High frequency asymptotics of global vibrations in a problem with concentrated mass

We consider an elastic system containing a small region where the density is very much higher then elsewhere. Such system possesses two types of eigenvibrations, which are local and global vibrations. Complete asymptotic expansions of global eigenvibrations for ordinary differential operator of the...

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Bibliographic Details
Published in:arXiv.org 2008-04
Main Author: Babych, Natalia
Format: Article
Language:English
Subjects:
Asymptotic series
Differential equations
Elastic systems
Operators (mathematics)
Online Access:Get full text
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Summary:We consider an elastic system containing a small region where the density is very much higher then elsewhere. Such system possesses two types of eigenvibrations, which are local and global vibrations. Complete asymptotic expansions of global eigenvibrations for ordinary differential operator of the fourth order are constructed using WKB--technique.
ISSN:2331-8422