This paper proposed multi-resonant electromagnetic (EM) shunt dampers and investigated the optimal designs and performances of shunt circuits for a single DOF primary system. The circuits are arranged in parallel or series based on the analogy of multiple tuned mass dampers (TMDs). The objective is to minimize the root-mean-square (RMS) vibration of the primary system subjected to random base excitations. For single resonant EM shunt damper, closed-form solutions of optimal system parameters are obtained. For multi-resonant EM shunt dampers, the system parameters are numerically optimized. The vibration suppression performance of multi-resonant EM shunt dampers are compared with double-mass TMDs under the same 5% total stiffness ratio. It shows that the parallel shunt damper can achieve slightly better performance than parallel TMDs while the series shunt damper behaves differently from series TMDs. The optimal result of the series shunt damper will be the same as the single resonant shunt damper. It is also found that the multi-resonant EM shunt damper is much more sensitive to the capacitance than the resistance in the shunt circuits.

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