A REDUCTION METHOD FOR LARGE-SCALE UNSYMMETRIC EIGENVALUE PROBLEMS INSTRUCTURAL DYNAMICS

The discussion begins with the classification of eigenvalue problems a rising from conservative and non-conservative structural systems. The conservative type includes undamped structural eigenvalue problems and undamped gyroscopic eigenvalue problems. The non-conservative type in cludes damped structural eigenvalue problems, damped gyroscopic eigenv alue problems and constrainedly damped eigenvalue problems. The method s for solving large scale unsymmetric eigenvalue problems are briefly reviewed. The advantages and properties of Arnoldi's method have also been discussed. Arnoldi's reduction method has been generalized and th e partial solution of large scale unsymmetric-definite eigenvalue prob lems in structural dynamics is presented in detail. A very simple redu ction algorithm is obtained by simplifying the proposed method for und amped gyroscopic eigenvalue problems. To make the proposed reduction m ethod feasible for engineering problems, a restart technique is introd uced to work with Arnoldi's reduction method for checking and computin g missing eigenvalues. Numerical examples are also presented to demons trate the effectiveness of the proposed reduction method. (C) 1997 Aca demic Press Limited.