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. © 2013 IEEE.

A parametrically excited vibration energy harvester

In the arena of vibration energy harvesting, the key technical challenges continue to be low power density and narrow operational frequency bandwidth. While the convention has relied upon the activation of the fundamental mode of resonance through direct excitation, this article explores a new paradigm through the employment of parametric resonance. Unlike the former, oscillatory amplitude growth is not limited due to linear damping. Therefore, the power output can potentially build up to higher levels. Additionally, it is the onset of non-linearity that eventually limits parametric resonance; hence, this approach can also potentially broaden the operating frequency range. Theoretical prediction and numerical modelling have suggested an order higher in oscillatory amplitude growth. An experimental macro-sized electromagnetic prototype (practical volume of ∼1800 cm3) when driven into parametric resonance, has demonstrated around 50% increase in half power band and an order of magnitude higher peak power density normalised against input acceleration squared (293 μW cm-3 m-2 s4 with 171.5 mW at 0.57 m s-2) in contrast to the same prototype directly driven at fundamental resonance (36.5 μW cm-3 m-2 s4 with 27.75 mW at 0.65 m s-2). This figure suggests promising potentials while comparing with current state-of-the-art macro-sized counterparts, such as Perpetuum's PMG-17 (119 μW cm-3 m-2 s4). © The Author(s) 2013.

Surface-waves, stability, and scattering for a lined duct with flow

We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass-spring-damper boundary model, for which one surface mode has previously been identified as a convective instability; however, we show the stability analysis used in such cases to be questionable. We investigate instead the stability of the surface modes using the Briggs-Bers criterion for a Flügge thin-shell boundary model. For modest frequencies and wavenumbers the thin-shell has an impedance which is effectively that of a mass-spring-damper, although for the large wavenumbers needed for the stability analysis the thin-shell and mass-spring-damper impedances diverge, owing to the thin shell's bending stiffness. The thin shell model may therefore be viewed as a regularization of the mass-spring-damper model which accounts for nonlocally-reacting effects. We find all modes to be stable for realistic thin-shell parameters, while absolute instabilities are demonstrated for extremely thin boundary thicknesses. The limit of vanishing bending stiffness is found to be a singular limit, yielding absolute instabilities of arbitrarily large temporal growth rate. We propose that the problems with previous stability analyses are due to the neglect of something akin to bending stiffness in the boundary model. Our conclusion is that the surface mode previously identified as a convective instability may well be stable in reality. Finally, inspired by Rienstra's recent analysis, we investigate the scattering of an acoustic mode as it encounters a sudden change from a hard-wall to a thin-shell boundary, using a Wiener-Hopf technique. The thin-shell is considered to be clamped to the hard-wall. The acoustic mode is found to scatter into transmitted and reflected acoustic modes, and surface modes strongly linked to the solid waves in the boundary, although no longitudinal or transverse waves within the boundary are excited. Examples are provided that demonstrate total transmission, total reflection, and a combination of the two. This thin-shell scattering problem is preferable to the mass-spring-damper scattering problem presented by Rienstra, since the thin-shell problem is fully determined and does not need to appeal to a Kutta-like condition or the inclusion of an instability in order to avoid a surface-streamline cusp at the boundary change.

A bulk acoustic mode single-crystal silicon microresonator with a high-quality factor

This paper details a bulk acoustic mode resonator fabricated in single-crystal silicon with a quality factor of 15 000 in air, and over a million below 10 mTorr at a resonant frequency of 2.18 MHz. The resonator is a square plate that is excited in the square-extensional mode and has been fabricated in a commercial foundry silicon-on-insulator (SOI) MEMS process through MEMSCAP. This paper also presents a simple method of extracting resonator parameters from raw measurements heavily buried in electrical feedthrough. Its accuracy has been demonstrated through a comparison between extracted motional resistance values measured at different voltage biases and those predicted from an analytical model. Finally, a method of substantially cancelling electrical feedthrough through system-level electronic implementation is also introduced. © 2008 IOP Publishing Ltd.

