The Convergence of Parametric Resonance and Vibration Energy Harvesting

Energy harvesting is an emerging technology that derives electricity from the ambient environment in a decentralised and self-contained fashion. Applications include self-powered medical implants, wearable electronics and wireless sensors for structural health monitoring. Amongst the vast options of ambient sources, vibration energy harvesting (VEH) has attracted by far the most research attention. Two of the key persisting issues of VEH are the limited power density compared to conventional power supplies and confined operational frequency bandwidth in light of the random, broadband and fast-varying nature of real vibration. The convention has relied on directly excited resonance to maximise the mechanical-to-electrical energy conversion efficiency. This thesis takes a fundamentally different approach by employing parametric resonance, which, unlike the former, its resonant amplitude growth does not saturate due to linear damping. Therefore, parametric resonance, when activated, has the potential to accumulate much more energy than direct resonance. The vibrational nonlinearities that are almost always associated with parametric resonance can offer a modest frequency widening. Despite its promising theoretical potentials, there is an intrinsic damping dependent initiation threshold amplitude, which must be attained prior to its onset. The relatively low amplitude of real vibration and the unavoidable presence of electrical damping to extract the energy render the onset of parametric resonance practically elusive. Design approaches have been devised to passively minimise this initiation threshold. Simulation and experimental results of various design iterations have demonstrated favourable results for parametric resonance as well as the various threshold-reduction mechanisms. For instance, one of the macro-scale electromagnetic prototypes (∼1800 cm3) when parametrically driven, has demonstrated around 50% increase in half power band and an order of magnitude higher peak power (171.5 mW at 0.57 ms−2) in contrast to the same prototype directly driven at fundamental resonance (27.75 mW at 0.65 ms−2). A MEMS (micro-electromechanical system) prototype with the additional threshold-reduction design needed 1 ms−2 excitation to activate parametric resonance while a comparable device without the threshold-reduction mechanism required in excess of 30 ms−2. One of the macro-scale piezoelectric prototypes operated into auto-parametric resonance has demon-strated notable further reduction to the initiation threshold. A vacuum packaged MEMS prototype demonstrated broadening of the frequency bandwidth along with higher power peak (324 nW and 160 Hz) for the parametric regime compared to when operated in room pressure (166 nW and 80 Hz), unlike the higher but narrower direct resonant peak (60.9 nW and 11 Hz in vacuum and 20.8 nW and 40 Hz in room pressure). The simultaneous incorporation of direct resonance and bi-stability have been investigated to realise multi-regime VEH. The potential to integrate parametric resonance in the electrical domains have also been numerically explored. The ultimate aim is not to replace direct resonance but rather for the various resonant phenomena to complement each other and together harness a larger region of the available power spectrum

Parametric resonance for vibration energy harvesting with design techniques to passively reduce the initiation threshold amplitude

A vibration energy harvester designed to access parametric resonance can potentially outperform the conventional direct resonant approach in terms of power output achievable given the same drive acceleration. Although linear damping does not limit the resonant growth of parametric resonance, a damping dependent initiation threshold amplitude exists and limits its onset. Design approaches have been explored in this paper to passively overcome this limitation in order to practically realize and exploit the potential advantages. Two distinct design routes have been explored, namely an intrinsically lower threshold through a pendulum-lever configuration and amplification of base excitation fed into the parametric resonator through a cantilever-initial-spring configuration. Experimental results of the parametric resonant harvesters with these additional enabling designs demonstrated an initiation threshold up to an order of magnitude lower than otherwise, while attaining a much higher power peak than direct resonance

An auto-parametrically excited vibration energy harvester

Parametric resonance, as a resonant amplification phenomenon, is a superior mechanical amplifier than direct resonance and has already been demonstrated to possess the potential to offer over an order of magnitude higher power output for vibration energy harvesting than the conventional direct excitation. However, unlike directly excited systems, parametric resonance has a minimum threshold amplitude that must be attained prior to its activation. The authors have previously presented the addition of initial spring designs to minimise this threshold, through non-resonant direct amplification of the base excitation that is subsequently fed into the parametric resonator. This paper explores the integration of auto-parametric resonance, as a form of resonant amplification of the base excitation, to further minimise this activation criterion and realise the profitable regions of parametric resonance at even lower input acceleration levels. Numerical and experimental results have demonstrated in excess of an order of magnitude reduction in the initiation threshold amplitude for an auto-parametric resonator (∼0.6 ms−2) as well as several folds lower for a parametric resonator with a non-resonant base amplifier (∼4.0 ms−2), as oppose to a sole parametric resonator without any threshold reduction mechanisms (10's ms−2). Therefore, the superior power performance of parametric resonance over direct resonance has been activated and demonstrated at much lower input levels.This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/I019308/1].This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.sna.2014.09.01

Review of nonlinear vibration energy harvesting: Duffing, bistability, parametric, stochastic and others

