Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Abstract: In this paper, a semi-infinite Kirchhoff plate with a traction-free edge, which rests partially on a heterogeneous Winkler foundation (the Neumann problem for the biharmonic operator perturbed by a small free term with a compact support), is considered. It is shown that, for arbitrary small ε > 0, a variable foundation compliance coefficient (defined nonuniquely) of order ε can be constructed, such that the plate obtains the eigenvalue ε4 that is embedded into a continuous spectrum, and the corresponding eigenfunction decays exponentially at infinity. It is verified that no more than one small eigenvalue can exist. It is noteworthy that a small perturbation cannot prompt an emergence of an eigenvalue near the cutoff point of the continuous spectrum in an acoustic waveguide (the Neumann problem for the Laplace operator).
Язык оригинала | английский |
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Страницы (с-по) | 1328-1339 |
Число страниц | 12 |
Журнал | Mechanics of Solids |
Том | 55 |
Номер выпуска | 8 |
DOI | |
Состояние | Опубликовано - дек 2020 |
ID: 88366220