Ultrasensitive mass balance based on a bulk acoustic mode single-crystal silicon resonator

A single-crystal silicon resonant bulk acoustic mass sensor with a measured resolution of 125 pg cm2 is presented. The mass sensor comprises a micromachined silicon plate that is excited in the square-extensional bulk acoustic resonant mode at a frequency of 2.182 MHz, with a quality factor exceeding 106. The mass sensor has a measured mass to frequency shift sensitivity of 132 Hz cm2 μg. The resonator element is embedded in a feedback loop of an electronic amplifier to implement an oscillator with a short term frequency stability of better than 7 ppb at an operating pressure of 3.8 mTorr. © 2007 American Institute of Physics.

Parasitic feedthrough cancellation techniques for enhanced electrical characterization of electrostatic microresonators

Capacitive parasitic feedthrough is an impediment that is inherent to all electrically interfaced micron scale resonant devices, resulting in increased challenges to their integration in more complex circuits, particularly as devices are scaled to operate at higher frequencies for RF applications. In this paper, a technique to cancel the undesirable effects of capacitive feedthrough that was previously proposed is here developed for an on-chip implementation. The method reported in this paper benefits from the simplicity of its implementation, and its effectiveness is demonstrated in this paper. This technique is demonstrated for two disk-plate resonators that have been excited in the wine glass mode at 5.4 MHz, though applicable to almost any electrically interfaced resonator. Measurements of the electrical transmission from these resonators show that the magnitude of the frequency response of the system is enhanced by up to 19 dB, while the phase is found to shift through a full 180° about the resonant frequency. This method is proposed as a useful addition to other techniques for enhancing the measured response of electrostatic micromechanical resonators. © 2009 Elsevier B.V. All rights reserved.

5.4-MHz single-crystal silicon wine glass mode disk resonator with quality factor of 2 million

This paper reports the design and electrical characterization of a micromechanical disk resonator fabricated in single crystal silicon using a foundry SOI micromachining process. The microresonator has been selectively excited in the radial extensional and the wine glass modes by reversing the polarity of the DC bias voltage applied on selected drive electrodes around the resonant structure. The quality factor of the resonator vibrating in the radial contour mode was 8000 at a resonant frequency of 6.34 MHz at pressure below 10 mTorr vacuum. The highest measured quality factor of the resonator in the wine glass resonant mode was 1.9 × 106 using a DC bias voltage of 20 V at about the same pressure in vacuum; the resonant frequency was 5.43 MHz and the lowest motional resistance measured was approximately 17 kΩ using a DC bias voltage of 60 V applied across 2.7 μm actuation gaps. This corresponds to a resonant frequency-quality factor (f-Q) product of 1.02 × 1013, among the highest reported for single crystal silicon microresonators, and on par with the best quartz crystal resonators. The quality factor for the wine glass mode in air was approximately 10,000. © 2009 Elsevier B.V. All rights reserved.

Low loss HF band SOI wine glass bulk mode capacitive square-plate resonator

This paper reports on the design and electrical characterization of a single crystal silicon micromechanical square-plate resonator. The microresonator has been excited in the anti-symmetrical wine glass mode at a resonant frequency of 5.166 MHz and exhibits an impressive quality factor (Q) of 3.7 × 106 at a pressure of 33 mtorr. The device has been fabricated in a commercial foundry process. An associated motional resistance of approximately 50 kΩ using a dc bias voltage of 60 V is measured for a transduction gap of 2 νm due to the ultra-high Q of the resonator. This result corresponds to a frequency-Q product of 1.9 × 1013, the highest reported for a fundamental mode single-crystal silicon resonator and on par with some of the best quartz crystal resonators. The results are indicative of the superior performance of silicon as a mechanical material, and show that the wine glass resonant mode is beneficial for achieving high quality factors allowed by the material limit. © 2009 IOP Publishing Ltd.

