To improve serviceability and occupant comfort, the passive tuned mass damper (TMD) has been widely applied since the 1970s on tall buildings, towers and chimneys, proving a simple, inexpensive and effective device to mitigate wind response. In most current installations on buildings, the damper mass consists of lead, steel or concrete blocks, having no purpose but the structural one [1].

Some applications exist worldwide, however, in which TMDs have been engineered without introducing additional weight to the structure, instead relying on available masses on the top floor, such as ice thermal or water tanks. To bring such concept to its limits, this paper investigates the possibility of turning into a tuned damping device any available source of mass already present on a building, specifically including those whose value is pliable of changing over time. If such a new passive mass-uncertain TMD (MUTMD) could be shown to still be effective, an innovative family of inexpensive and unobtrusive TMDs would be exploitable, ranging from mass-uncertain fluid reservoirs or installations to roof gardens to the very idea of floating floors [2].

Unfortunately, mass variation in a TMD inevitably degrades its performance with respect to the case of a constant mass, potentially inducing severe off-tuning effects against which the TMD is notoriously little robust.

In this paper, such performance degradation is discussed and a proper robust synthesis is presented providing the control design which minimizes the envelope of some response transfer function over the whole prescribed range of variation for the uncertain mass. A comparison is conducted, considering different numbers of dampers, different mass ratios and different mass uncertainties, between the two classical schemes of tuned mass dampers, which exhibit a dissimilar robust behaviour against mass variations and yet look indistinguishable in the case of a constant mass: the translational TMD and the pendulum TMD.

For each design scenario, the robust synthesis results in a Min.Max. problem (the "Min" term being related to scanning the search domain and the "Max" term to evaluating the objective function) which is solved through a branch & bound algorithm, here preferred to alternative techniques [3] in that it applies the same criterion of progressive convergence towards optimality to both the "Min" and the "Max" terms, thus offering a unifying approach to the worst-case robust synthesis.

Preliminary addressing the control of a single-degree-of-freedom structure (SDOF), the paper first demonstrates that, when a proper robust selection of the control parameters is conducted, the translational MUTMD can retain enough of its nominal performance only if its percentage mass uncertainty is small with respect to its mass ratio, whilst the pendulum MUTMD displays a satisfactory behaviour under virtually any conditions, due to its superior intrinsic robustness.

A more realistic case is then considered consisting in the design of a multiple MUTMD to be placed atop the 76-storey Melbourne office building proposed as a benchmark problem for the response control of wind-excited tall buildings [4]. The robust design is again performed as the minimization of the worst-case norm of the response transfer function for the equivalent SDOF condensed structural model, but the robust performance is now assessed on the complete 76-DOF model subjected to either harmonic excitations or to the across-wind forces recorded during wind tunnel tests conducted on a scaled model at the University of Sydney. The nominal/robust trade-off is underlined and the advantage of the pendulum configuration is confirmed.

In conclusion, this paper demonstrates that, if robustly designed, the MUTMD prove a promising alternative to traditional TMD, compensating for a slight effectiveness reduction with the advantage of cost saving and multitasking. The pendulum configuration is generally preferable, but the translational scheme too shows adequate robustness in a number of situations of practical interest.

1

T.T. Soong, G.F. Dargush, "Passive energy dissipation systems in structural engineering", John Wiley & Sons, New York, 1997.

2

E. Matta, "Mass-uncertain tuned mass dampers for the dynamic protection of buildings", PhD Thesis, Polytechnic Institute of Turin, Turin, 2006.

3

N. Hoang, P. Warnitchai, "Design of multiple tuned mass dampers by using a numerical optimizer", Earthquake Engineering and Structural Dynamics, 34, 125-144, 2005. doi:10.1002/eqe.413

4

J.N. Yang, A.K. Agraval, B.Samali, J.C. Wu, "Benchmark problem for response control of wind-excited tall buildings", Journal of Engineering Mechanics (ASCE), 130(4), 437-446, 2004. doi:10.1061/(ASCE)0733-9399(2004)130:4(437)

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