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Research Papers

Stiffness Matrix Properties for Reduced Order Models of Linear Structural Systems

[+] Author and Article Information
Jun Yu

LZA Technology, The Thornton Tomasetti Group, Inc., 24 Commerce Street, Newark, NJ 07102jy232@columbia.edu

Maura Imbimbo

Department of Mechanics, Structures and Environment, University of Cassino, Via G. Di Biasio 43, Cassino 03043, Italymimbimbo@unicas.it

Raimondo Betti

Department of Civil Engineering and Engineering Mechanics, Columbia University, 640 Southwest Mudd Building, New York, NY 10027betti@civil.columbia.edu

J. Appl. Mech 77(6), 061013 (Sep 01, 2010) (8 pages) doi:10.1115/1.4001118 History: Received October 18, 2006; Revised December 12, 2009; Published September 01, 2010; Online September 01, 2010

This paper discusses a theoretical approach to investigate the dependency relationship between the stiffness matrix and the complex eigenvectors in the identification of structural systems for the case of insufficient instrumentation setup. The main result of the study consists of proving, in the case of classical damping, the independency of the stiffness subpartition corresponding to the measured degrees-of-freedom from the unmeasured ones. The same result is shown to be valid in the case of nonclassical damping but only for tridiagonal sparse stiffness matrix systems. A numerical procedure proves the above results and also shows the dependency relationship for the general nonclassical damping cases.

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Copyright © 2010 by American Society of Mechanical Engineers
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3DOF shear-type building system

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Figure 2

3DOF spring system

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