Edge resonance in an elastic semi-strip
- 1 February 1998
- journal article
- research article
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics
- Vol. 51 (1), 1-14
- https://doi.org/10.1093/qjmam/51.1.1
Abstract
We study the elasticity operator in a semi-strip subject to free boundary conditions. In the case of zero Poisson ratio we prove the existence of a positive eigenvalue embedded in the essential spectrum. Physically, the eigenvalue corresponds to a 'trapped mode', that is, a harmonic oscillation of the semi-strip localized near the edge. This effect, known in mechanics as the 'edge resonance', has been extensively studied numerically and experimentally. Our result provides a mathematical justification.Keywords
This publication has 1 reference indexed in Scilit:
- Extensional Vibrations and Waves in a Circular Disk and a Semi-Infinite PlateJournal of Applied Mechanics, 1960