Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts
A model of a strongly inhomogeneous medium with simultaneous perturbation of the rigidity and mass density is studied. The medium has strongly contrasting physical characteristics in two parts with the ratio of rigidities being proportional to a small parameter ". Additionally, the ratio of mas...
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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2008
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/124262 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts / N. Babych, Yu. Golovaty // Нелинейные граничные задачи. — 2008. — Т. 18. — С. 194-217. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1242622017-09-24T03:03:13Z Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts Babych, N. Golovaty, Yu. A model of a strongly inhomogeneous medium with simultaneous perturbation of the rigidity and mass density is studied. The medium has strongly contrasting physical characteristics in two parts with the ratio of rigidities being proportional to a small parameter ". Additionally, the ratio of mass densities is of order " ε⁻¹. We investigate the asymptotic behaviour of the spectrum and eigensubspaces as ε → 0. Complete asymptotic expansions of eigenvalues and eigenfunctions are constructed and justified. We show that the limit operator is nonself-adjoint in general and possesses two-dimensional Jordan cells in spite of the singular perturbed problem is associated with a self-adjoint operator in appropriated Hilbert space Lε. This may happen if the metric in which the problem is self-adjoint depends on small parameter " in a singular way. In particular, it leads to a loss of completeness for the eigenfunction collection. We describe how root spaces of the limit operator approximate eigenspaces of the perturbed operator. 2008 Article Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts / N. Babych, Yu. Golovaty // Нелинейные граничные задачи. — 2008. — Т. 18. — С. 194-217. — Бібліогр.: 22 назв. — англ. 0236-0497 MSC (2000): 35P20; 74H45; 35J25 http://dspace.nbuv.gov.ua/handle/123456789/124262 en Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A model of a strongly inhomogeneous medium with simultaneous perturbation of the rigidity and mass density is studied. The medium has strongly contrasting physical characteristics in two parts with the ratio of rigidities being proportional to a small parameter ". Additionally, the ratio of mass densities is of order " ε⁻¹. We investigate the asymptotic behaviour of the spectrum and eigensubspaces as ε → 0. Complete asymptotic expansions of eigenvalues and eigenfunctions are constructed and justified. We show that the limit operator is nonself-adjoint in general and possesses two-dimensional Jordan cells in spite of the singular perturbed problem is associated with a self-adjoint operator in appropriated Hilbert space Lε. This may happen if the metric in which the problem is self-adjoint depends on small parameter " in a singular way. In particular, it leads to a loss of completeness for the eigenfunction collection. We describe how root spaces of the limit operator approximate eigenspaces of the perturbed operator. |
| format |
Article |
| author |
Babych, N. Golovaty, Yu. |
| spellingShingle |
Babych, N. Golovaty, Yu. Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts |
| author_facet |
Babych, N. Golovaty, Yu. |
| author_sort |
Babych, N. |
| title |
Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts |
| title_short |
Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts |
| title_full |
Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts |
| title_fullStr |
Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts |
| title_full_unstemmed |
Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts |
| title_sort |
asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/124262 |
| citation_txt |
Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts / N. Babych, Yu. Golovaty // Нелинейные граничные задачи. — 2008. — Т. 18. — С. 194-217. — Бібліогр.: 22 назв. — англ. |
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AT babychn asymptoticanalysisofavibratingsystemcontainingstiffheavyandflexiblelightparts AT golovatyyu asymptoticanalysisofavibratingsystemcontainingstiffheavyandflexiblelightparts |
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2023-10-18T20:46:02Z |
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2023-10-18T20:46:02Z |
| _version_ |
1796151055482880000 |