Vibration energy harvesting typically involves a mechanical oscillatory mechanism to accumulate ambient kinetic energy, prior to the conversion to electrical energy through a transducer. The convention is to use a simple linear mass-spring-damper oscillator with its resonant frequency tuned towards that of the vibration source. In the past decade, there has been a rapid expansion in research of vibration energy harvesting into various nonlinear vibration principles such as Duffing nonlinearity, bistability, parametric oscillators, stochastic oscillators and other nonlinear mechanisms. The intended objectives for using nonlinearity include broadening of frequency bandwidth, enhancement of power amplitude and improvement in responsiveness to non-sinusoidal noisy excitations. However, nonlinear vibration energy harvesting also comes with its own challenges and some of the research pursuits have been less than fruitful. Previous reviews in the literature have either focussed on bandwidth enhancement strategies or converged on select few nonlinear mechanisms. This article reviews eight major types of nonlinear vibration energy harvesting reported over the past decade, covering underlying principles, advantages and disadvantages, and application-specific guidance for researchers and designers

Slow wave ion heating and parametric instabilities in the HELIX helicon source

The primary focus of the experiments described here is to determine the mechanism responsible for intrinsic ion heating in helicon sources. Two possible mechanisms have been identified: ion Landau damping of the slow wave and parametrically driven instabilities. Consistent with ion Landau damping of the slow wave, the perpendicular ion temperatures 35 cm downstream of the RF antenna are largest when the RF frequency matches the local lower hybrid frequency; the condition at which the slow wave has a maximum in perpendicular wave number (perpendicular with respect to the applied magnetic field) due to a lower hybrid resonance. The ion temperatures also peak at the edge of the plasma where theory predicts the slow wave should have the largest amplitude and perpendicular wave number. Consistent with ion heating due to parametrically driven instabilities, parametrically driven low frequency waves are observed for the same conditions at which the ion temperatures 5 cm downstream of the RF antenna are largest. The measured characteristics of the low frequency wave suggest that the wave is an electrostatic ion acoustic wave. The electrostatic and electromagnetic features of the parametrically driven waves as a function of magnetic field and RF frequency are also presented and discussed

A parametric resonator with low threshold excitation for vibration energy harvesting

A parametric resonator for vibration energy harvesting is presented. Despite large responses from parametric resonance, two major drawbacks of parametric resonance harvesters are the high threshold excitation and narrow bandwidth. We addressed these two shortcomings by adding magnetic nonlinearity to the system. The proposed vibration energy harvester consists of two piezoelectric cantilevers beams, each with a magnetic tip. By controlling the distance between the two magnets, the threshold excitation level needed to trigger the parametric resonance decreases. Combining the softening and hardening behavior of the two magnetically coupled beams increases the frequency bandwidth. In addition, the amplitude of the response increases with the merger of the direct and parametric resonances of the two beams. We present a mathematical model of the system consisting of two lumped systems coupled by the magnetic force. The coupled governing equations are solved numerically, analytically, and are verified by experiments. Unique characteristics of wider bandwidth, larger response, and lower threshold excitation occur at the low frequency because of the added magnetic nonlinearity to the two-beam system. These properties can improve the efficiency of vibration energy harvesters

Parametric vibration of composite beams with integrated shape memory alloy elements

This research is concerned with parametric vibration in composite beam structures with shape memory alloy elements. As a precursor to this investigation, a flexible steel beam of rectangular uniform cross-section is considered with a lumped end mass under a parametric excitation. A single frequency harmonic excitation in the vertical direction is applied to the system. As an extension of previsouly developed model by Cartmell (1990) and Forehand and Cartmell (2001), three nonlinear equations of motion, representing the first and second bending modes and the first torsion modes, are derived by recourse to the Lagrangian formulation. The variables in the equations of motions are , and respectively. They are coupled together and various nonlinearities appear in the equations. The three equations are used to predict different parametric resonances of the form , , by application of the perturbation method of multiple scales. Expressions for the transition curves for the three resonances have been derived which show the regions of stable and unstable solutions in a detuning parameter-excitation amplitude plane. Very close agreement is obtained between theoretical and experimental results for all the three resonance conditions. Laboratory tests confirm that these instabilities are bounded in practice by nonlinear effects. To investigate the effects of shape memory alloy on the dynamical properties of a composite material beam structure, two shape memory alloy strips are centrally-bonded to a glass epoxy beam with a lumped end mass. The two SMA strips are theoretically pre-strained and heated up to their full austenitic phase, and shown to generate large recovery forces due to this phase transformation. The forces are considered as compressive forces, and a theoretical model is introduced to evaluate the influences of the forces on the natural frequencies and the bending modes of the composite beam structure. The results show that the increase of the forces decrease the natural frequencies and reduce the excursion of the first and second bending modes. The beam system is then subjected to a vertical excitation. In order to utilize the Lagrangian formulation once again, the generalised forces corresponding to the generalised coordinates , and are derived in terms of the SMA recovery force. The three equations of motion of the free lateral vibration of the beam system are then derived. Three different parametric resonances are also predicted. Further study shows that the increase of the magnitude of the recovery force results in an increase of the instability region. An experimental investigation is conducted on two composite beam structures and each with an end mass, one with two centrally-bonded shape memory alloy (SMA) strips and the other with two diagonally-bonded SMA strips. The study suggests that when the strips are activated, the central-strip configuration can increase the natural frequencies of the bending modes noticeably more than the diagonal-strip one under certain circumstances, whilst the diagonal-strip configuration can easily be seen to change the frequencies of the torsion modes than the central-strip set-up