Effects of non-linear stiffness on performance of an energy harvesting device

Abstract

Vibration-based energy harvesting devices have received much attention over the past few years due to the need to power wireless devices in remote or hostile environments. To date, resonant linear generators have been the most common type of generators used in harvesting energy for such devices. Simple tuning and modelling methods make it a more favourable solution theoretically if not practically. This thesis considers the limitations of resonant linear devices and investigates two non-linear generators to see if they can outperform the linear devices in certain situations. So far, in most of the literature, the energy harvester is assumed to be very small dynamically compared to the source so the source is not affected by the presence of the device. This thesis considers how the dynamics of the source is affected by the device if its impedance is significant compared to the source. A tuning condition for maximum power transfer from the source to the device is derived. This tuning condition converges to the one presented in most of the literature when the impedance of the device is assumed to be very small compared to that of the source i.e. tuned so that the natural frequency of the device equals the excitation frequency. For the case when the impedance of the device has a negligible effect on the source, the performance of the device is only limited to a narrow frequency band and drops off rapidly if mistuned. To accommodate the mistuning limitations, new types of generators are proposed mainly by using a non-linear mechanism.These mechanisms are made up of a non-linear spring connected together with a mass and a linear viscous damper i.e. the energy harvesting component. The analysis of the fundamental performance limit of any non-linear device compared to that of a tuned linear device is carried out using the principal of conservation of energy. The analysis reveals that the performance of a non-linear device in terms of the power harvested is at most 4x greater than that of a tuned linear system and is strongly dependent upon the type of the non-linearity used. Two types of non-linear mechanisms are studied in this thesis. The first one is a non-linear bi-stable mechanism termed a snap-through mechanism which rapidly moves the mass between two stable states. The aim is to steepen the displacement response curve as a function of time which results in the increase of velocity for a given excitation, thus increasing the amount of power harvested. This study reveals that the performance of the mechanism is better than a linear system when the natural frequency of the system is much higher than the excitation frequency. The study also shows that the power harvested by this mechanism rolls off at a slower rate compared to that of the linear system. Another non-linear mechanism described in this thesis uses a hardening-type spring. The aim of this mechanism is to provide a wider bandwidth over which the power can be harvested. This thesis presents numerical solutions and approximate analytical solutions for the bandwidth and effective viscous damping of a non-linear device employing a hardening-type stiffness. Unlike the linear system, in which the bandwidth is only dependent on the damping ratio, it is found that the bandwidth of the nonlinear device depends on both the strength of the nonlinearity and the damping ratio. Experimental results are presented to validate the theoretical results. This thesis also investigates the benefits of the non-linear device for a low frequency and high amplitude application using the measured vibration inputs from human motion such as walking and running. The effect of harmonics on the power harvested is also studied. Numerical simulations are carried out using measured input vibrations from human motion to study the best placement of the natural frequency of the device across the range of harmonics