Analytical Solutions to H2 and Hâˆ‍ Optimizations of Resonant Shunted Electromagnetic Tuned Mass Damper and Vibration Energy Harvester

Abstract

When optimized, tuned mass dampers (TMDs) can effectively mitigate the vibration of the primary structure, because additional resonance and damping are introduced by the auxiliary massspringdamper system. Similar effect can be realized without auxiliary mass when an electromagnetic transducer shunt with the RLC resonant circuit is placed between the primary structure and the base. This paper is to analytically optimize the parameters of the RLC circuits for vibration mitigation. Both H2 and Hâˆ‍ optimization criteria are investigated, which are to minimize the rootmeansquare (RMS) vibration under random excitation and the peak magnitude in the frequency domain, respectively. The concise closedform solutions of the optimal parameters are then summarized together with the ones obtained the using fixedpoint method, for practical implementation convenience. The H2 and Hâˆ‍ optimizations of energy harvesting are also discussed in this paper. Furthermore, we also investigate the sensitivity of system performances to the tuning parameter changes of the electromagnetic shunt circuit.