Thin film monitoring with silicon bulk acoustic resonators

Abstract-This paper reports a single-crystal silicon mass sensor based on a square-plate resonant structure excited in the wine glass bulk acoustic mode at a resonant frequency of 2.065 MHz and an impressive quality factor of 4 million at 12 mtorr pressure. Mass loading on the resonator results in a linear downshift in the resonant frequency of this device, wherein the measured sensitivity is found to be 175 Hz cm2/μg. The silicon resonator is embedded in an oscillator feedback loop, which has a short-term frequency stability of 3 mHz (approximately 1.5 ppb) at an operating pressure of 3.2 mtorr, corresponding to an equivalent mass noise floor of 17 pg/cm2. Possible applications of this device include thin film monitoring and gas sensing, with the potential added benefits of scalability and integration with CMOS technology. © 2008 IEEE.

Square wine glass mode resonator with quality factor of 4 million

We report on the experimental characterization of a single crystal silicon square-plate microresonator. The resonator is excited in the square wine glass (SWG) mode at a mechanical resonance frequency of 2.065 MHz. The resonator displays quality factor of 9660 in air and an ultra-high quality factor of Q = 4.05 × 106 in 12 mtorr vacuum. The SWG mode may be described as a square plate that contracts along one axis in the fabrication plane, while simultaneously extending along an orthogonal axis in the same plane. The resonant structure is addressed in a 2-terminal configuration by utilizing equal and opposite drive polarities on surrounding capacitor electrodes, thereby decreasing the motional resistance of the resonator. The resonant micromechanical device has been fabricated in a commercial silicon-on-insulator process through the MEMSCAP foundry utilising a minimum electrostatic gap of 2 μm. © 2008 IEEE.

169 GHz repetition rate passively harmonically mode-locked VECSEL emitting 265 fs pulses

High repetition rate passively mode-locked sources are of significant interest due to their potential for applications including optical clocking, optical sampling, communications and others. Due to their short excited state lifetimes mode-locked VECSELs are ideally suited to high repetition rate operation, however fundamentally mode-locked quantum well-based VECSELs have not achieved repetition rates above 10 GHz due to the limitations placed on the cavity geometry by the requirement that the saturable absorber saturates more quickly than the gain. This issue has been overcome by the use of quantum dot-based saturable absorbers with lower saturation fluences leading to repetition rates up to 50 GHz, but sub-picosecond pulses have not been achieved at these repetition rates. We present a passively harmonically mode-locked VECSEL emitting pulses of 265 fs duration at a repetition rate of 169 GHz with an output power of 20 mW. The laser is based around an antiresonant 6 quantum well gain sample and is mode-locked using a semiconductor saturable absorber mirror. Harmonic modelocking is achieved by using an intracavity sapphire etalon. The sapphire then acts as a coupled cavity, setting the repetition rate of the laser while still allowing a tight focus on the saturable absorber. RF spectra of the laser output show no peaks at harmonics of the fundamental repetition rate up to 26 GHz, indicating stable harmonic modelocking. Autocorrelations reveal groups of pulses circulating in the cavity as a result of an increased tendency towards Q-switched modelocking due to the low pulse energies.

Vortices, sound and flames - a damaging combination

The interaction between vortices, sound and combustion can lead to self-excited oscillations of such large amplitudes that structural damage is done. These occur because any small unsteadiness in the rate of combustion is a source of sound, generating pressure and velocity fluctuations. However, the velocity fluctuations perturb the flame, thereby altering the instantaneous rate of heat release. Instability is then possible because while acoustic waves perturb the combustion, the unsteady combustion generates yet more sound! Combustion oscillations can occur in afterburners and at idle in conventional aeroengine combustors. Lean premixed, prevapourized technology has tremendous potential to reduce NOx emissions, but is proving highly susceptible to self-excited oscillations. An overview of the physics of the interaction between vortices, sound and flames is presented, and illustrated by examples of instability in generic premixed ducted flames and in aeroengine combustors. The potential for both passive and active control is discussed.

