Keywords: seismic protection, passive control, robustness, optimization, tuned mass damper, roof-garden.

Commonly used for mitigating wind- and traffic-induced vibrations in flexible structures [1], passive tuned mass dampers (TMDs) are rarely applied to the seismic control of buildings [2,3], their effectiveness to impulsive loads being conditional upon adoption of large mass ratios [4]. Instead of recurring to cumbersome metal or concrete devices, this paper suggests meeting the conditions by turning to TMDs non-structural masses that are sometimes available atop buildings. In particular, a roof-garden TMD looks like a very promising solution that is capable of combining environmental and structural protection into one tool. Namely, this new device is conceived as a traditional tuned absorber but for its mass, which consists of a tank filled with planted soil.

Unfortunately, the amount of the planted mass is generally variable with the soil water content, the value of the variable load and the natural vegetation growth, so that the roof-garden TMD is a special example of the broader class of mass-uncertain TMDs (MUTMDs), therefore prone to mistuning and control loss [5].

In this study, robust analysis and synthesis against mass variations are applied to two types of MUTMDs: the translational TMD (TTMD) and the (rolling-)pendulum TMD (PTMD), under varying intensities of ground motion. At low intensity, both types behave linearly and the PTMD proves more robust, its natural period being mass-independent. At a higher intensity, the TTMD remains linear whilst the PTMD response becomes non-linear and dependent on the shape of the rolling path, herein assumed of the circular type.

Through simulations under harmonic and recorded ground motions, a trade-off between the TTMD and the PTMD is outlined depending on the expected mass uncertainty and input intensity, showing that in typical applications MUTMDs can become a viable alternative to traditional TMDs, compensating for a certain reduction of effectiveness with the advantage of flexibility and multitasking. A possible implementation of a roof-garden TMD for the reduction of the seismic response of a multi-storey building structure recently completed in Central Italy is described and its control efficacy numerically demonstrated.

1

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

2

G. Chen, J. Wu, "Optimal placement of multiple tuned mass dampers for seismic structures", Journal of Structural Engineering, 127(9), 1054-1062, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:9(1054)

3

T. Pinkaew, P. Lukkunaprasit, P. Chatupote, "Seismic effectiveness of tuned mass dampers for damage reduction of structures", Engineering Structures, 25, 39-46, 2003. doi:10.1016/S0141-0296(02)00115-3

4

N. Hoang, Y. Fujino, P. Warnitchai, "Optimal tuned mass damper for seismic applications and practical design formulas", Engineering Structures (accepted May 2007, in press). doi:10.1016/j.engstruct.2007.05.007

5

E. Matta, A. De Stefano, "Robust design of mass-uncertain rolling-pendulum TMDs for the seismic protection of buildings", Mechanical Systems & Signal Processing (accepted August 2007, in press). doi:10.1016/j.ymssp.2007.08.012

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