  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.
