Control of Oscillators, Temporal Homogenization, and Energy Harvest by Super-Parametric Resonance

Applied and Computational Mathematics Seminar
Monday, April 6, 2015 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech School of Math.
We show how to control an oscillator by periodically perturbing its stiffness, such that its amplitude follows an arbitrary positive smooth function. This also motivates the design of circuits that harvest energies contained in infinitesimal oscillations of ambient electromagnetic fields. To overcome a key obstacle, which is to compensate the dissipative effects due to finite resistances, we propose a theory that quantifies how small/fast periodic perturbations affect multidimensional systems. This results in the discovery of a mechanism that reduces the resistance threshold needed for energy extraction, based on coupling a large number of RLC circuits.