Edge resonance in an elastic semi-strip

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 oscill...

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Bibliographic Details
Published in:Quarterly journal of mechanics and applied mathematics 1998-02, Vol.51 (1), p.1-14
Main Authors: Roitberg, I, Vassiliev, D, Weidl, T
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Vibrations and mechanical waves
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Summary: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.
ISSN:0033-5614
1464-3855
DOI:10.1093/qjmam/51.1.1