Investigating criteria for the optimization of single and multiple tuned mass dampers

Tuned mass dampers (TMDs) are commonly used to mitigate undesirable structural vibrations caused by wind or earthquakes due to their effectiveness, cost efficiency, and ease of installation. Selecting the optimal values for TMD parameters, such as stiffness and damping, is critical for achieving the best performance. This study presents a novel classification framework for optimisation criteria in TMD design, dividing them into two categories: (1) steady-state response of the primary system, focusing on dynamic amplification, and (2) pole localisation for coupled systems (main structure + multiple TMDs (MTMDs)). Two case studies (single TMD and MTMDs) are presented to investigate optimisation criteria using a single degree of freedom primary system under base excitation. Numerical simulations assess the performance and robustness of these optimised configurations. Sensitivity analysis demonstrates that frequency-based criteria are less affected by uncertainties in optimal TMD parameters than pole-related criteria. The frequency-based criteria, which minimises vibration energy, demonstrates improved performance under seismic excitation and reduced sensitivity to changes in primary structural parameters. Frequency-based criteria enhance system efficiency, particularly with MTMDs, while pole-related criteria lead to higher damping ratios, challenging design feasibility. These findings highlight the effectiveness of frequency-based criteria in optimising TMD performance and structural robustness.