Fundamental limits to nonlinear energy harvesting

Ease of miniaturization, and less or no maintenance, among other advantages, have pushed towards replacement of conventional batteries with energy harvesters in particular, vibratory energy harvesters. In the recent years, nonlinearity has been intentionally introduced into the otherwise linear energy harvesters in the hope of increasing the frequency bandwidth and power density. However, fundamental limits on the harvestable energy of a harvester subjected to an arbitrary excitation force is yet unknown. Understanding of these limits is not only essential for assessment of the technology potential, but also provides a broader prospective on the current harvesting mechanisms and guidance in their improvement. Here we derive the fundamental limits on output power of an ideal energy harvester, and develop an analysis framework for simple computation of this limit for more sophisticated set-ups. We show that the optimal harvester maximizes the harvested energy through a mechanical analogue of 'buy low-sell high' strategy. Inspired by this strategy we propose a novel concept of latch-assisted harvesting that is shown to harvest energy more efficiently than its linear and bistable counterparts over a wider range of excitation frequencies and amplitudes.