A numerical approach towards best tuning of Tuned Mass Dampers

The present study investigates the optimal tuning of the free parameters of Tuned Mass Damper (TMD) devices. A numerical optimization method is developed and its outcomes are compared to the output from known tuning formulas. Appropriate analytical fittings of the achieved numerical results are proposed as well. Specifically, once a TMD is attached to a primary Structure, the best tuning of its free parameters, namely mass ratio (often assumed to be given from scratch), frequency ratio and TMD damping ratio, leads to the minimization of structural vibration. Often, the tuning concept is developed first for SDOF structural systems, with added TMD, selectively subjected to ideal loadings, such as harmonic or white noise, as point force or base acceleration. Within this context, various tuning formulas have been derived in the literature via analytical or numerical procedures, in each selected case of the above. The present tuning method is rather general and based on a numerical optimization technique, formulated by a Minimax algorithm, complemented by appropriate calibrated analytical fittings, by taking into account and comparing all together the outcomes from the four different loading cases above.