The fluctuation-dissipation theorem used as a proxy for damping variations in real engineering structures

The damping ratio and the resonance frequency represent relevant health indicators in structural health monitoring, and they are key parameters in the design of buildings. The combination of two modal parameters (i.e., damping, frequency) is reported to vary in time due to changes in environmental conditions, and with damage to the structure and dynamic loading. Amplitude dependence of the damping and frequency parameters has also been reported for strong loading, such as strong winds. However, none of these reasons can explain the much higher fluctuations of the damping values compared to the resonance frequency in the amplitude range of natural ambient vibrations. The objective here is to investigate if any amplitude dependence in this lower range of loading can explain the observed differences in the scattering of these two modal parameters. To do so, the first approach consists of a study of vertical clamp-free beams made out of different materials. Secondly, the observations and interpretations obtained are scaled up to buildings under continuous monitoring. Finally, we consider the fluctuation-dissipation theorem to explain these uncommon results.