A computationally efficient algorithm for the solution of eigenproblems for large structures with non-proportional dam ping using Lanczos method

In this paper, a solution method is presented to solve the eigenproblem ari sing in the dynamic analysis of non-proportional damping systems with symme tric matrices. The method is based on the Lanczos method to generate one pa ir of Krylov subspaces consisting of trial vectors, which is then used to r educe a large eigenvalue problem into a much smaller one. The method retain s the n order quadratic eigenproblem, without employing the method of matri x augmentation traditionally used to cast the problem as a linear eigenprob lem of order 2n. In this process, the method preserves the sparseness and s ymmetry of the system matrices and does not invoke complex arithmetic; thus making it very economical for use in solving large problems. Numerical res ults are presented to demonstrate the efficiency and accuracy of the propos ed method. Copyright (C) 1999 John Wiley & Sons, Ltd.