Spray visualisation and acoustic analysis in a gas-turbine type burner

This paper presents the characterisation of self-excited oscillations in a kerosene burner. The combustion instability exhibits two different modes and frequencies depending on the air flow rate. Experimental results reveal the influence of the spray to shift between these two modes. Pressure and heat release fluctuations have been measured simultaneously and the flame transfer function has been calculated from these measurements. The Mie scattering technique has been used to record spray fluctuations in reacting conditions with a high speed camera. Innovative image processing has enabled us to obtain fluctuations of the Mie scattered light from the spray as a temporal signal acquired simultaneously with pressure fluctuations. This has been used to determine a transfer function relating the image intensity and hence the spray fluctuations to changes in air velocity. This function has identified the different role the spray plays in the two modes of instability. At low air flow rates, the spray responds to an unsteady air flow rate and the time varying spray characteristics lead to unsteady combustion. At higher air flow rates, effective evaporation means that the spray dynamics are less important, leading to a different flame transfer function and frequency of self-excited oscillation. In conclusion, the combustion instabilities observed are closely related with the fluctuations of the spray motion and evaporation.

Numerical simulations of unsteady wet steam flows with non-equilibrium condensation in the nozzle and the steam turbine

Numerical techniques for non-equilibrium condensing flows are presented. Conservation equations for homogeneous gas-liquid two-phase compressible flows are solved by using a finite volume method based on an approximate Riemann solver. The phase change consists of the homogeneous nucleation and growth of existing droplets. Nucleation is computed with the classical Volmer-Frenkel model, corrected for the influence of the droplet temperature being higher than the steam temperature due to latent heat release. For droplet growth, two types of heat transfer model between droplets and the surrounding steam are used: a free molecular flow model and a semi-empirical two-layer model which is deemed to be valid over a wide range of Knudsen number. The computed pressure distribution and Sauter mean droplet diameters in a convergent-divergent (Laval) nozzle are compared with experimental data. Both droplet growth models capture qualitatively the pressure increases due to sudden heat release by the non-equilibrium condensation. However the agreement between computed and experimental pressure distributions is better for the two-layer model. The droplet diameter calculated by this model also agrees well with the experimental value, whereas that predicted by the free molecular model is too small. Condensing flows in a steam turbine cascade are calculated at different Mach numbers and inlet superheat conditions and are compared with experiments. Static pressure traverses downstream from the blade and pressure distributions on the blade surface agree well with experimental results in all cases. Once again, droplet diameters computed with the two-layer model give best agreement with the experiments. Droplet sizes are found to vary across the blade pitch due to the significant variation in expansion rate. Flow patterns including oblique shock waves and condensation-induced pressure increases are also presented and are similar to those shown in the experimental Schlieren photographs. Finally, calculations are presented for periodically unsteady condensing flows in a low expansion rate, convergent-divergent (Laval) nozzle. Depending on the inlet stagnation subcooling, two types of self-excited oscillations appear: a symmetric mode at lower inlet subcooling and an asymmetric mode at higher subcooling. Plots of oscillation frequency versus inlet sub-cooling exhibit a hysteresis loop, in accord with observations made by other researchers for moist air flow. Copyright © 2006 by ASME.

Laser-vapour interaction in high-power cw Nd:YAG laser welding

During high-power cw Nd:YAG laser welding a vapour plume is formed containing vaporised material ejected from the keyhole. Spectroscopic studies of the vapour emission have demonstrated that the vapour can be considered as thermally excited gas with a stable temperature (less than 3000K), not as partially ionised plasma. In this paper, a review of temperatures in the vapour plume is presented. The difficulties in the analysis of the plume spectroscopic results are reviewed and explained. It is shown that particles present in the vapour interact with the laser beam, attenuating it. The attenuation can be calculated with Mie scattering theory, however, vaporisation and particle formation also both play a major role in this process. The laser beam is also defocused due to the scattering part of the attenuation mechanism, changing the energy density in the laser beam. Methods for mitigating the effects of the laser beam-vapour interaction, using control gases, are presented together with their advantages and disadvantages. This 'plume control' has two complementary roles: firstly, the gas must divert the vapour plume from out of the laser beam path, preventing the attenuation. Secondly, the gas has to stabilise the front wall of the keyhole, to prevent porosity formation.