COMPUTATIONAL METHODS FOR DIFFERENTIAL EIGENSYSTEMS

Two methods are presented here for analyses of differential eigensyste ms with variable coefficients and homogeneous boundary conditions. The se methods can be used to compute derivatives and extremum points of e igenvalues with respect to the chosen free parameters in the considere d system. In one method, adjoint equations and solvability conditions are used to derive expressions for the derivatives of eigenvalues with respect to the free parameters in the design vector, and this express ion is used to determine an extremum point with the help of an iterati on scheme. In another method, the differential eigensystem is augmente d with additional differential equations corresponding to the free par ameters, and the augmented (nonlinear) system subjected to the origina l and differential boundary conditions is solved in one step. Both of these computational methods are illustrated with examples from structu ral mechanics. (C) 1997 Elsevier Science Ltd.