Edge resonance in an elastic semiinfinite cylinder
(2000) In Applicable Analysis 74(34). p.479495 Abstract
 We study the threedimensional elasticity operator in a semiinfinite 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, 113; 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... (More)
 We study the threedimensional elasticity operator in a semiinfinite 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, 113; 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 threedimensional setting. (Less)
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https://lup.lub.lu.se/record/1220484
 author
 Holst, Anders ^{LU} and Vassiliev, Dmitri G.
 organization
 publishing date
 2000
 type
 Contribution to specialist publication or newspaper
 publication status
 published
 subject
 categories
 Popular Science
 in
 Applicable Analysis
 volume
 74
 issue
 34
 pages
 479  495
 publisher
 Taylor & Francis
 external identifiers

 scopus:33748086244
 ISSN
 00036811
 language
 English
 LU publication?
 yes
 id
 4f934eb00a2247a999713ff4d550a8fb (old id 1220484)
 date added to LUP
 20160401 11:53:45
 date last changed
 20220420 23:25:20
@misc{4f934eb00a2247a999713ff4d550a8fb, abstract = {{We study the threedimensional elasticity operator in a semiinfinite 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, 113; 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 threedimensional setting.}}, author = {{Holst, Anders and Vassiliev, Dmitri G.}}, issn = {{00036811}}, language = {{eng}}, number = {{34}}, pages = {{479495}}, publisher = {{Taylor & Francis}}, series = {{Applicable Analysis}}, title = {{Edge resonance in an elastic semiinfinite cylinder}}, volume = {{74}}, year = {{2000}}, }