A state space technique for modal identification of coupled structure–tuned mass damper systems from vibration measurement

Modal properties of the primary structure and tuned mass dampers are basic parameters for in situ tuned mass damper frequency tuning and periodic condition assessment of the structure–tuned mass damper system. In this study, a state space technique is developed for identifying the respective modal properties of structure and tuned mass damper device from the dynamic responses of the coupled structure–tuned mass damper systems. The coupled structure–tuned mass damper system is represented by a reduced two-degree-of-freedom model which characterizes the coupled dynamics of the structural mode under control and tuned mass damper. A simple expression is derived for calculating the respective modal properties of the structural mode and tuned mass damper from the modal properties of the coupled two-degree-of-freedom model. Stochastic subspace identification is employed to estimate the modal properties of the combined system from ambient or free vibration responses. Numerical simulation of two structures and experimental validation of a laboratory steel frame equipped with a tuned mass damper are carried out to verify the proposed method. It is shown the proposed method successfully identifies the modal properties of both the structural mode under control and the tuned mass damper. Compared to the ambient vibration data, the identification results are superior when using the free decay responses. When the tuned mass damper is not perfectly tuned to the primary structure, much accurate identification results can be obtained, especially for the damping ratios of the primary structure and the tuned mass damper