A Symmetric Inverse Vibration Problem

[+] Author and Article Information
L. Starek

Faculty of Mechanical Engineering, Slovak Technical University at Bratislava, 81231 Bratislava, Czechoslovakia

D. J. Inman, A. Kress

Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260

J. Vib. Acoust 114(4), 564-568 (Oct 01, 1992) (5 pages) doi:10.1115/1.2930299 History: Received October 01, 1991; Revised January 01, 1992; Online June 17, 2008


This paper considers the inverse eigenvalue problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices. The inverse problem of interest here is that of determining real symmetric coefficient matrices, assumed to represent the mass, damping, and stiffness matrices, given the natural frequencies and damping ratios of the structure (i.e., the system eigenvalues). The approach presented here allows for repeated eigenvalues, whether simple or not, and for rigid body modes. The method is algorithmic and results in a computer code for determining mass normalized damping, and stiffness matrices for the case that each mode of the system is underdamped.

Copyright © 1992 by The American Society of Mechanical Engineers
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