This paper studies the performance of an electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI) in terms of simultaneously suppressing unwanted vibration and harvesting energy in a vibrating building. The ERS-TMDI is attached to a building, which is subjected to an earthquake excitation. An inerter is connected between the TMD and the ground. The electromagnetic transducer and associated circuit, which replaces the viscous damping in the classical tuned mas-damper (TMD), is assumed to be an ideal transducer shunted with a resistor, an inductor, and a capacitor (RLC) circuit. Two RLC circuit configurations are investigated: one in series and another in parallel. The governing equations of motion are presented and H2 optimization technique is employed to derive explicit expressions for the optimal mechanical tuning ratio, electrical damping ratio, electrical tuning ratio, and electromagnetic mechanical coupling coefficient. The validity of the obtained closed-form expressions is examined using Matlab optimization toolbox. Parametric studies are carried out to investigate the effect of the mass and inertance ratios on the obtained optimal parameters. Numerical examples are also conducted to demonstrate the role of key design variables on vibration mitigation and energy harvesting performances. Also, the performance of a parallel RLC circuit configuration is compared to that of a series configuration.

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