Distributed parameter modelling of cutout 2-DOF cantilevered piezo-magneto-elastic energy harvester

Energy harvesters play the vital role in replacing/ recharging the electrochemical batteries in low-power electronic devices. Non-linear piezoelectric energy harvesters generate electrical power from broadband frequency spectrum using ambient vibrational sources. Non-linear cutout 2- degree of freedom (DOF) piezo-magneto-elastic (PME) energy harvester has been proposed to enhance the bandwidth where two close resonant peaks are achieved using magnetic interaction. In this paper, the novel theoretical distributed parametric model of cutout 2-DOF energy harvester is presented which can predict the dynamic behavior of the linear (without magnetic force) and non-linear monostable configurations accurately. The closed-form analytical solutions are derived for the harvested electrical responses and displacements using forcing function, forward and backward coupling factors through Extended Hamilton principle, Galerkin approach, and Euler-Lagrange equations. Specifically, the static displacements and tuned resonant frequencies are obtained as a function of the initial distance between the two magnets in attractive and repulsive configurations. The theoretical findings are validated with COMSOL simulation results and experimental data. The comparison among theoretical, finite-element, and experimental results show that the developed model of cutout 2-DOF piezo-magneto-elastic energy harvester can accurately predict the response for linear and non-linear monostable configurations