Optimization of Viscoelastic Tuned Mass Damper Systems Subjected to Coloured Excitations

In recent decades, there has been growing interest in innovative vibration control strategies to improve the structural reliability of buildings and civil structures against earthquakes, windstorms and other dynamic excitations. One of the most effective methods for reducing dynamic responses is the implementation of tuned mass dampers (TMDs), which leverage the interaction between primary and secondary subsystems. Most optimization procedures in the literature use a Kelvin–Voigt (KV) link to model this interaction. Still, when frequency-dependent devices like viscoelastic dampers and isolation bearings are involved, more refined models should be adopted. This paper extends existing optimization approaches by using the standard linear solid (SLS) model to more accurately represent the connection between the dynamic absorber and the primary structure. We also emphasize the importance of accounting for the damping in the primary system, which is often overlooked but can significantly affect the overall primary–secondary dynamic interaction. Additionally, we explore the sensitivity of optimal TMD parameters to multi-chromatic excitations, which are typically neglected, using the Kanai–Tajimi model to simulate realistic seismic accelerograms. To validate our approach, we performed time-history analyses on lumped-mass models using a selection of natural seismic events, comparing the uncontrolled configurations with KV- and SLS-type TMDs. Our results demonstrate that incorporating the frequency content of seismic inputs is crucial for optimizing the structural control system and show the potential and the effectiveness of our analytical/numerical strategy in facing general viscoelastic TMD design problems considering any kind of seismic excitation