Ravindra Masana

On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion

The last two decades have witnessed several advances in microfabrication technologies and electronics, leading to the development of small, low-power devices for wireless sensing, data transmission, actuation, and medical implants. Unfortunately, the actual implementation of such devices in their respective environment has been hindered by the lack of scalable energy sources that are necessary to power and maintain them. Batteries, which remain the most commonly used power sources, have not kept pace with the demands of these devices, especially in terms of energy density. In light of this challenge, the concept of vibratory energy harvesting has flourished in recent years as a possible alternative to provide a continuous power supply. While linear vibratory energy harvesters have received the majority of the literature’s attention, a significant body of the current research activity is focused on the concept of purposeful inclusion of nonlinearities for broadband transduction. When compared to their linear resonant counterparts, nonlinear energy harvesters have a wider steady-state frequency bandwidth, leading to a common belief that they can be utilized to improve performance in ambient environments. Through a review of the open literature, this paper highlights the role of nonlinearities in the transduction of energy harvesters under different types of excitations and investigates the conditions, in terms of excitation nature and potential shape, under which such nonlinearities can be beneficial for energy harvesting. [DOI: 10.1115/1.4026278]

Energy harvesting in the super-harmonic frequency region of a twin-well oscillator

Nonlinear dynamical systems exhibit super-harmonic resonances that can activate large-amplitude motions at fraction integers of the fundamental frequency of the system. Such resonances offer a unique and untapped opportunity for harnessing vibratory energy from excitation sources with low-frequency components. To that end, this paper exploits the super-harmonic frequency bands of a nonlinear twin-well (bi-stable) oscillator for harvesting energy from low-frequency excitations. Theoretical and experimental studies are performed on an axially loaded clamped-clamped piezoelectric beam harvester with bi-stable potential characteristics. Voltage- and power-frequency bifurcation maps are generated near the super-harmonic resonance of order two. It is shown that, for certain base acceleration levels, the harvester can exhibit responses that are favorable for energy harvesting. These include a unique branch of large-orbit periodic inter-well oscillations, coexisting branches of large-orbit solutions, and a bandwidth of frequencies where a unique chaotic attractor exists. In these frequency regions, the harvester can produce power levels at half its fundamental frequency that are comparable to those obtained near the fundamental frequency.

Comparing the Performance of a Nonlinear Energy Harvester in Mono- and Bi-Stable Potentials

The quest to develop broadband vibratory energy harvesters (VEHs) has recently motivated researchers to explore introducing nonlinearities into the harvester’s design. Some research efforts have demonstrated that this new class of nonlinear harvesters can outperform their traditional linear (resonant) counterparts; some others however concluded that nonlinearities can diminish the harvester’s transduction. Through this effort, we compare the performance of a nonlinear VEH operating in mono- and bi-stable potentials. With that objective, we consider an axially-loaded clamped-clamped piezoelectric beam which functions as an energy harvester in the mono-stable (pre-buckling) and bistable (post-buckling) configurations. For the purpose of fair performance comparison, the oscillation frequency around the stable equilibria of the harvester is tuned to equal values in both configurations. The harvester is then subjected to harmonic base excitations of different magnitudes and a slowly-varying frequency which spans a wide range around the tuned oscillation frequency. The output voltage measured across an arbitrarily chosen electric load is used as a relative performance measure. Both numerical and experimental results demonstrate that the shape of the potential function plays an essential role in conjunction with the magnitude of the base excitation to determine whether the bi-stable harvester can outperform the mono-stable one and for what range of frequencies.Copyright

Performance of a Randomly-Excited Nonlinear Energy Harvester in Mono- and Bi-Stable Potentials: An Experimental Investigation

This paper aims to experimentally investigate the influence of stiffness-type nonlinearities on the transduction of vibratory energy harvesters (VEHs) under random white and colored excitations. For the purpose of the study, an energy harvester consisting of a clamped-clamped piezoelectric beam bi-morph is considered. The shape of the harvester’s potential function is altered by applying a static compressive axial load at one end of the beam. The axial load permits the harvester to operate with different potential energy characteristics; namely, the mono-stable (pre-buckling) and bi-stable (post-buckling) configurations. The performance of the harvester in both configurations is investigated and compared by tuning the harvester’s oscillation frequencies around the static equilibria such that they have equal values in both scenarios. The harvester is then subjected to random base excitations of different levels, bandwidths, and center frequencies. The variance of the output voltage is measured across an arbitrary, purely resistive load and used for the purpose of performance comparison. Critical conclusions pertinent to the influence of the nonlinearity and relative performance in both configurations are presented and discussed.Copyright

Exploiting Super-Harmonic Resonances of a Bi-Stable Axially-Loaded Beam for Energy Harvesting Under Low-Frequency Excitations

A research paradox currently lies in the design of miniaturized vibratory energy harvesters capable of harnessing energy efficiently from low-frequency excitations. To address this problem, this effort investigates the prospect of utilizing super-harmonic resonances of a bi-stable system to harvest energy from excitation sources with low-frequency components. Towards that objective, the paper considers the electromechanical response of an axially-loaded clamped-clamped piezoelectric beam harvester with bi-stable potential characteristics. By numerically constructing the voltage-frequency bifurcation maps of the response near the super-harmonic resonance of order two, it is shown that, for certain base excitation levels, the harvester can exhibit responses that are favorable for energy harvesting. These include a unique branch of large-orbit periodic inter-well oscillations, coexisting branches of large-orbit solutions, and a bandwidth of frequencies where a unique chaotic attractor exists. In these regions, the harvester can produce power levels that are comparable to those obtained near the primary resonance.Copyright

