Excitation of multiple 2-mode parametric resonances by a single driven mode

We demonstrate autoparametric excitation of two distinct sub-harmonic mechanical modes by the same driven mechanical mode corresponding to different drive frequencies within its resonance dispersion band. This experimental observation is used to motivate a more general physical picture wherein multiple mechanical modes could be excited by the same driven primary mode within the same device as long as the frequency spacing between the sub-harmonic modes is less than half the dispersion bandwidth of the driven primary mode. The excitation of both modes is seen to be threshold-dependent and a parametric back-action is observed impacting on the response of the driven primary mode. Motivated by this experimental observation, modified dynamical equations specifying 2-mode auto-parametric excitation for such systems are presented.Comment: 8 pages, 3 figure

Power Optimisation by Mass Tuning for MEMS Piezoelectric Cantilever Vibration Energy Harvesting

A cantilever with an end mass is one of the most popular designs for piezoelectric MEMS vibration energy harvesting. The inclusion of a proof mass near the free end of a micro-cantilever can significantly enhances the power responsiveness of a vibration energy harvester per unit acceleration. However, the accommodation of the proof mass comes at the expense of the active piezoelectric area. This paper numerically and experimentally investigates this compromise and explores the optimal proof-mass-to-cantilever-length ratio for power maximisation. It was found that an end mass occupying about 60% to 70% of the total cantilever length is optimal within linear response, and they notably outperform comparable cantilevers with 40% and 50% of end mass. Additionally, nonlinear squeeze film air damping within the chip package was found to adversely affect the cantilevers with larger mass more significantly. A harvester prototype with 70% of the length covered by end mass (5.0 mm^3 ) was able to generate 1.78 μW at 0.6 ms^-2 and up to 20.5 μW at 2.7 ms^-2 and 210 Hz when not limited by nonlinear damping. This result outperforms the previously reported counterparts in the literature by nearly an order of a magnitude in terms of power density normalised against acceleration squared.This work was supported by Innovate UK and GE Aviation.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/JMEMS.2015.249634

An analytical formulation for phase noise in MEMS oscillators.

In recent years, there has been much interest in the design of low-noise MEMS oscillators. This paper presents a new analytical formulation for noise in a MEMS oscillator encompassing essential resonator and amplifier nonlinearities. The analytical expression for oscillator noise is derived by solving a second-order nonlinear stochastic differential equation. This approach is applied to noise modeling of an electrostatically addressed MEMS resonator-based square-wave oscillator in which the resonator and oscillator circuit nonlinearities are integrated into a single modeling framework. By considering the resulting amplitude and phase relations, we derive additional noise terms resulting from resonator nonlinearities. The phase diffusion of an oscillator is studied and the phase diffusion coefficient is proposed as a metric for noise optimization. The proposed nonlinear phase noise model provides analytical insight into the underlying physics and a pathway toward the design optimization for low-noise MEMS oscillators.The authors would like to thank the UK-Indian Education and Research Initiative (grant SA06-250) and the Cambridge Trusts for funding support.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TUFFC.2014.00651

Directly and parametrically excited bi-stable vibration energy harvester for broadband operation

Despite many recent advances, the wide-spread adoption of vibrational energy harvesting has been limited by the low levels of generated output power and confined operational frequency band. Recent work by the authors on parametrically excited harvesters has demonstrated over an order of magnitude power improvement. This paper presents an investigation into the simultaneous employment of both direct and parametric resonance, as well as the incorporation of bi-stability, in an attempt to further improve the mechanical-to-electrical energy conversion efficiency by broadening the output power spectrum. Multiple direct and parametric resonant peaks from a multi-degree-of-freedom system were observed and an accumulative ~10 Hz half-power bandwidth was recorded for the first 40 Hz. Real vibration data was also employed to analysis the RMS power response effectiveness of the proposed system

Power Optimization by Mass Tuning for MEMS Piezoelectric Cantilever Vibration Energy Harvesting

