Modeling Viscous Damping in Nonlinear Response History Analysis of Buildings

Abstract eng:
The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop “spurious” damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the “spurious” damping forces. Based on response results, we conclude that the classical Rayleigh damping model is inappropriate. The two preferred damping models are (1) a modified Rayleigh damping model in which the stiffness-proportional term is based on a k that omits contributions from all rotational springs used to model plastic hinges; and (2) a damping matrix defined by superposition of modal damping matrices. The first of these two models is easier to understand and implement, whereas the second model has the advantage that it eliminates the spurious damping forces even if rotational springs that model plastic hinges include damping, as in some widely used computer programs.

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