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Edge resonance in a...
Edge resonance in an elastic semi-infinite cylinder
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- Holst, Anders (författare)
- Lund University,Lunds universitet,Partiella differentialekvationer,Forskargrupper vid Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Partial differential equations,Lund University Research Groups,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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Vassiliev, Dmitri G. (författare)
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(creator_code:org_t)
- 2000
- 2000
- Engelska.
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Ingår i: Applicable Analysis. - 0003-6811. ; 74:3-4, s. 479-495
- Relaterad länk:
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https://lup.lub.lu.s...
Abstract
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- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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