Optimization of Nonlinear Tuned Mass Dampers Under Stationary and Nonstationary Excitations

Nonlinear tuned mass dampers, and in particular hysteretic absorbers, have been increasingly investigated as alternatives to linear viscoelastic devices for vibration control under variable and uncertain dynamic loading conditions. Rather than assuming an a priori superiority over linear tuned mass dampers, this work aims to discuss under which conditions and operating scenarios hysteretic mass dampers may provide advantages, and to clarify the conceptual meaning of optimality and robustness in the presence of nonlinear dissipation mechanisms. The hysteretic behavior of the absorber is described through an enhanced Bouc–Wen model with pinching, allowing for amplitude-dependent stiffness and energy dissipation. The response of the hysteretic tuned mass damper is first analyzed under periodic stationary excitations, where comparisons with linear absorbers are used to identify the regimes in which performance improvements may occur. In this context, different optimization approaches are discussed, highlighting the excitation-dependent nature of optimal configurations in nonlinear systems. A sensitivity analysis is then performed to assess uncertain structural parameters, such as mass and damping. Nonstationary seismic excitations are considered, for which the limitations of frequency-based optimization approaches are highlighted and time-domain performance measures become essential. Overall, a systematic interpretation of performance, optimality, sensitivity, and robustness is achieved for hysteretic tuned mass dampers, offering insights into their potential role as robust vibration control devices in practical engineering applications.