Edge resonance in an elastic semi-infinite cylinder

Anders Holst, Dmitri G. Vassiliev

Research output: Contribution to specialist publication or newspaperSpecialist publication articlePopular science

15 Citations (SciVal)

Abstract

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.
Original languageEnglish
Pages479-495
Volume74
No.3-4
Specialist publicationApplicable Analysis
PublisherTaylor & Francis
Publication statusPublished - 2000

Subject classification (UKÄ)

  • Mathematics

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