Seismic control of a SDOF structure through electromagnetic resonant shunt tuned mass-damper-inerter and the exact H2 optimal solutions

This paper proposes a novel inerter-based component dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To analyze the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are developed. The h(2) norm performances of the ERS-TMDI, whose aim is to minimize the root mean square (RMS) value of structure damage under random ground acceleration excitation, are introduced in comparison with the energy-harvesting series electromagnetic tuned mass dampers (ERS-TMDs), tuned mass-damper-inerter (TMDI) and the classical tuned mass damper (TMD). The closed-form solutions, including the optimal mechanical tuning ratio, the optimal electrical damping ratio, the optimal electrical tuning ratio and the optimal electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to both the classical TMD and the ERS-TMD systems for protection from structure damage. Specifically, from the frequency-domain analyses, a case study is performed to illustrate the effectiveness, robustness of the ERS-TMDI and the sensitivity to the parameter changes. From the time-domain analyses, four types of earthquakes are studied to demonstrate the performances of vibration suppression. National Key Basic Research Scheme of China (973 Program) [2015CB057702]; National Natural Science Foundation of China [51508185, 51378203]; Natural Science Foundation of Hunan Province of China [2015JJ3073]; China Scholarship Council This work was supported by National Key Basic Research Scheme of China (973 Program) under Grant 2015CB057702, National Natural Science Foundation of China under Grant 51508185 and 51378203, and Natural Science Foundation of Hunan Province of China under Grant 2015JJ3073. The author Hongxin Sun is also grateful to the financial support from China Scholarship Council to conduct research as a visiting scholar in Lei Zuo's Lab at Virginia Tech.