Investigating vibration dyanmics of cross-coupled MEMS resonators for reduced motional resistance

This paper investigates the vibration dynamics of a closed-chain, cross-coupled architecture of MEMS resonators. The system presented here is electrostatically transduced and operates at 1.04 MHz. Curve veering of the eigenvalue loci is used to experimentally quantify the coupling spring constants. Numerical simulations of the motional resistance variation against induced perturbation are used to assess the robustness of the cross-coupled system as opposed to equivalent traditional open-ended linear one-dimensional coupling scheme. Results show improvements of as much as 32% in the motional resistance between the cross-coupled system and its one-dimensional counterpart. © 2013 IEEE.

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.

Multi-frequency operation of a mems vibration energy harvester by accessing five orders of parametric resonance

The mechanical amplification effect of parametric resonance has the potential to outperform direct resonance by over an order of magnitude in terms of power output. However, the excitation must first overcome the damping-dependent initiation threshold amplitude prior to accessing this more profitable region. In addition to activating the principal (1st order) parametric resonance at twice the natural frequency ω0, higher orders of parametric resonance may be accessed when the excitation frequency is in the vicinity of 2ω0/n for integer n. Together with the passive design approaches previously developed to reduce the initiation threshold to access the principal parametric resonance, vacuum packaging (< 10 torr) is employed to further reduce the threshold and unveil the higher orders. A vacuum packaged MEMS electrostatic harvester (0.278 mm3) exhibited 4 and 5 parametric resonance peaks at room pressure and vacuum respectively when scanned up to 10 g. At 5.1 ms-2, a peak power output of 20.8 nW and 166 nW is recorded for direct and principal parametric resonance respectively at atmospheric pressure; while a peak power output of 60.9 nW and 324 nW is observed for the respective resonant peaks in vacuum. Additionally, unlike direct resonance, the operational frequency bandwidth of parametric resonance broadens with lower damping. © Published under licence by IOP Publishing Ltd.

Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads

The paper deals with the static analysis of pre-damaged Euler-Bernoulli beams with any number of unilateral cracks and subjected to tensile or compression forces combined with arbitrary transverse loads. The mathematical representation of cracks with a bilateral behaviour (i.e. always open) via Dirac delta functions is extended by introducing a convenient switching variable, which allows each crack to be open or closed depending on the sign of the axial strain at the crack centre. The proposed model leads to analytical solutions, which depend on four integration constants (to be computed by enforcing the boundary conditions) along with the Boolean switching variables associated with the cracks (whose role is to turn on and off the additional flexibility due to the presence of the cracks). An efficient computational procedure is also presented and numerically validated. For this purpose, the proposed approach is applied to two pre-damaged beams, with different damage and loading conditions, and the results so obtained are compared against those given by a standard finite element code (in which the correct opening of the cracks is pre-assigned), always showing a perfect agreement. © 2013 Elsevier Ltd. All rights reserved.

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.

Noise and vibration in brushless doubly fed machine and brushless doubly fed reluctance machine

This study investigates modes of vibration in brushless doubly fed machine and brushless doubly fed reluctance machine due to the interaction of its fundamental magnetic fields, via the bending forces they set up in the back iron. It is shown that the presence of two field components of different pole numbers leads to vibration components in addition to those that would be expected in single field machines such as the induction motor. Formulations for the frequencies and magnitudes of the expected vibration components are given and verified experimentally. It is shown that the strength of the vibration components is highly dependent on the choice of pole numbers in the machine, with some much worse than equivalent induction machines and some very similar. The methodology presented enables designers to determine whether their machines are likely to suffer from vibration problems in advance of construction, and to apply remedies where appropriate. © The Institution of Engineering and Technology 2014.

The dynamic effect of a piled-foundation building on an incident vibration field from an underground railway tunnel

This paper presents a three-dimensional comprehensive model for the calculation of vibration in a building based on pile-foundation due to moving trains in a nearby underground tunnel. The model calculates the Power Spectral Density (PSD) of the building's responses due to trains moving on floating-slab tracks with random roughness. The tunnel and its surrounding soil are modelled as a cylindrical shell embedded in half-space using the well-known PiP model. The building and its piles are modelled as a 2D frame using the dynamic stiffness matrix. Coupling between the foundation and the ground is performed using the theory of joining subsystems in the frequency domain. The latter requires calculations of transfer functions of a half-space model. A convenient choice based on the thin-layer method is selected in this work for the calculations of responses in a half-space due to circular strip loadings. The coupling considers the influence of the building's dynamics on the incident wave field from the tunnel, but ignores any reflections of building's waves from the tunnel. The derivation made in the paper shows that the incident vibration field at the building's foundation gets modified by a term reflecting the coupling and the dynamics of the building and its foundation. The comparisons presented in the paper show that the dynamics of the building and its foundation significantly change the incident vibration field from the tunnel and they can lead to loss of accuracy of predictions if not considered in the calculation.

