Synchronous motion of two vertically excited planar elastic pendula

The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and anti-phase synchronous states always co-exist. The complete bifurcational scenario leading from synchronous to asynchronous motion is shown. We argue that our results are robust as they exist in the wide range of the system parameters.Comment: Submitte

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