A REFORMULATED ARNOLDI ALGORITHM FOR NONCLASSICALLY DAMPED EIGENVALUEPROBLEMS

In applying Arnoldi method to non-symmetric eigenvalue problems for da mped structures, a structure of the projected upper Hessenberg matrix is obtained in this paper. By exploiting the structure of the upper He ssenberg matrix and taking advantages of the block properties of syste m matrices, the Arnoldi reduction algorithm is reformulated for less c omputation and higher accuracy. In conjunction with the reformulated A rnoldi algorithm, real Schur decomposition instead of Jordan decomposi tion is adopted aiming at non-complex arithmetic, non-discriminative p rocessing of defective and non-defective systems and numeric stability . A concise reduction algorithm for eigenproblems for undamped gyrosco pic systems is obtained by directly degenerating from the reformulated Arnoldi algorithm. For safely solving engineering problems without om itting eigenvalues, a restart reduction procedure is proposed in terms of the reformulated reduction algorithm with deflation developed in t his paper. Numerical examples once solved with algorithms originated f rom Lanczos methods were re-solved. In addition, the non-symmetric eig envalue problem for a shear wall by BEM modeling and a damped gyroscop ic system with eigenvalues of high multiplicity were also used to demo nstrate the efficacy of the presented methods. (C) 1997 John Wiley & S ons, Ltd.