  A wideband vibration energy harvester with multiple nonlinear forces is
investigated. The nonlinearities are due to repulsive magnets and hardening
springs, which gives rise to multistabilities between a number of energy
branches. Not all branches are accessible by a simple up or down sweep of the
driving frequency and in particular the highest energy branch is often hidden,
requiring a suitable frequency schedule to be accessed. Detailed theoretical
understanding of the energy branch structure along with robust experimental
methods are essential for characterizing each of the energy branches to enhance
the energy output from such vibration energy harvesting system. We introduce a
graphical representation in the form of eye diagrams based on time-resolved
measurements of acceleration and output voltage to study the dynamical features
of the different branches. This generic approach allows us to optimize the
design, which results in 1.3mW of power generated at 1g over 44Hz frequency
bandwidth while maintaining a small footprint of $1.23 cm^3$. The energy
conversion ratio of the energy harvester at 120Hz drive frequency is 0.52 for
the high energy branch.
