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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 55
ADVANCES IN COMPUTATIONAL STRUCTURAL MECHANICS
Edited by: B.H.V. Topping
Paper IV.1

Solution of Eigen Problems for Non-Proportional Damping Systems by Lanczos Method

I.W. Lee, M.-C. Kim and H.J. Jung

Department of Civil Engineering, Korea Advanced Institute of Science and Technology, Taejon, Korea

Full Bibliographic Reference for this paper
I.W. Lee, M.-C. Kim, H.J. Jung, "Solution of Eigen Problems for Non-Proportional Damping Systems by Lanczos Method", in B.H.V. Topping, (Editor), "Advances in Computational Structural Mechanics", Civil-Comp Press, Edinburgh, UK, pp 69-75, 1998. doi:10.4203/ccp.55.4.1
Abstract
A solution method is presented to solve the eigenproblem arising in the dynamic analysis of non-proportional damping systems with symmetric matrices. The method is based on the use of Lanczos method to generate one pair of Krylov subspaces of trial vectors, which is then used to reduce a large eigenvalue problem to a much smaller one. The method retains the n order quadratic eigenproblem, without the need to use the method of matrix augmentation traditionally used to cast the problem as a linear eigenproblem of order 2n. In the process, the method preserves the sparseness and symmetry of the system matrices and does not invoke complex arithmetic, therefore, making it very economical for use in solving large problems. Numerical results are presented to demonstrate the good efficiency and accuracy of the method.

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