96-390 I. Roitberg, D. Vassiliev, T. Weidl

Edge resonance in an elastic semi-strip (385K, Postscript) Aug 28, 96

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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 justifi- cation.

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