Coupled optimization of tuned-mass energy harvesters accounting for host structure dynamics

A tuned-mass electromagnetic energy harvester mounted on a vibrating structure is studied here, accounting for the dynamic coupling between harvester and host structure. The latter is modeled as a modal mass-spring-dashpot system, whereas the harvester device is composed of an electromagnetic transducer and a tunable secondary mass-spring-dashpot system. A thorough analytical coupled optimization of the harvested power with respect to the harvester components is presented here. Closed-form design formulas are supplied for the optimal values of the electromagnetic damping coefficient and tuning frequency, as functions of the excitation frequency, mass ratio, and mechanical damping coefficients. The optimized parameters yield a wide effective harvesting bandwidth when proper values of the mass ratio and device mechanical damping are chosen. It is shown that neglecting in the design process the dynamic coupling between harvesting device and vibrating host structure, that is, treating the latter as a mere vibration source as generally assumed in the literature, leads to a significant degradation of the harvesting performance.