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Diagonal Dominance and the Decoupling Approximation in Damped Discrete Linear Systems

[+] Author Affiliations
Matthias Morzfeld, Fai Ma

University of California at Berkeley, Berkeley, CA

Nopdanai Ajavakom

Chulalongkorn University, Bangkok, Thailand

Paper No. DETC2007-35690, pp. 109-117; 9 pages
doi:10.1115/DETC2007-35690
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 27th Computers and Information in Engineering Conference, Parts A and B
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4803-5 | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

The principal coordinates of a non-classically damped linear system are coupled by nonzero off-diagonal element of the modal damping matrix. In the analysis of non-classically damped systems, a common approximation is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is widely accepted that if the modal damping matrix is diagonally dominant, then errors due to the decoupling approximation must be small. In addition, it is intuitively believed that the more diagonal the modal damping matrix, the less will be the errors in the decoupling approximation. Two quantitative measures are proposed in this paper to measure the degree of being diagonal dominant in modal damping matrices. It is demonstrated that, over a finite range, errors in the decoupling approximation can continuously increase while the modal damping matrix becomes more and more diagonal with its off-diagonal elements decreasing in magnitude continuously. An explanation for this unexpected behavior is presented. Within a practical range of engineering applications, diagonal dominance of the modal damping matrix may not be sufficient for neglecting modal coupling in a damped system.

Copyright © 2007 by ASME

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