On the Approximate Solution of Nonclassically Damped Linear Systems

[+] Author and Article Information
J. H. Hwang, F. Ma

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Appl. Mech 60(3), 695-701 (Sep 01, 1993) (7 pages) doi:10.1115/1.2900860 History: Received January 16, 1991; Revised January 22, 1992; Online March 31, 2008


A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated modal damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. In the present paper, the error introduced by disregarding the off-diagonal elements is evaluated, and a quadrature formula for the approximation error is derived. A tight error bound is then obtained. In addition, an effective scheme to improve the accuracy of the approximate solution is outlined.

Copyright © 1993 by The American Society of Mechanical Engineers
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