C. Förster, und T. Weidl. St. Petersburg Mathematical Journal, 23 (1):
179-202(2012)
Zusammenfassung
Summary (translated from the Russian): "We consider an infinite linearly elastic plate with a stress-free boundary. We study the trapped modes arising around the holes in the plate. We discuss the eigenvalues of the elastostatic operator acting in L2 on the area of the plate that arises from the removal of a hole in the plate. Neumann boundary conditions (`stress-free' conditions) are imposed on the boundary of the plate and on the boundary of a hole. We prove that the perturbation leads to the appearance of infinitely many eigenvalues embedded into the essential spectrum. The eigenvalues accumulate to a positive threshold. We obtain an estimate for the accumulation rate.''
%0 Journal Article
%1 forster2012trapped
%A Förster, Clemens
%A Weidl, Timo
%D 2012
%J St. Petersburg Mathematical Journal
%K iadm from:elkepeter Förster elastic plate Weidl
%N 1
%P 179-202
%T Trapped modes in an elastic plate with a hole.
%V 23
%X Summary (translated from the Russian): "We consider an infinite linearly elastic plate with a stress-free boundary. We study the trapped modes arising around the holes in the plate. We discuss the eigenvalues of the elastostatic operator acting in L2 on the area of the plate that arises from the removal of a hole in the plate. Neumann boundary conditions (`stress-free' conditions) are imposed on the boundary of the plate and on the boundary of a hole. We prove that the perturbation leads to the appearance of infinitely many eigenvalues embedded into the essential spectrum. The eigenvalues accumulate to a positive threshold. We obtain an estimate for the accumulation rate.''
@article{forster2012trapped,
abstract = {
Summary (translated from the Russian): "We consider an infinite linearly elastic plate with a stress-free boundary. We study the trapped modes arising around the holes in the plate. We discuss the eigenvalues of the elastostatic operator acting in L2 on the area of the plate that arises from the removal of a hole in the plate. Neumann boundary conditions (`stress-free' conditions) are imposed on the boundary of the plate and on the boundary of a hole. We prove that the perturbation leads to the appearance of infinitely many eigenvalues embedded into the essential spectrum. The eigenvalues accumulate to a positive threshold. We obtain an estimate for the accumulation rate.''},
added-at = {2021-11-04T06:35:05.000+0100},
author = {Förster, Clemens and Weidl, Timo},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2d6f3785aca4f8b9d60c60d9691cc49a5/mathematik},
interhash = {a094843a77c47354e249ebfbf5283a3c},
intrahash = {d6f3785aca4f8b9d60c60d9691cc49a5},
journal = {St. Petersburg Mathematical Journal},
keywords = {iadm from:elkepeter Förster elastic plate Weidl},
language = {translation from Russian into English},
number = 1,
pages = {179-202},
timestamp = {2021-11-04T05:35:05.000+0100},
title = {Trapped modes in an elastic plate with a hole.},
volume = 23,
year = 2012
}
