Technical Papers
Feb 10, 2014

Damping Matrices Revisited

Publication: Journal of Engineering Mechanics
Volume 140, Issue 8

Abstract

After a brief review of the problems entailed by the so-called proportional damping matrices, this paper elaborates on a simple technique to construct damping matrices that guarantee the fraction of damping in each mode to be positive and adequate and accomplishes this without solving for either the modes or the natural frequencies. Although the resulting matrices do not generally satisfy the proportionality condition, this fact is irrelevant for the purposes to which such matrices are put.

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References

Caughey, T. K. (1960). “Classical normal modes in damped linear dynamic systems.” J. Appl. Mech., 27(2), 269–271.
Caughey, T. K., and O’Kelly, M. E. J. (1965). “Classical normal modes in damped linear dynamic systems.” J. Appl. Mech., 32(3), 583–588.
Clough, R. W., and Penzien, J. (1993). Dynamics of structures, 2nd Rev. Ed., McGraw Hill, New York.
Denman, E. D., and Beavers, A. N. (1976). “The matrix sign function and computations in systems.” Appl. Math. Comput., 2(1), 63–94.
Hall, J. F. (2006). “Problems encountered from the use (or misuse) of Rayleigh damping.” Earthquake Eng Struct. Dyn., 35(5), 522–545.
Kausel, E. (2008). “Letter to the editor: ‘A note on classical damping matrices’ by J. E. Luco.” Earthquake Eng. Struct. Dyn., 37(15), 1801–1804.
Luco, J. E. (2008a). “A note on classical damping matrices.” Earthquake Eng. Struct. Dyn., 37(4), 615–626.
Luco, J. E. (2008b). “Author’s reply: ‘A note on classical damping matrices’ by J. E. Luco.” Earthquake Eng. Struct. Dyn., 37(15), 1805–1809.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 140Issue 8August 2014

History

Received: Sep 19, 2013
Accepted: Jan 6, 2014
Published online: Feb 10, 2014
Discussion open until: Jul 10, 2014
Published in print: Aug 1, 2014

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Authors

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Eduardo Kausel, F.ASCE [email protected]
Professor, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. E-mail: [email protected]

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