Post-grazing dynamics of a vibro-impacting energy generator

Larissa Serdukova, PDRA in Mathematics of Planet Earth – Project TiPES, will be presenting ‘Post-grazing dynamics of a vibro-impacting energy generator’ as part of the University of Bath’s AIMS seminar series on Tuesday 9th February at 1.15pm.

Zoom Meeting
https://bath-ac-uk.zoom.us/j/98901674720?pwd=VXFac3Vqc1o2SU85WG9Gc29EQ
Meeting ID: 989 0167 4720
Passcode: 641774

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.