Natural frequency coalescing and amplitude dependent damping in the wind-excited response of tall buildings

During the analysis of data from the full scale monitoring of the dynamic response of tall buildings, it has been observed that under certain conditions the fundamental natural frequencies of the structure can coalesce for moderate wind excitation. Together with this phenomenon, the dependency of damping on the amplitude of the response was also noted. Recently, a detailed description of this amplitude dependency has been made possible by a new generation of concept-based damping models, developed following the boom in the collection of full scale data from the monitoring of tall buildings. In light of this new knowledge, this paper investigates the possibility that the amplitude dependency of damping could be at the root of the frequency coalescing phenomenon. To this end, a concept-based probabilistic damping model is coupled with a reduced order two-degrees-of-freedom system that reproduces the two coalescing modes of a building. For this system, the analytical time-invariant conditions under which the frequency coalescence can occur are firstly identified. Then, the inherent variability of the amplitude dependent damping, described by the concept-based model, is considered as a means for instantaneously satisfying the aforementioned conditions. By exciting the reduced system through experimentally determined wind loads, the direct observation of the phenomenon-through time-frequency wavelet analysis-is achieved.