Nonlinear Harvester Research Articles

A Measurement Methodology for the Characterization of a Compensated Nonlinear Energy Harvester for Vertical Operation

In this paper, a measurement methodology for the characterization of the mechanical and electrical behavior of a nonlinear vibrational harvester is discussed and demonstrated on a real case study. The harvester, here considered, takes advantage of a flexible beam in a snap-through-buckling configuration and a novel magnetic repulsion mechanism to compensate for the asymmetric behavior of the device, in the vertical direction, due to the effect of the proof mass load. A measurement protocol aimed at the device performance estimation in terms of the minimum acceleration, the number of switching events, the output voltage, the generated power, and the mechanical-to-electrical conversion efficiency of the system is discussed. The advantages of the proposed compensation strategy are highlighted by evaluating the device’s performances in the range of frequency 0.5–12 Hz for different tilts applied to the device and compared to the performance of the same device without the repulsion mechanism. The harvester is capable of scavenging energy in the range 0.5–5 Hz with acceptable efficiency; it can, however, be exploited up to 12 Hz with an acceptable loss of efficiency. A power of about $412~\mu \text{W}$ with a root-mean-square acceleration of 10.22 m/s2 at 5 Hz and an efficiency of about 23.5% has been measured for the harvester, with the repulsive mechanism, operated in the vertical position. The power generated is suitable for powering wireless devices.

A non-autonomous Leslie\u2013Gower model with Holling type IV functional response and harvesting complexity

This paper considers a non-autonomous modified Leslie–Gower model with Holling type IV functional response and nonlinear prey harvesting. The permanence of the model is obtained, and sufficient conditions for the existence of a periodic solution are presented. Two examples and their simulations show the validity of our results.

A Nonlinear Broadband Electromagnetic Vibration Energy Harvester Based on Double-Clamped Beam

The performance of vibration energy harvesters is usually restricted by their frequency bandwidth. The double-clamped beam with strong natural nonlinearity is a simple way that can effectively expand the frequency bandwidth of the vibration energy harvester. In this article, a nonlinear electromagnetic vibration energy harvester with monostable double-clamped beam was proposed. A systematic analysis was conducted and a distributed parameter analytical model was established. On this basis, the output performance was estimated by the analytical model. It was found that the nonlinearity of the double-clamped beam had little influence on the maximum output, while broadening the frequency bandwidth. In addition, the resonant frequency, the frequency bandwidth, and the maximum output all increased following the increase of excitation level. Furthermore, the resonant frequency varies with the load changes, due to the electromagnetic damping, so the maximum output power should be gained at its optimum load and frequency. To experimentally verify the established analytical model, an electromagnetic vibration energy harvester demonstrator was built. The prediction by the analytical model was confirmed by the experiment. As a result, the open-circuit voltage, the average power and the frequency bandwidth of the electromagnetic vibration energy harvester can reach up to 3.6 V, 1.78 mW, and 11 Hz, respectively, under only 1 G acceleration, which shows a prospect for the application of the electromagnetic vibration energy harvester based on a double-clamped beam.

Design Procedure and Experimental Verification of a Broadband Quad-Stable 2-DOF Vibration Energy Harvester.

Vibration-based energy harvesters brought the idea of self-powered sensors to reality in the past few years. Many strategies to improve the performance of linear vibration energy harvesters that collect energy over a limited bandwidth have been proposed. In this paper, a bi-stable two degrees of freedom (2-DOF) cut-out vibration energy harvester employing a pair of permanent magnets is designed through a proposed design methodology. Based on this methodology, the nonlinear harvesters can be optimally designed such that the bandwidth can be widened for a targeted output voltage. The proper selection of the harvester parameters as well as the gap distances between the tip and the fixed magnets are the bases of this methodology. The mathematical modeling of the proposed harvester and the formula for the potential energy between the tip and the fixed magnets are presented. Additionally, to enhance the performance of the bi-stable energy harvester (BEH), a quad-stable energy harvester (QEH) was configured by adding more fixed magnets. Experiments were performed to validate the numerical simulations and the results showed that, the simulation and experimental results are consistent. The results indicate that, the QEH covers a wider bandwidth than the BEH and based on a figure of merit the QEH shows the best performance among many harvesters presented in the literature.

Uncertainty Analysis of Excitation Conditions on Performance of Nonlinear Monostable Energy Harvesters

Nonlinear energy harvesters were found to be sensitive to excitation conditions. In order to reveal the influence mechanism of the excitation condition on the energy harvesting performance, this paper presents an uncertainty analysis for nonlinear monostable energy harvesters (NMEHs). An improved interval extension based on the second-order Taylor’s series is presented as a new uncertainty analysis method. A mathematic example is used to demonstrate that the bounds of responses based on this method are more accurate than the classic interval extension when the dependence of the response on the uncertain variable is nonlinear. Meanwhile, the results from the Monte Carlo simulation are used to verify the accuracy of the proposed method. It is confirmed that the proposed method is suitable for quantifying the propagation of the uncertain level and frequency of the excitation for the NMEH. The results show that the output voltage of the NMEH is more sensitive to the frequency than the level of excitation, for which the influence mechanism is revealed.

