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TECHNICAL BRIEFS

Approximate Decoupling of Weakly Nonclassically Damped Linear Second-Order Systems Under Harmonic Excitations

[+] Author and Article Information
S. M. Shahruz

Berkeley Engineering Research Institute, Berkeley, CA 94709

A. K. Packard

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

J. Dyn. Sys., Meas., Control 115(1), 214-218 (Mar 01, 1993) (5 pages) doi:10.1115/1.2897403 History: Received December 20, 1991; Revised May 12, 1992; Online March 17, 2008

Abstract

A simple and commonly used approximate technique of solving the normalized equations of motion of a nonclassically damped linear second-order system is to decouple the system equations by neglecting the off-diagonal elements of the normalized damping matrix, and then solve the decoupled equations. This approximate technique can result in a solution with large errors, even when the off-diagonal elements of the normalized damping matrix are small. Large approximation errors can arise in lightly damped systems under harmonic excitations when some of the undamped natural frequencies of the system are close to the excitation frequency. In this paper, a rigorous analysis of the approximation error in lightly damped systems is given. Easy-to-check conditions under which neglecting the off-diagonal elements of the normalized damping matrix can result in large approximation errors are presented.

Copyright © 1993 by The American Society of Mechanical Engineers
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