Difficulties about computing the transient free vibration in this case have been discussed by many authors along the years. The main objective of the present paper is to clarify a few questions involving numerical implementation of a constant hysteretic model proposed recently. After the presentation of Ribeiro et al. [1], many discussions have taken place on the formalism that has been applied. One of the authors of the original article decided to review the fundamentals of the problem [2] in a broader way and try to find everything that could be criticized. The main points of the comments presented in [2] are summarised as follows:

First, the main discussions and difficulties in understanding the contribution of Ribeiro et al. [1] are, in our point of view, the fact that apparently the proposed solution shows a causal behaviour! Second, that the free vibration solution obtained is complex. Third, that one cannot simply take the real part of a complex result, since some physical meaning must come into play earlier in the process. Such a generalization has been abandoned and replaced by an equivalent viscously damped model.

A numerical methodology based on modal superposition was implemented. Finally, a comparison between numerical and experimental data for transversal vibration of a clamped-free beam is presented.

1

A.M.R. Ribeiro, N.M.M. Maia, J.M.M. Silva, M. Freitas, L. Reis, "Free Vibration Response Using the Constant Hysteretic Damping Model", Proceedings of the XIth Int. Conf. on Vibration Engineering, Timisoara, Romania, 65-70, 2005.

2

N. Maia, "On the Free Vibration Response with the Constant Hysteretic Damping Model", (submitted to JSV), 2008.

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