Keywords: wind control, tuned mass damper, bidirectional tuning, rolling-pendulum bearing, non-holonomic mechanics, non-linearity.

In recent years, light-weight and high-strength materials have been widely used in the construction of high-rise buildings. These structures generally have flexible and low damping characteristics and are therefore susceptible to vibration problems due to wind loads. To reduce wind-induced response of tall structures, the passive tuned mass damper (TMD) has been applied since the 1970s to tall buildings, towers and chimneys, proving a simple, inexpensive and effective device.

In most installations in buildings, the damper mass consists of metal or concrete blocks, having no purpose but the structural one. Some applications exist worldwide in which TMDs have been engineered without introducing additional weight, instead relying on masses already available atop the building, such as water tanks. Bringing such concept to its extremes, the author already proposed to turn any available masses already present in buildings into TMDs, including those that vary with time [1].

Since a varying mass implies a varying natural frequency and thus a loss of the optimal tuning (mistuning) for a TMD of the translational type, a pendulum arrangement is commendable since it is characterized by a mass-independent natural frequency and consequently by a greater robustness.

The current pendulous arrangements are incapable of simultaneously tuning the vibration absorber to the structure in both the horizontal directions. In this paper, a new rolling-pendulum TMD, the BTPVA is presented which can attain bidirectional tuning using an innovative three-dimensional rolling surface.

Unlike existing pendulum configurations, such as the axial-symmetrical ball absorber [2], the BTPVA can use the same rolling mass to simultaneously control two distinct natural frequencies of the hosting structure along two mutually orthogonal axes, ensuring cost-saving and compactness. These advantages, together with the further merit of keeping the tuning under mass variations, make the BTPVA the ideal solution for implementing the aforesaid concept of a mass-uncertain TMD. In this respect, the robustness against mass variations, already proven significant in seismic applications, becomes crucial in wind applications for high-rise buildings, where the small mass ratios increase sensitivity to mistuning.

To characterize the BTPVA, first a thorough non-linear model is derived in this paper using Appel's non-holonomic approach, subsequently a linearized model is deduced, which points out the motion uncoupling capabilities of the device and simplifies its optimization. The basic design procedure is demonstrated on a tall building structure equipped with a BTPVA for wind-induced acceleration response reduction. Through numerical simulations under both head- and cross-wind loads, it is shown that, even using small mass ratios, the BTPVA can significantly reduce accelerations with limited strokes, therefore allowing for compact, low-cost rolling-pendulum bearings. The BTPVA works well inside the linear domain of small angular displacements.

1

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

2

M. Pirner, "Actual behaviour of a ball vibration absorber", Journal of Wind Engineering and Industrial Aerodynamics, 90, 987-1005, 2002. doi:10.1016/S0167-6105(02)00215-5

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