A cantilever with an end mass is one of the most popular designs for piezoelectric MEMS vibration energy harvesting. The inclusion of a proof mass near the free end of a micro-cantilever can significantly enhances the power responsiveness of a vibration energy harvester per unit acceleration. However, the accommodation of the proof mass comes at the expense of the active piezoelectric area. This paper numerically and experimentally investigates this compromise, and explores the optimal proof-mass-to-cantilever-length ratio for power maximization. It was found that an end mass occupying about 60%-70% of the total cantilever length is optimal within linear response, and they notably outperform comparable cantilevers with 40% and 50% of end mass. In addition, nonlinear squeeze film air damping within the chip package was found to adversely affect the cantilevers with larger mass more significantly. A harvester prototype with 70% of the length covered by end mass (5 mm 3 ) was able to generate 1.78 μW at 0.6 ms -2 and up to 20.5 μW at 2.7 ms -2 and 210 Hz when not limited by nonlinear damping. This result outperforms the previously reported counterparts in the literature by nearly an order of a magnitude in terms of power density normalized against acceleration squared

White Noise Responsiveness of an AlN Piezoelectric MEMS Cantilever Vibration Energy Harvester

This paper reports the design, analysis and experimental characterisation of a piezoelectric MEMS cantilever vibration energy harvester, the enhancement of its power output by adding various values of end mass, as well as assessing the responsiveness towards white noise. Devices are fabricated using a 0.5 μm AlN on 10 μm doped Si process. Cantilevers with 5 mm length and 2 mm width were tested at either unloaded condition (MC0: fn 577 Hz) or subjected to estimated end masses of 2 mg (MC2: fn 129 Hz) and 5 mg (MC5: fn 80 Hz). While MC0 was able to tolerate a higher drive acceleration prior to saturation (7 g with 0.7 μW), MC5 exhibited higher peak power attainable at a lower input vibration (2.56 μW at 3 ms−2). MC5 was also subjected to band-limited (10 Hz to 2 kHz) white noise vibration, where the power response was only a fraction of its resonant counterpart for the same input: peak instantaneous power >1 μW was only attainable beyond 2 g of white noise, whereas single frequency resonant response only required 2.5 ms−2. Both the first resonant response and the band-limited white noise response were also compared to a numerical model, showing close agreements

Comparison of Five Topologies of Cantilever-based MEMS Piezoelectric Vibration Energy Harvesters

In the realm of MEMS piezoelectric vibration energy harvesters, cantilever-based designs are by far the most popular. Despite being deceptively simple, the active piezoelectric area near the clamped end is able to accumulate maximum strain-generated-electrical-charge, while the free end is able to accommodate a proof mass without compromising the effective area of the piezoelectric generator since it experiences minimal strain anyway. While other contending designs do exist, this paper investigates five micro-cantilever (MC) topologies, namely: a plain MC, a tapered MC, a lined MC, a holed MC and a coupled MC, in order to assess their relative performance as an energy harvester. Although a classical straight and plain MC offers the largest active piezoelectric area, alternative MC designs can potentially offer higher average mechanical strain distribution for a given mechanical loading. Numerical simulation and experimental comparison of these 5 MCs (0.5 μ AlN on 10 μm Si) with the same practical dimensions of 500 μm and 2000 μm, suggest a cantilever with a coupled subsidiary cantilever yield the best power performance, closely followed by the classical plain topology

Twenty-Eight Orders of Parametric Resonance in a Microelectromechanical Device for Multi-band Vibration Energy Harvesting.

This paper contends to be the first to report the experimental observation of up to 28 orders of parametric resonance, which has thus far only been envisioned in the theoretical realm. While theory has long predicted the onset of n orders of parametric resonance, previously reported experimental observations have been limited up to about the first 5 orders. This is due to the rapid narrowing nature of the frequency bandwidth of the higher instability intervals, making practical accessibility increasingly more difficult. Here, the authors have experimentally confirmed up to 28 orders of parametric resonance in a micromachined membrane resonator when electrically undamped. While the implication of this finding spans across the vibration dynamics and transducer application spectrum, the particular significance of this work is to broaden the accumulative operational frequency bandwidth of vibration energy harvesting for enabling self-powered microsystems. Up to 5 orders were recorded when driven at 1.0 g of acceleration across a matched load of 70 kΩ. With a natural frequency of 980 Hz, the fundamental mode direct resonance had a -3 dB bandwidth of 55 Hz, in contrast to the 314 Hz for the first order parametric resonance; furthermore, the half power bands of all 5 orders accumulated to 478 Hz.Engineering and Physical Sciences Research Council (Grant ID: EP/L010917/1)This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/srep3016