Viscous Damping in Inelastic Structural Response
Publication: Journal of Structural Engineering
Volume 120, Issue 4
Abstract
The behavior of initially orthogonal damping during inelastic response is examined. It is shown that in systems with massless coordinates, or where a subset of the total number of degrees‐of‐freedom (DOF) is associated with small inertias, loss of damping orthogonality can lead to the generation of spurious damping forces. Analytical inspection illustrates that these forces depend on the form of the damping matrix and on the changes in the statical relationship between primary and secondary DOF introduced by yielding. Numerical results are obtained to validate the analytical observations and to examine the quantitative significance of the spurious forces on the computed response. It is shown that in systems with massless coordinates the potential for spurious behavior is obviated when the damping matrix is assembled restricting the exponents of the Caughey series to zero or negative. The foregoing constrain, which is equivalent to requiring that massless coordinates be condensed from the stiffness prior to assembly of the damping, is shown to be necessary for the damping matrix to be unique for a given set of modal damping ratios.
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References
1.
Allahabadi, R., and Powell, G. H. (1988). “DRAIN‐2DX, a user guide,” Rep. No. UCB/EERC 88‐06, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
2.
Caughey, T. K. (1960). “Classical normal modes in damped linear systems.” J. Appl. Mech., 27, 269–271.
3.
Caughey, T. K., and O'Kelly, M. E. J. (1965). “Classical normal modes in damped linear systems.” J. Appl. Mech., 32, 583–588.
4.
Clough, R. W., and Mojtahedi, S. (1976). “Earthquake response analysis considering non‐proportional damping.” Earthquake Engrg. Struct. Dyn., 4, 489–496.
5.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw‐Hill, New York, N.Y.
6.
Foss, K. A. (1956). “Coordinates which uncouple the equations of motion of damped linear systems,” Tech. Rep. 25‐30, Massachusetts Institute of Technology. Cambridge, Mass.
7.
Kannan, A. E., and Powell, G. H. (1973). “DRAIN‐2D, a general purpose computer program for dynamic analysis of inelastic plane structures,” Report No. UCB/EERC 73‐6, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
8.
Porter, F., and Powell, G. H. (1971). “Static and dynamic analysis of inelastic frame structures.” Rep. No. UCB/EERC 71‐3, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
9.
Shing, P. S., and Mahin, S. A. (1987). “Elimination of spurious higher‐mode response in pseudodynamic tests,” Earthquake Engrg. Struct. Dyn., 15, 425–445.
10.
Thomson, W. T., Calkins, T., and Caravani, P. (1974). “A numerical study of damping,” Earthquake Engrg. Struct. Dyn., 3, 97–103.
11.
Warburton, G. B., and Soni, S. R. (1977). “Errors in response calculations for non‐classically damped structures,” Earthquake Engrg. Struct. Dyn., 5, 365–376.
12.
Wilson, E. L., and Penzien, J. (1972). “Evaluation of orthogonal damping matrices,” Int. J. Num. Meth. Engrg., 4, 5–10.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 120 • Issue 4 • April 1994
Pages: 1240 - 1254
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jan 25, 1993
Published online: Apr 1, 1994
Published in print: Apr 1994
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