On asymptotic analysis of spectral problems in elasticity
The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymp...
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| Format: | Article |
| Language: | English |
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Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252011000100003&lng=en&tlng=en |
| _version_ | 1818062213437456384 |
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| author | S.A. Nazarov J. Sokolowski |
| author_facet | S.A. Nazarov J. Sokolowski |
| author_sort | S.A. Nazarov |
| collection | DOAJ |
| description | The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems. |
| first_indexed | 2024-12-10T14:00:38Z |
| format | Article |
| id | doaj.art-846cc1b9fe9e438c919c1e172e4ee2f5 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-12-10T14:00:38Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-846cc1b9fe9e438c919c1e172e4ee2f52022-12-22T01:45:48ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-782581275410.1590/S1679-78252011000100003S1679-78252011000100003On asymptotic analysis of spectral problems in elasticityS.A. Nazarov0J. Sokolowski1Institute of Mechanical Engineering ProblemsUniversité de LorraineThe three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252011000100003&lng=en&tlng=ensingular perturbationsspectral problemasymptotics of eigenfunctions and eignevalueselasticity boundary value problem |
| spellingShingle | S.A. Nazarov J. Sokolowski On asymptotic analysis of spectral problems in elasticity Latin American Journal of Solids and Structures singular perturbations spectral problem asymptotics of eigenfunctions and eignevalues elasticity boundary value problem |
| title | On asymptotic analysis of spectral problems in elasticity |
| title_full | On asymptotic analysis of spectral problems in elasticity |
| title_fullStr | On asymptotic analysis of spectral problems in elasticity |
| title_full_unstemmed | On asymptotic analysis of spectral problems in elasticity |
| title_short | On asymptotic analysis of spectral problems in elasticity |
| title_sort | on asymptotic analysis of spectral problems in elasticity |
| topic | singular perturbations spectral problem asymptotics of eigenfunctions and eignevalues elasticity boundary value problem |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252011000100003&lng=en&tlng=en |
| work_keys_str_mv | AT sanazarov onasymptoticanalysisofspectralproblemsinelasticity AT jsokolowski onasymptoticanalysisofspectralproblemsinelasticity |