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On the Uniqueness of Solutions for the Identification of Linear Structural Systems

[+] Author and Article Information
Guillermo Franco

The Earth Institute, Columbia University, 634A S. W. Mudd Building, New York, NY 10027franco@civil.Columbia.edu.

Raimondo Betti

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

Richard W. Longman

Department of Mechanical Engineering, Columbia University, 232 S. W. Mudd Building, New York, NY 10027RWL14@Columbia.edu

J. Appl. Mech 73(1), 153-162 (Jul 30, 2005) (10 pages) doi:10.1115/1.2062829 History: Received July 09, 2003; Revised July 30, 2005

This work tackles the problem of global identifiability of an undamped, shear-type, N degrees of freedom linear structural system under forced excitation without any prior knowledge of its mass or stiffness distributions. Three actuator/sensor schemes are presented, which guarantee the existence of only one solution for the mass and stiffness identification problem while requiring a minimum amount of instrumentation (only 1 actuator and 1 or 2 sensors). Through a counterexample for a 3DOF system it is also shown that fewer measurements than those suggested result invariably in non-unique solutions.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

One-dimensional shear-type building model with N degrees of freedom, input located at the jth story and output measured at all locations

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Figure 2

Possible configurations for unique identification

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Figure 3

Collocated configuration for the 3DOF system

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Figure 4

Comparison of measurements between the two physically possible solutions for the 3DOF system with collocated input-output measurement at the second DOF

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