| Title | Edge resonance in an elastic semi-infinite cylinder |
| Authors | Anders Holst, Dmitri G. Vassiliev |
| Publication | Applicable Analysis. An International Journal |
| Year | 2000 |
| Volume | 74 |
| Issue | 3-4 |
| Pages | 479 - 495 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Taylor & Francis 4 Park Square Milton Park Abingdon 0X14 4RN England |
| Abstract English | We study the three-dimensional elasticity operator in a semi-infinite circular cylinder subject to free boundary conditions, in the case of zero Poisson ratio. We prove, adapting the method from I. Roitberg, D. G. Vasilʹev and T. Weidl Quart. J. Mech. Appl. Math. 51 (1998), no. 1, 1--13; MR1610688 (98m:73041), i.e., by first finding an invariant subspace for the elasticity operator such that the essential spectrum has a strictly positive lower bound and then finding a test function in this space for which the variational quotient takes a value below the bottom of the essential spectrum, that there is an eigenvalue embedded in the continuous spectrum. Physically, an eigenvalue corresponds to a `trapped mode', that is, a harmonic oscillation localized near the edge. This effect, known in mechanics as the `edge resonance', has been extensively studied numerically and experimentally. Our paper extends the mathematical justification of such phenomena provided by Roitberg et al. op. cit. to a three-dimensional setting. |
| ISBN/ISSN/Other | ISSN: 0003-6811 |
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