SOLUTION OF EIGENPROBLEMS FOR DAMPED STRUCTURAL SYSTEMS BY THE LANCZOS ALGORITHM

Abstract A variant of the Lanczos algorithm is deduced to solve the eigenproblem arising in the analysis of viscously damped structural systems. Re-orthogonalization schemes are employed to restore the required orthogonality between the Lanczos vectors. A projection of the original eigen-problem onto the Krylov subspace spanned by the Lanczos vectors gives a standard tri-diagonal eigenproblem, of which the solutions are the Ritz approximations to the eigenpairs sought. An advantage of the algorithm is the fact that the Lanczos vectors are all real, even though the final solution is complex. A number of problems are solved by the algorithm and the results are very good.