Reflections on the Hysteretic Damping Model

Abstract

Abstract. This paper presents a reflection on a recently proposed solution to the problem of the free vibration response with the constant hysteretic damping model, that has been presented in some conferences in recent years, by the author himself and some of his colleagues. On the one hand, as expected, the subject has been received with natural criticism, mainly due to the well-known non-causal behaviour of the model in free vibration. On the other hand, it was not easy to understand what could be wrong in that proposal, as apparently everything was perfect from a mathematical point of view. The author decided that this subject deserved a more careful and detailed analysis and -in this kind of tutorial paper -the issue seems to have been clarified. It is concluded that the proposed solution involving the constant hysteretic damping corresponds in fact to an equivalent viscously damped model; it is therefore concluded that the application of the constant hysteretic damping to model the free vibration of practical engineering problems should be considered only in the perspective of an equivalent viscously damped model.

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“…In 2009, Maia compared viscous damping and hysteresis damping for a single degree of freedom. She proved a causal behavior of hysteresis damping because they are the solutions of an equivalent viscously damped system [4]. Besides that, Choi et al proposed to separate the estimated tension into two parts: the pure applied axial load and the stretching force due to selfweight and re-estimate with real data at Alamillo Bridge [5].…”

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“…The time-domain motion equation of hysteretic damping model for the single degree of freedom (SDOF) system is expressed as 8,10 m d 2 yðtÞ dt 2 þ iηkyðtÞ þ kyðtÞ ¼ Pe iθt (1)…”

“…The time-domain motion equation of hysteretic damping model for the single degree of freedom (SDOF) system is expressed as 8,10 where m is the mass of system; k is the stiffness of system; η is the loss factor; i is the imaginary unit, i=−1; P is the vibration amplitude of harmonic wave; θ is the vibration frequency of harmonic wave. x(t) is the displacement; x′(t) is the dual item of x(t).…”