Optimal parameters of rotational inerter double tuned mass damper for different excitation and response combinations

The Rotational Inerter Double Tuned Mass Damper (RIDTMD) is a vibration mitigation device derived by substituting the damping element in a conventional Tuned Mass Damper (TMD) with an inerter-based system. Under the same tuned mass ratio condition, RIDTMD has better vibration damping effectiveness than TMD. However, it is difficult to obtain the analytical solution of RIDTMD optimal parameters, which severely limits the application of RIDTMD in the engineering field. To address this problem, this study utilizes the Genetic Algorithm-Nonlinear Programming (GA-NLP) algorithm to obtain the analytical solution of RIDTMD, and the optimal parameters formulation of RIDTMD is given by numerical fitting technique. Under random force excitation, the optimal parameters of the RIDTMD are obtained based on optimization criteria $H_2$ and $H_{\infty }$, with the displacement and acceleration of primary structure serving as the optimization objectives, respectively. The same method is used to obtain the optimal parameters of RIDTMD under base displacement excitation. Finally, the validity of the optimal parameters of RIDTMD was verified through frequency-domain analysis and time-domain analysis.