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

Abstract

AbstractThe 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.