Low and high frequency approximations to eigenvibrations of string with double contrasts

We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density inhomogeneity is the same as the order of stiffn...

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Bibliographic Details
Published in:arXiv.org 2009-09
Main Authors: Babych, Natalia, Golovaty, Yuri
Format: Article
Language:English
Subjects:
Density
Eigenvalues
Eigenvectors
High frequencies
Inhomogeneity
Perturbation
Stiffness
Online Access:Get full text
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Summary:We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density inhomogeneity is the same as the order of stiffness inhomogeneity, with heavier part being softer. The limit problem for high frequency approximations depends nonlinearly on the spectral parameter. The quantization of the spectral semiaxies is applied in order to get a close approximations of eigenvalues as well as eigenfunctions for the prime problem under perturbation.
ISSN:2331-8422
DOI:10.48550/arxiv.0804.2620