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


Reference:

Babych, N. and Golovaty, Y., 2010. Low and high frequency approximations to eigenvibrations of string with double contrasts. Journal of Computational and Applied Mathematics, 234 (6), pp. 1860-1867.

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Official URL:

http://dx.doi.org/10.1016/j.cam.2009.08.037

Abstract

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 semiaxis is applied in order to get a close approximations of eigenvalues as well as eigenfunctions for the prime problem under perturbation.

Details

Item Type Articles
CreatorsBabych, N.and Golovaty, Y.
DOI10.1016/j.cam.2009.08.037
Uncontrolled Keywordsquantization, wkb method, eigenfunction approximation, mass perturbation, stiff problem, high frequency
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code19410
Additional Information8th International Conference on Mathematical and Numerical Aspects of Waves. 23-27 July 2007. Reading, UK. Sp. Iss. SI

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