This paper summarizes the authors’ previous efforts on solving inverse eigenvalue problems for linear vibrating systems described by a vector differential equations with constant coefficient matrices and nonproportional damping. The inverse problem of interest here is that of determining symmetric, real, positive definite coefficient matrices assumed to represent mass normalized velocity and position coefficient matrices, given a set of specified complex eigenvalues and eigenvectors. Two previous solutions to the symmetric inverse eigenvalue problem, presented by Starek and Inman, are reviewed and then extended to the design of underdamped vibrating systems with nonproportional damping.
Design of Nonproportional Damped Systems via Symmetric Positive Inverse Problems
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 2002; Revised Oct. 2003. Associate Editor: L. Bergman.
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Starek, L., and Inman, D. J. (May 4, 2004). "Design of Nonproportional Damped Systems via Symmetric Positive Inverse Problems ." ASME. J. Vib. Acoust. April 2004; 126(2): 212–219. https://doi.org/10.1115/1.1688760
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