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


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
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In