Closure to “Discussion of ‘On the Role of Nonlinearities in Energy Harvesting: A Critical Review and Discussion’” (Daqaq, M., Masana, R., Erturk, A., and Quinn, D. D., 2014, ASME Appl. Mech. Rev., 66(4), p. 040801)

The authors would like to thank Professor Brian Mann for taking the time to read this paper and provide his insightful perspective into the role of nonlinearities in energy harvesting. Professor Mann has significant expertise in the field of energy harvesting and his commentary identifies several of the key advantages that result from the deliberate introduction of nonlinearities into energy harvesting devices. The goal of this closure is to complement his commentary by sharing additional thoughts that could be beneficial for the energy harvesting research community. To begin, we would like to point out that the complexity of the response behavior of nonlinear harvesters as compared to their linear counterparts remains the biggest challenge preventing us from optimizing their performance and fully reaping their potential benefits. Nonlinear harvesters exhibit different behaviors that are not seen in linear systems including sub-harmonic, superharmonic, quasi-periodic, aperiodic and chaotic responses. The long time response of the system depends on its initial conditions, and they can undergo different bifurcations in the parameter space as compared to those observed in linear systems, yielding sudden jumps in the response amplitude and/or switching in its period (doubling/halving). While we are currently able to show that, for some design parameters a nonlinear harvester can outperform a linear one, we are still unable to provide distinctive guidelines on how to properly design a nonlinear energy harvester for a given excitation source. Furthermore, we are still many steps away from designing electronic circuits specifically optimized to maximize the advantages of the nonlinearity and to properly condition the complex responses typical of their behavior. Based on the research results reported in the open literature, we can say with confidence that the influence of nonlinearities on the performance of energy harvesters depends on the nature of the excitation source. If the excitation source is harmonic with a fixed frequency, the nonlinearity can be used to potentially decrease the sensitivity to uncertainties in the design parameters permitting the device to account for small variations in the excitation and/or natural frequency around their originally designed values. However, this advantage comes at an additional cost. Often, the nonlinearity yields coexisting steady-state responses with vastly different power outputs for a given excitation frequency. As a result, depending on the competing basins of attraction of these responses, the harvester can either provide high or low levels of output power. We agree with Professor Mann that this issue can be overcome by designing certain mechanisms that provide external input to guarantee that the harvester operates at its high power level capacity. However, as discussed in the manuscript, such mechanisms have yet to be thoroughly investigated and understood. When the excitation source has Gaussian stationary random characteristics with a bandwidth much larger than that of the excitation (White Noise), a nonlinear harvester with a monostable potential energy function does not seem capable of offering any additional advantages over the linear design. However, when properly designed, based on the intensity of the input excitation, a harvester with a bistable potential well was shown to provide performance enhancements over the linear design. This, however, requires prior knowledge of the noise intensity because the optimal shape of the bistable potential is very sensitive to variations in the noise intensity. As a result, when the noise intensity changes, the mean output power drops significantly if the shape of the potential function is not adjusted accordingly. This, in the authors’ opinion, constitutes a very interesting area for future research. The nonlinearity seems to have its most benefits when the random excitation is colored, i.e., it has a bandwidth comparable to that of the harvester. Recently, Stanton et al. [1] illustrated these advantages by using Melnikov theory to find the combination of design parameters for which a bistable harvester can be designed to outperform the linear design. Masana and Daqaq [2] also illustrated experimentally that the bistable harvester is much less sensitive to changes in the center frequency, bandwidth, and intensity of the colored excitation than a monostable design. To close, we note that few engineering examples exist where large nonlinearities are deliberately introduced to enhance performance [3]. The field of energy harvesting is certainly one such example, and has opened new avenues of research into the design of nonlinear systems. Performance benefits in harvesting devices can be achieved with the inclusion of phenomena that have been previously considered as undesirable or of lesser practical value. As such, we believe that nonlinear dynamics benefits from the problems arising in the field of energy harvesting as much as nonlinearities can be beneficial for the performance of energy harvesting systems.

Investigating the energy harvesting potential of ferro-fluids sloshing in base-excited containers

This paper investigates the potential of designing a vibratory energy harvester which utilizes a ferrofluid sloshing in a seismically excited tank to generate electric power. Mechanical vibrations change the orientational order of the magnetic dipoles in the ferrofluid and create a varying magnetic flux which induces an electromotive force in a coil wound around the tank, thereby generating an electric current according to Faradays law. Several experiments are performed on a cylindrical container of volume 5x10-5 m3 carrying a ferrofluid and subjected to different base excitation levels. Initial results illustrate that the proposed device can be excited at one or multiple modal frequencies depending on the containers size, can exhibit tunable characteristics by adjusting the external magnetic field, and currently produces 28 mV of open-circuit voltage using a base excitation of 2.5 m/s2 at a frequency of 5.5 Hz.