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

A parametric electrostatic resonator using repulsive force

In this paper, parametric excitation of a repulsive force electrostatic resonator is studied. A theoretical model is developed and validated by experimental data. A correspondence of the model to Mathieu\u27s Equation is made to prove the existence and location of parametric resonance. The repulsive force creates a combined response that shows parametric and subharmonic resonance when driven at twice its natural frequency. The resonator can achieve large amplitudes of almost 24 μm and can remain dynamically stable while tapping on the electrode. Because the pull-in instability is eliminated, the beam bounces off after impact instead of sticking to the electrode. This creates larger, stable trajectories that would not be possible with traditional electrostatic actuation. A large dynamic range is attractive for MEMS resonators that require a large signal-to-noise ratio

Nonlinear vibration energy harvesting based on variable double well potential function

Converting ambient mechanical energy to electricity, vibration energy harvesting, enables powering of the low-power remote sensors. Nonlinear energy harvesters have the advantage of a wider frequency spectrum compared to linear resonators making them more efficient in scavenging the broadband frequency of ambient vibrations. To increase the output power of the nonlinear resonators, we propose an energy harvester composed of a cantilever piezoelectric beam carrying a movable magnet facing a fixed magnet at a distance. The movable magnet on the beam is attached to a spring at the base of the beam. The spring-magnet system on the cantilever beam creates the variable double well potential function. The spring attached to the magnet is in its compressed position when the beam is not deflected, as the beam oscillates, the spring energy gradually releases and further increases the amplitude of vibration. To describe the motion of the cantilever beam, we obtained two coupled partial differential equations by assuming the cantilever beam as EulerBernoulli beam considering the effect of the moving magnet. Method of multiple scales is used to solve the coupled equations. The cantilever beam with the two magnets is a bi-stable system. Making one magnet movable can create internal resonance that is explored as a mechanism to increase the frequency bandwidth. The effect of system parameters on the frequency bandwidth of the resonator is investigated through numerical solutions. This study benefits vibration energy harvesting to achieve a higher performance when excited by the wideband ambient vibrations

A Reliable MEMS Switch Using Electrostatic Levitation

In this study an electrostatic MEMS beam is experimentally released from pull-in using electrostatic levitation. A MEMS cantilever with a parallel plate electrode configuration is pulled-in by applying a voltage above the pull-in threshold. Two more electrodes are fixed to the substrate on both sides of the beam to create electrostatic levitation. Large voltage pulses upwards of 100 V are applied to the side electrodes to release the pulled-in beam. A high voltage is needed to overcome the stronger parallel plate electrostatic force and stiction forces, which hold the beam in its pulled-in position. A relationship between bias voltage and release voltage is experimentally extracted. This method of releasing pulled in beams is shown to be reliable and repeatable without causing any major damage to the cantilever or electrodes. This is of great interest for any MEMS component that suffers from the pull-in instability, which is usually irreversible and permanently destroys the device, as it allows pulled-in structures to be released and reused. It also has a promising application in MEMS switches by opening up the possibility of a normally closed switch as opposed to current MEMS switches, which are normally open

A Hybrid Nonlinear Vibration Energy Harvester

Vibration energy harvesting converts mechanical energy from ambient sources to electricity to power remote sensors. Compared to linear resonators that have poor performance away from their natural frequency, nonlinear vibration energy harvesters perform better because they use vibration energy over a broader spectrum. We present a hybrid nonlinear energy harvester that combines bi-stability with internal resonance to increase the frequency bandwidth. A two-fold increase in the frequency bandwidth can be obtained compared to a bi-stable system with fixed magnets. The harvester consists of a piezoelectric cantilever beam carrying a movable magnet facing a fixed magnet. A spring allows the magnet to move along the beam and it provides an extra stored energy to further increase the amplitude of vibration acting as a mechanical amplifier. An electromechanically coupled mathematical model of the system is presented to obtain the dynamic response of the cantilever beam, the movable magnet and the output voltage. The perturbation method of multiple scales is applied to solve these equations and obtain approximate analytical solutions. The effects of various system parameters on the frequency responses are investigated. The numerical approaches of the long time integration (Runge-Kutta method) and the shooting technique are used to verify the analytical results. The results of this study can be used to improve efficiency in converting wasted mechanical vibration to useful electrical energy by broadening the frequency bandwidth

Feasibility study of a MEMS threshold-pressure sensor based on parametric resonance: experimental and theoretical investigations

A tunable threshold pressure sensor based on para- metric resonance of a microbeam subjected to electrostatic levitation is proposed. Parametric excitation can trigger a large amplitude vibration at twice the natural frequency if the mag- nitude of the driving force is large enough to overcome energy loss mechanisms in the system such as squeeze film damping. This causes a temporarily unstable response with a significant gain in oscillation amplitude over time until it is eventually capped by nonlinearities in the force or material or geometric properties. The instability divides the frequency region into two regions: distinct responses bounded by the system nonlinearity, and trivial responses with very low oscillation amplitudes. It is shown experimentally that the appearance of parametric resonance depends on the pressure, which influences the amount of energy loss from squeeze film damping. Therefore, the distinct difference in the vibration amplitude can be used to detect when the pressure passes a threshold level. The activation of parametric resonance also depends on the amplitude of the driving force (Vac). This voltage amplitude can be set to trigger parametric resonance when the pressure drops below a predetermined threshold. A reduced-order model is developed using the Euler- Bernoulli beam theory to elucidate the nonlinear dynamics of the system. The simulation results from the mathematical model are in good agreement with the experimental data. The advantages of the proposed sensor over pull-in based sensors are its reliability and improved resolution from a large signal-to-noise ratio

