Eigenvector Relations for Natural Vibrations of Damped Systems

In the analysis of a discrete system for its damped free vibrations with damping non-proportional, the second order algebraic eigenvalue problem, [K]{U} + \gl[C]{U} + \gl\u2[M]{U} = O, is reduced to one of first order. Three forms of the first order system are possible depending on the auxiliary equation used. Two systems involve symmetric but non-positive definite matrices, and the other contains a nonsymmetric matrix. The eigenvalues of these three algebraic systems are the same, but the eigenvectors may differ from one system to another because of phase relations. In this paper, the inter-relations between the different sets of eigenvectors for the damped free motions are established.

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