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An integral equation method for non‐self‐adjoint eigenvalue problems and its applications to non‐conservative stability problems
Author(s) -
Tosaka Nobuyoshi,
Kakuda Kazuhiko
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200110
Subject(s) - mathematics , integral equation , eigenvalues and eigenvectors , mathematical analysis , stability (learning theory) , self adjoint operator , inverse problem , elasticity (physics) , hilbert space , computer science , physics , materials science , quantum mechanics , machine learning , composite material
Abstract The aim of the work reported in this paper is to present the new formulation of the integral equation method for non‐self‐adjoint problems and to apply the method to stability problems of elastic continua subjected to non‐conservative loadings. A general non‐self‐adjoint eigenvalue problem stated in terms of differential operators is transformed into a set of coupled integral equations. Our derivation of integral equations is based on an inverse formulation of a canonical form for the original problem and the corresponding fundamental solution pair. Three well‐known non‐conservative stability problems in elasticity are examined by this integral equation method as illustrative examples. The approximate values of the critical parameters of sample problems demonstrate a sufficient accuracy through a comparison of other values.