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Technical Briefs

Reduced Mass-Weighted Proper Decomposition for Modal Analysis

[+] Author and Article Information
Venkata K. Yadalam

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824kalyan.612@gmail.com

B. F. Feeny

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824feeny@egr.msu.edu

J. Vib. Acoust 133(2), 024504 (Mar 22, 2011) (5 pages) doi:10.1115/1.4002960 History: Received August 27, 2009; Revised August 10, 2010; Published March 22, 2011; Online March 22, 2011

A method of modal analysis by a mass-weighted proper orthogonal decomposition for multi-degree-of-freedom and distributed-parameter systems of arbitrary mass distribution is outlined. The method involves reduced-order modeling of the system mass distribution so that the discretized mass matrix dimension matches the number of sensed quantities, and hence the dimension of the response ensemble and correlation matrix. In this case, the linear interpolation of unsensed displacements is used to reduce the size of the mass matrix. The idea is applied to the modal identification of a mass-spring system and an exponential rod.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Estimated mode shapes from the reduced mass-weighted POD obtained from 16 fundamental periods (denoted by circles) and one fundamental period (“x” symbols) of data, in comparison with the 24 mass structural modal vectors (dots connected by lines): (a) mode shape associated with the lowest modal frequency and (b)–(h) mode shapes associated with increasing modal frequencies

Grahic Jump Location
Figure 2

Estimated mode shapes of the exponential rod from the reduced mass-weighted POD obtained using linear interpolation functions (denoted by circles), piecewise constant interpolation functions (dots), and unweighted POD (“x” symbols), in comparison with structural modal functions (denoted by lines): (a) mode shape associated with the lowest modal frequency and (b)–(h) mode shapes associated with increasing modal frequencies

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