez; M. Lobo; E. Pérez

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 339 KB
• Volume: 26
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.342

✦ Synopsis

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.