An integral equation method for non-self-adjoint eigenvalue problems and its applications to non-conservative stability problems

✍ Scribed by Nobuyoshi Tosaka; Kazuhiko Kakuda

• Publisher: John Wiley and Sons
• Year: 1984
• Tongue: English
• Weight: 507 KB
• Volume: 20
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620200110

✦ Synopsis

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.