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. vii