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RESEARCH PAPERS

Approximate Decoupling of the Equations of Motion of Linear Underdamped Systems

[+] Author and Article Information
S. M. Shahruz, F. Ma

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

J. Appl. Mech 55(3), 716-720 (Sep 01, 1988) (5 pages) doi:10.1115/1.3125855 History: Received August 07, 1987; Revised March 11, 1988; Online July 21, 2009

Abstract

One common procedure in the solution of a normalized damped linear system with small off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight error bounds are derived. Moreover, if the normalized damping matrix is diagonally dominant, it is shown that decoupling the system by neglecting the off-diagonal elements indeed minimizes the error bound.

Copyright © 1988 by ASME
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