Vibration of pressurised, elastic, spherical shells

Balloons are one example of pressurised, elastic, spherical shells. Whilst analytical solutions exist for the vibration of pressurised spheres, these models only incorporate constant tension in the membrane. For elastic shells, changes in curvature will result in restoring forces that are proportional to the elasticity in the membrane; hence the assumption of constant tension is not valid. This paper describes an analytical solution for the natural frequencies of an elastic spherical shell subject to internal pressure. When the membrane tension is set to zero, the results are shown to converge to the analytical solution for a spherical shell, and when the skin elasticity is neglected, the results converge to the constant-tension solution. This analytical solution is used to predict the natural frequencies of a small balloon, based on a value for the elastic modulus that is determined using biaxial tensile testing. These predictions are compared to experimental measurements of balloon vibrations using impact hammer testing, and good agreement is seen.

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. © 2014 IOP Publishing Ltd.

An energy-efficient hopping robot based on free vibration of a curved beam

This paper explores a design strategy of hopping robots, which makes use of free vibration of an elastic curved beam. In this strategy, the leg structure consists of a specifically shaped elastic curved beam and a small rotating mass that induces free vibration of the entire robot body. Although we expect to improve energy efficiency of locomotion by exploiting the mechanical dynamics, it is not trivial to take advantage of the coupled dynamics between actuation and mechanical structures for the purpose of locomotion. From this perspective, this paper explains the basic design principles through modeling, simulation, and experiments of a minimalistic hopping robot platform. More specifically, we show how to design elastic curved beams for stable hopping locomotion and the control method by using unconventional actuation. In addition, we also analyze the proposed design strategy in terms of energy efficiency and discuss how it can be applied to the other forms of legged robot locomotion. © 1996-2012 IEEE.

Hopping robot based on free vibration of an elastic curved beam

This study presents a novel approach to the design of low-cost and energy-efficient hopping robots, which makes use of free vibration of an elastic curved beam. We found that a hopping robot could benefit from an elastic curved beam in many ways such as low manufacturing cost, light body weight and small energy dissipation in mechanical interactions. A challenging problem of this design strategy, however, lies in harnessing the mechanical dynamics of free vibration in the elastic curved beam: because the free vibration is the outcome of coupled mechanical dynamics between actuation and mechanical structures, it is not trivial to systematically design mechanical structures and control architectures for stable locomotion. From this perspective, this paper investigates a case study of simple hopping robot to identify the design principles of mechanics and control. We developed a hopping robot consisting of an elastic curved beam and a small rotating mass, which was then modeled and analyzed in simulation. The experimental results show that the robot is capable of exhibiting stable hopping gait patterns by using a small actuation with no sensory feedback owing to the intrinsic stability of coupled mechanical dynamics. Furthermore, an additional analysis shows that, by exploiting free vibration of the elastic curved beam, cost of transport of the proposed hopping locomotion can be in the same rage of animals' locomotion including human running. © 2011 IEEE.

Morphological computation of multi-gaited robot locomotion based on free vibration.

In recent years, there has been increasing interest in the study of gait patterns in both animals and robots, because it allows us to systematically investigate the underlying mechanisms of energetics, dexterity, and autonomy of adaptive systems. In particular, for morphological computation research, the control of dynamic legged robots and their gait transitions provides additional insights into the guiding principles from a synthetic viewpoint for the emergence of sensible self-organizing behaviors in more-degrees-of-freedom systems. This article presents a novel approach to the study of gait patterns, which makes use of the intrinsic mechanical dynamics of robotic systems. Each of the robots consists of a U-shaped elastic beam and exploits free vibration to generate different locomotion patterns. We developed a simplified physics model of these robots, and through experiments in simulation and real-world robotic platforms, we show three distinctive mechanisms for generating different gait patterns in these robots.

Effects of lattice vibration on the effective mass of quasi-two-dimensional strong-coupling polaron

The effects of lattice vibration on the system in which the electron is weakly coupled with bulk longitudinal optical phonons and strongly coupled with interface optical phonons in an infinite quantum well were studied by using Tokuda' linear-combination operator and a modified LLP variational method. The expressions for the effective mass of the polaron in a quantum well QW as functions of the well's width and temperature were derived. In particular, the law of the change of the vibration frequency of the polaron changing with well' s width and temperature are obtained. Numerical results of the effective mass and the vibration frequency of the polaron for KI/AgCl/Kl QW show that the vibration frequency and the effective mass of the polaron decrease with increasing well's width and temperature, but the contribution of the interaction between the electron and the different branches of phonons to the effective mass and the vibration frequency and the change of their variation with the well's width and temperature are greatly different.

Transverse magnetic field effect on the current hysteresis of doped GaAs/AlAs superlattice

The influence of a transverse magnetic field up to 13 T at 1.6 K on the current-voltage, I (V), characteristics of a doped GaAs/AlAs superlattice was investigated. Current hysteresis was observed in the domain formation regions of the I (V) at zero magnetic field while applied bias was swept in both up (0-6 V) and down (6-0 V) directions. The magnitude of current hysteresis was reduced and finally disappeared with increasing transverse magnetic field. The effect is explained as the modification of the current density versus electric field characteristic by transverse magnetic fields. Calculated results based on the tunnelling current formula in a superlattice support our interpretation.