Measuring inherent structural damping of structure-TMD systems

A practical method is proposed to enable the inherent structural damping of structures equipped with tuned mass dampers (TMDs) to be quantified. While the traditional random decrement technique cannot be applied to structure-TMD systems, a modified version is presented which accommodates the energy transfer between the structure and TMD. It is shown that cross-correlation functions can be used to determine the random decrement signatures of the structural and TMD responses. Linear regression is combined with an energy balance approach to estimate the inherent structural damping. The total effective damping of the structure is then estimated by using an existing method to predict the added effective damping provided by the TMD. Numerical simulations reveal that the method predicts the inherent structural damping with acceptable accuracy if the duration of the measured response captures at least two thousand structural oscillation cycles, which corresponds to 3–6 h of data for most tall buildings. The method is most accurate when the inherent structural damping is relatively high, and the TMD mass ratio is relatively low. The method is applied to data collected from an anonymous super-tall building equipped with a TMD. The TMD is found to increase the effective damping of the tower from 1.0% to 3.0% of critical. These damping values are supported by measurements conducted when the TMD was briefly locked from moving, and also by theoretical predictions using the assessed dynamic properties of the structure and TMD.