Representation of Damping Matrix
Publication: Journal of Engineering Mechanics
Volume 117, Issue 5
Abstract
This paper deals with the representation of the damping matrix in terms of mass and stiffness matrices. A relationship is proposed that can represent not only Rayleigh damping, but also the general nonproportional damping. This proposed relationship is mathematically based on a theorem of matrix representation that, under certain circumstance (which can be easily checked), a matrix C can be represented accurately by a polynomial of two given matrices M and K. In engineering applications, in the sense of least‐squares approach or series solutions, the first few terms of the polynomial of the given matrices M and K are shown to be sufficiently accurate to represent the damping matrix. An attempt is made to interpret the physical meaning of some of the parameters of the proposed damping matrix. Numerical examples are given to illustrate the simplicity and accuracy of the proposed method as applied to nonproportional damping problems in structural dynamics. The proposed approach can also be applied in system identification problems.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 117 • Issue 5 • May 1991
Pages: 1005 - 1019
Copyright
Copyright © 1991 ASCE.
History
Published online: May 1, 1991
Published in print: May 1991
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