Post-grazing dynamics of a vibro-impacting energy generator

The motion of a forced vibro-impacting inclined energy harvester is investigated in parameter regimes with asymmetry in the number of impacts on the bottom and top of the device. This motion occurs beyond a grazing bifurcation, at which alternating top and bottom impacts are supplemented by a zero velocity impact with the bottom of the device. For periodic forcing, we obtain semi-analytical expressions for the asymmetric periodic motion with a ratio of 2:1 for the impacts on the device bottom and top, respectively. These expressions are derived via a set of nonlinear maps between different pairs of impacts, combined with impact conditions that provide jump discontinuities in the velocity. Bifurcation diagrams for the analytical solutions are complemented by a linear stability analysis around the 2:1 asymmetric periodic solutions, and are validated numerically. For smaller incline angles, a second grazing bifurcation is numerically detected, leading to a 3:1 asymmetry. For larger incline angles, period doubling bifurcations precede grazing bifurcations. The converted electrical energy per impact is reduced for the asymmetric motions, and therefore less desirable under this metric. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

The motion of a forced vibro-impacting incline energy harvester is investigated in parameter regimes with asymmetry in the number of impacts on the bottom and top. Semi-analytical expressions for asymmetric periodic motion with a ratio of 2:1 for impacts on the device bottom and top are obtained, derived through nonlinear maps and impact conditions. Bifurcation diagrams and linear stability analysis validate the numerical solutions for asymmetric motions with different incline angles.