Seismic Optimization for Hysteretic Damping-Tuned Mass Damper (HD-TMD) Subjected to White-Noise Excitation

The hysteretic damping tuned mass damper (HD-TMD) is composed of a spring element, a hysteretic damping (HD) element, and a mass. The HD force is proportional to the displacement of the tuned mass damper (TMD). Recently, the application of HD-TMD has emerged, but its optimal design is still lacking. To fill this academic gap, numerical solutions for optimal parameters of HD-TMD subjected to white-noise excitation were obtained based on the H₂ optimization criterion. Performance balance optimization with a weighting factor was carried out to improve the response of a structure with the HD-TMD system. A set of earthquake records and harmonic excitations were conducted to prove the effectiveness of the optimal numerical solutions and the performance balance design. It was found that the performance of the HD-TMD is slightly better than that of the traditional optimized TMD. As a real TMD application of HD-TMD, the variable friction pendulum TMD (VFP-TMD) was selected to experience earthquakes with the proposed optimal methods. Results showed that the optimal solutions provided the best performance but raised the problem of difficulty in maintaining linearity with a large displacement. Nevertheless, the performance balance design helped reduce this defect and provided impressive seismic mitigation capacity. Compared with the optimal numerical solution results, the performance balance design demonstrated 2.847% of loss in the maximum structural displacement reduction rate and 3.709% of loss in the root mean square reduction rate during the earthquake-excited period, respectively.