A Large-Stroke Electrostatic Micro-Actuator

Parallel-plate electrostatic actuators driven by a voltage difference between two electrodes suffer from an operation range limited to 30% of the gap that has significantly restrained their applications in Microelectromechanical systems (MEMS). In this thesis, the travel range of an electrostatic actuator made of a micro-cantilever beam electrode above a fixed electrode is extended quasi-statically to 90% of the capacitor gap by introducing a voltage regulator (controller) circuit designed for low frequency actuation. The developed large-stroke actuator is valuable contribution to applications in optical filters, optical modulators, digital micro-mirrors and micro-probe based memory disk drives. To implement the low-frequency large-stroke actuator, the beam tip velocity is measured by a vibrometer, the corresponding signal is integrated in the regulator circuit to obtain the displacement feedback, which is used to modify the input voltage of the actuator to reach a target location. The voltage regulator reduces the total voltage, and therefore the electrostatic force, once the beam approaches the fixed electrode so that the balance is maintained between the mechanical restoring force and the electrostatic force that enables the actuator to achieve the desired large stroke. A mathematical model is developed for the actuator based on the mode shapes of the cantilever beam using experimentally identified parameters that yields good accuracy in predicting both the open loop and the closed loop responses. The low-frequency actuator also yields superharmonic resonances that are observed here for the first time in electrostatic actuators. The actuator can also be configured either as a bi-stable actuator using a low-frequency controller or as a chaotic resonator using a high-frequency controller. The high-frequency controller yields large and bounded chaotic attractors for a wide range of excitation magnitudes and frequencies making it suitable for sensor applications. Bifurcation diagrams reveal periodic motions, softening behavior, period doubling cascades, one-well and two-well chaos, superharmonic resonances and a reverse period doubling cascade. To verify the observed chaotic oscillations, Lyapunov exponents are calculated and found to be positive. Furthermore, a chaotic resonator with a quadratic controller is designed that not only requires less voltage, but also produces more robust and larger motions. Another metric of chaos, information entropy, is used to verify the chaotic attractors in this case. It is found that the attractors have a common information entropy of 0.732 independent of the excitation amplitude and frequency

A Cylindrical Triboelectric Energy Harvester for Capsule Endoscopes

Capsule endoscopy is a new technology that has the potential to replace conventional endoscopy in the near future due to its non-invasive nature. A major limitation for their functionality is the limited battery life. We have investigated a triboelectric energyharvester inside a capsule endoscope that can generate power from natural contractions of gastrointestinal (GI) tract. The periodic contacts and separations of two triboelectric materials inside the capsule endoscope create an alternating current that can be used to charge the capsule endoscope battery, which is used for imaging the GI tract. This study presents an analytical closed form solution for the output power of a cylindrical triboelectric energy harvester. Energy harvester sizes have been optimized to maximize the output power

Experimental characterization of the electrostatic levitation force in MEMS transducers

In this study, a two-step experimental procedure is described to determine the electrostatic levitation force in MEMS transducers. In these two steps, the microstructure is excited quasi-statically and dynamically and its response is used to derive the electrostatic force. The experimental results are obtained for a 1 by 1 plate that employs 112 levitation units. The experimentally obtained force is used in a lumped parameter model to find the microstructure response when it is subjected to different dynamical loads. The natural frequency and the damping ratios in the model are identified from the experimental results. The results show this procedure can be used as a method to extract the electrostatic force as a function of the microstructure’s degrees of freedom. The procedure can be easily used for any microstructure with a wide variety of electrode configurations to predict the response of the system to any input excitation

Feasibility study of a micro-electro-mechanical-systems threshold-pressure sensor based on parametric resonance: experimental and theoretical investigations

A tunable threshold pressure sensor based on parametric resonance of a microbeam subjected to electrostatic levitation is proposed. Parametric excitation can trigger a large amplitude vibration at twice the natural frequency if the magnitude of the driving force is large enough to overcome energy loss mechanisms in the system such as squeeze film damping. This causes a temporarily unstable response with a significant gain in oscillation amplitude over time until it is eventually capped by nonlinearities in the force or material or geometric properties. The instability divides the frequency region into two regions: distinct responses bounded by the system non-linearity, and trivial responses with very low oscillation amplitudes. It is shown experimentally that the appearance of parametric resonance depends on the pressure, which influences the amount of energy loss from squeeze film damping. Therefore, the distinct difference in the vibration amplitude can be used to detect when the pressure passes a threshold level. The activation of parametric resonance also depends on the amplitude of the driving force (). This voltage amplitude can be set to trigger parametric resonance when the pressure drops below a predetermined threshold. A reduced-order model is developed using the Euler–Bernoulli beam theory to elucidate the non-linear dynamics of the system. The simulation results from the mathematical model are in good agreement with the experimental data. The advantages of the proposed sensor over pull-in based sensors are its reliability and improved resolution from a large signal-to-noise ratio