Nonlinear Energy Harvesting

The concept of harvesting electrical energy from ambient vibration sources has been
a popular topic of research in recent years. The motivation behind this research
is largely due to recent advancements in microelectromechanical systems (MEMS)
technology - specifically the construction of small low powered sensors which are
capable of being placed in inaccessible or hostile environments. The main drawback
with these devices is that they require an external power source. For example, if
one considers large networks of low powered sensors (such as those which may be
attached to a bridge as part of a structural health monitoring system) then one can
envisage a scenario where energy harvesters are used to transfer the vibration energy
of the bridge into electrical energy for the sensors. This would alleviate the need for
batteries which, in this scenario, would be difficult to replace.
Initial energy harvester designs suffered from a major flaw: they were only able to
produce useful amounts of power if they were excited close to their resonant frequency.
This narrow bandwidth of operation meant that they were poorly suited
to harvesting energy from ambient vibration sources which are often broadband
and have time dependent dominant frequencies. This led researchers to consider
the concept of nonlinear energy harvesting - the hypothesis that the performance
of energy harvesters could be improved via the deliberate introduction of dynamic
nonlinearities. This forms the main focus of the work in this thesis.
The first major part of this work is concerned with the development of an experimentally
validated physical-law based model of an electromagnetic energy harvester
with Duffing-type nonlinearities. To this end, a self-adaptive differential evolution
vi
(SADE) algorithm is used in conjunction with experimental data to estimate the
parameters needed to accurately model the behaviour of the device. During this
investigation it is found that the response of the energy harvesting device in question
is very sensitive to the effects of friction. Consequently, a detailed study is
undertaken with the aim of finding whether the model performance could be improved
by accounting for this complex nonlinear phenomenon. After investigating
several different friction models, a reliable and extensively validated digital model
of a nonlinear energy harvesting device is realised. With the appropriate equations
of motion identified, analytical approximation methods are used to analyse the response
of the device to sinusoidal excitations.
The motivation for the second main part of this work arises from the fact that ambient
excitations are often stochastic in nature. As a result, much of the work in this
section is directed towards gaining an understanding of how nonlinear energy harvesters
respond to random excitations. This is an interesting problem because, as a
result of the random excitation, it is impossible to say exactly how such a device will
respond - the problem must be tackled using a probabilistic approach. To this end,
the Fokker-Planck-Kolmogorov (FPK) equation is used to develop probability density
functions describing how the nonlinear energy harvester in question responds to
Gaussian white noise excitations. By conducting this analysis, previously unrecognised
benefits of Duffing-type nonlinearities in energy harvesters are identified along
with important findings with regards to device electrical optimisation. As for friction
effects, the technique of equivalent linearisation is employed alongside known
solutions of the FPK equation to develop expressions approximating the effect of
friction on randomly excited energy harvesters. These results are then validated
using Monte-Carlo methods thus revealing important results about the interaction
between Duffing-type and friction nonlinearities.
Having investigated sinusoidal and random excitations, the final part of this work
focuses on the application of nonlinear energy harvesting techniques to real energy
harvesting scenarios. Excitation data from human walking motion and bridge vibrations
is used to excite digital models of a variety of recently proposed nonlinear
energy harvesters. This analysis reveals important information with respect to how
well energy harvesting solutions developed under the assumption of Gaussian white
noise excitations can be extended to real world scenarios.