Rachel Kuske: Computer-assisted global analysis of non-smooth impact dynamics inspired by energy...

(09 octobre 2024/October 09, 2024) Série de conférences de la Chaire Aisenstadt.
www.crmath.ca/...
Rachel Kuske: Computer-assisted global analysis of non-smooth impact dynamics inspired by energy harvesting
Abstract: We discuss a novel return map approach for studying the global dynamics of a vibro-impact (VI) pair, that is, a ball moving in a harmonically forced capsule. Results are relevant for recent designs of VI-based energy harvesters and nonlinear energy transfer, and hold promise for other non-smooth systems. Computationally efficient short-time realizations are based on “words” that represent key impact sequences and divide the state space according to different dynamics. The resulting maps define surfaces that illuminate weak and strong attraction to certain periodic and complex states of interest for energy output. A small collection of reduced piece-wise polynomial approximations for the maps on these surfaces yields a composite map. They capture transients and focus the analysis on maps (surfaces) with attracting properties, confirming and complementing the bifurcation structure of the full system. Valuable for cobweb analysis, this framework inspires auxiliary maps based on the extreme bounds of the maps, yielding global dynamics of energetically favorable states. We apply this framework to understand how the surfaces explain stochastically enhanced grazing and bi-stability when the scales of noise and attraction compete. .