Edge resonance in an elastic semi-infinite cylinder
(2000) In Applicable Analysis 74(3-4). p.479-495- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
http://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
- 3-4
- pages
- 479 - 495
- publisher
- Taylor & Francis
- ISSN
- 0003-6811
- language
- English
- LU publication?
- yes
- id
- 4f934eb0-0a22-47a9-9971-3ff4d550a8fb (old id 1220484)
- date added to LUP
- 2008-09-01 11:08:43
- date last changed
- 2017-02-09 12:02:28
@misc{4f934eb0-0a22-47a9-9971-3ff4d550a8fb, 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.}, author = {Holst, Anders and Vassiliev, Dmitri G.}, issn = {0003-6811}, language = {eng}, number = {3-4}, pages = {479--495}, publisher = {Taylor & Francis}, series = {Applicable Analysis}, title = {Edge resonance in an elastic semi-infinite cylinder}, volume = {74}, year = {2000}, }