Generalization of the Den Hartog model and rule-of-thumb formulas for optimal tuned mass dampers

In recent years, the need of improving safety standards for both existing and new buildings against earthquake and wind loads has created a growing interest in the use of the so-called tuned mass dampers, exploited to control, in active or passive way, the dynamic response of structures. To design and optimize tuned mass damper systems, the effective analytical procedure proposed by Den Hartog in his seminal work (Den Hartog, 1985) has been widely adopted over the years, without including damping of the main structure. However, in many cases of engineering interest, the damping of the primary system plays a key role in the overall mechanical response, with the result of an increase in compl…