Design optimisation and performance evaluation of single and multiple tuned mass dampers controlling multiple degrees of freedom structures

Structures with high flexibility and low inherent damping are susceptible to dynamic excitations such as traffic, wind and earthquakes. To ensure their stability, vibration control systems such as tuned mass dampers (TMDs) are used to reduce excessive vibrations. In this paper, a novel numerical optimisation criterion is proposed for identifying the appropriate TMD parameters, specifically stiffness and damping, to improve vibration attenuation. The first part focuses on the optimisation of single TMDs, where the proposed numerical criterion is compared with three established optimisation approaches from the literature. The optimum analytical parameters of three approaches for single degree of freedom (SDOF) structures are extended to multiple degrees of freedom (MDOF) systems through modal transformation. Results show that the proposed criterion takes into account the main structure’s higher modes, enabling reduction of the total response instead of targeting a single mode's response. The second part extends the analysis to multiple TMDs for MDOF systems. Results show that using multiple TMDs enhances the ability to tune frequencies to different structural vibration modes, significantly improving energy dissipation and vibration control. The performance of optimally tuned multiple TMDs was assessed with real earthquake records, showing their effectiveness in dissipating energy and reducing vibrations.