Optimal solutions for enhanced TMDs with tuned-inerter-based dampers to minimize acceleration responses

Emerging Tuned Mass Dampers (TMDs) enhanced by tuned inerter dampers (TMD-TIBDs) offer substantial advantages over traditional TMDs in suppressing resonant responses. However, studies that focus on the optimal design of TMD-TIBDs with acceleration amplitude, crucial for comfort design, as the primary objective remain scarce, as do investigations into their potential for mass reduction in engineering applications. To address these gaps, this study derives optimal parameters for both undamped and damped single-degree-of-freedom (SDOF) structures under harmonic excitation, using fixed-point theory and numerical optimization to minimize acceleration. Results show that the proposed design achieves the optimal acceleration frequency response, whereas displacement-based design parameters fail to attain the same performance. Furthermore, TMD-TIBD can reduce the required tuned mass by up to 40 % in low-damping structures, while TMD-TIBD reduces mass by over 30 % at worst, albeit with a 1.5–1.7 fold increase in mass stroke. In a nine-story building, TMD-TIBD reduces the tuned mass by 40 % while effectively suppressing resonant acceleration under harmonic loading. For the analyzed 9-DOF structure under wind and seismic excitations, a 25 % reduction in tuned mass is feasible at small tuned mass ratios (μ<0.02[jls-end-space/]). The observed decrease in the mass-reduction ratio is attributable to changes in the participation of the targeted mode, moreover, the achievable mass-reduction ratio decreases as μ increases. These findings demonstrate that lightweight TMD-TIBD can provide control effects similar to larger-mass TMDs, although increased mass stroke warrants careful consideration. Overall, this study both advances the understanding of TMD-TIBDs’ mass reduction effects and informs optimal design strategies for minimizing acceleration in practical engineering contexts.