The paper describes a method of combined expansion and orthogonalization (CEO) of experimental modeshapes. Most model updating and error localization methods require a set of full length, orthogonal with respect to the mass matrix, eigenvectors. In practically every modal experiment, the number of measurements is less than the order of the model, and hence modeshape expansion, i.e., adding the unmeasured degrees of freedom, is required. This step is then followed by orthogonalization with respect to the mass matrix. Most current methods use two separate steps for expansion and orthogonalization, each one optimal by itself, but their combination is not optimal. The suggested method combines the two steps into one optimization problem for both steps, and minimizes a quadratic criterion. In the case of an equal number of analytical and experimental modeshapes, the problem coincides with the Procrustes problem and has a closed form solution. Otherwise the solution involves nonlinear equations. Several examples show the advantage of CEO, especially in cases where the measurements are limited either in number or in space, i.e., not spanned through the entire structure.
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April 2005
Technical Papers
Combined Expansion and Orthogonalization of Experimental Modeshapes
Y. Halevi,
Y. Halevi
Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering,
e-mail: yoramh@vt.edu
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061-0261
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C. A. Morales,
C. A. Morales
Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering,
e-mail: cmorales@vt.edu
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061-0261
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D. J. Inman
D. J. Inman
Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering,
e-mail: dinman@vt.edu
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061-0261
Search for other works by this author on:
Y. Halevi
Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering,
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061-0261e-mail: yoramh@vt.edu
C. A. Morales
Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering,
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061-0261e-mail: cmorales@vt.edu
D. J. Inman
Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering,
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061-0261e-mail: dinman@vt.edu
J. Vib. Acoust. Apr 2005, 127(2): 188-196 (9 pages)
Published Online: June 4, 2004
Article history
Received:
December 22, 2003
Revised:
June 4, 2004
Citation
Halevi, Y., Morales, C. A., and Inman, D. J. (June 4, 2004). "Combined Expansion and Orthogonalization of Experimental Modeshapes." ASME. J. Vib. Acoust. April 2005; 127(2): 188–196. https://doi.org/10.1115/1.1891817
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