Optimal tuning and assessment of non-grounded regenerative tuned mass damper inerter (RE-TMDI) configurations for concurrent motion control and energy harvesting

This paper addresses the optimal tuning and numerical performance assessment of regenerative tuned mass damper inerters (RE-TMDIs) in three different configurations with non-grounded inerters attached to cantilevered primary structures under Gaussian white noise base excitation. The studied RE-TMDI configurations behave linearly and differ in the placement of the electromagnetic motor (EM), modelled as viscous damping element used for transforming kinetic energy to electricity, with respect to the inerter element. The primary structure is modelled as a linear damped generalized single-degree-of-freedom system, while a connectivity index is used to account for the location of the two RE-TMDI attachment points to the primary structure. A bi-objective optimization problem formulation is adopted and numerically solved for determining optimal RE-TMDI stiffness and EM damping coefficients that minimize primary structure displacement variance and maximize the available energy for harvesting by the EM. Parametric numerical results are reported for different RE-TMDI configurations, connectivity, inertance, secondary mass ratio and relative weighting between the two optimal design objectives. These results demonstrate that improved energy generation and vibration suppression is concurrently achieved with increasing inertance and/or increasing the distance of the host structure locations where the RE-TMDI is attached to. Recommendations are provided establishing the most advantageous RE-TMDI configuration.