Modeling and Analysis of Galfenol Nonlinear Cantilever Energy Harvester With Elastic Magnifier

To improve low-frequency broadband performances of a traditional cantilever energy harvester (TCEH), a nonlinear CEH (NCEH) with elastic magnifier (EM) (NCEH + EM) is studied. Based on the constitutive equations with the variable piezomagnetic coefficient, Faraday law, dynamic equilibrium, and harmonic balance theories, the two-degree-of-freedom lumped parameter nonlinear coupled model of NCEH + EM is established and the frequency analytical expressions are derived. Comparisons between the calculated and measured results show that the model can describe the nonlinear behaviors of TCEH. Simulated results show that the designed hard-spring NCEH + EM with two resonant frequencies can magnify low-frequency vibration amplitude, thus can lie in the high-energy orbit, and can generate much higher voltage and power than TCEH and NCEH in the broader low frequency range.

Stabilization of a General Trophic Model via Nonlinear Feedback Harvesting

Stabilization of a General Trophic Model via Nonlinear Feedback Harvesting

Dynamics of Modified Leslie-Gower Harvested Predator-Prey Model with Beddington-DeAngelis Functional Response

This paper considers a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and nonlinear prey harvesting strategy subject to the zero-flux boundary conditions. To understand the dynamics of the considered system, we derive sufficient conditions for permanence analysis, local stability, global stability and Hopf bifurcation of interior equilibrium point. Further we also investigate the existence and non-existence of non-constant positive steady state solutions.

Modeling a Nonlinear Harvester for Low Energy Vibrations

The availability of reliable analytical models is essential to the optimal design of energy harvesters and for the prediction of the system behavior. In this paper, we consider a low-input nonlinear system based on a flexible buckled beam forced in a bistable configuration. The harvester has been demonstrated to generate power in the excess of $400~\mu \text{W}$ with the optimal resistive load of 15 $\text{k}\Omega $ and a monotonic input with root-mean-square accelerations of 13.35 m/s2. The power generated is suitable for powering low-power measurement systems or sensor nodes. This paper focuses on a methodology for the modeling of the mechanical dynamical behavior of the device subject to a periodic impulsive signal. A measurement protocol for the evaluation of system’s hidden quantities, the beam’s restoring force, and the beam’s displacement between its stable states is introduced. A second-order behavioral model with a nonlinear term representing the beam’s restoring force has been used. In order to model the nonlinearity, two different potential energy functions have been compared by fitting the models to the experimental data with different constrains, through a performance index evaluating the fitting error.

Study on the Output Performance of a Nonlinear Hybrid Piezoelectric-Electromagnetic Harvester under Harmonic Excitation

The nonlinear energy harvester has become a hot topic due to its broad bandwidth and lower resonant frequency. Based on the preliminary test and analyses in our previous work, further analyses and tests on the influence of parameters, including the nonlinear magnetic force of the hybrid energy harvesting structure on its output performance under harmonic excitation, are performed in this paper, which will provide powerful support for structural optimization. For designing a nonlinear piezoelectric-electromagnetic hybrid energy harvester, the state equation of electromechanical coupling, the harmonic response and average output power, voltage, and current of a nonlinear hybrid energy harvester under harmonic excitation are derived by the harmonic balance method. The effects of the excitation acceleration and the external load on the output performance of the nonlinear hybrid energy harvester are verified through experimental tests. The results showed that the output power of the nonlinear hybrid energy harvester increases with the increase in the acceleration of harmonic excitation, and the increase is affected by external load. When the piezoelectric-electromagnetic hybrid harvester operates at the optimal load and the resonant frequency, the average output power reaches its maximum value and the increase of the load of the piezoelectric unit makes the resonant frequency of the energy harvesting system increase. Compared with linear harvesting structures, the nonlinear hybrid harvester has better flexibility of environmental adaptability and is more suitable for harvesting energy in low-frequency environments.

Orbit jump in bistable energy harvesters through buckling level modification

Abstract In the aim of giving an alternative to chemical batteries for energy supply of wireless autonomous devices, the present work focuses on ambient vibration energy harvesting using harvesters taking benefit of energy stored in an oscillating mass subjected to acceleration. More particularly, the attention is put on nonlinear bistable harvesters which offer a wider bandwidth than linear ones. However, due to their nonlinearities, these bistable harvesters exhibit different coexisting behaviors (orbits) on their operating frequency range. Only some of them are interesting for energy harvesting because of their high amplitude of oscillations inducing high energy levels (high orbits). Nevertheless, those high orbits are coexisting with low orbits (i.e., low harvestable energy) on a major portion of their frequency range and thus are not automatically reached. This work hence introduce new strategies to experience orbit jumps from low to high orbits playing with different parameters of the bistable harvester. Preliminary analyses based on energy considerations demonstrates that the most technically achievable strategy, adopted for the experimental analysis, is the orbit jump with fast modifications of its buckling level. More particularly, the bistable harvester is first quickly over-buckled at a particular instant and then quickly released to its initial buckling level when the mass reaches a maximum of displacement (in order to maximize the potential energy brought to the mass). Two elements of this strategy were adjustable: the amplitude of the buckling level variation and the instant at which this change starts. Experimental results show that choosing a good combination of those two elements leads to a high probability to jump from low to high orbits on the whole frequency range concerned by high orbits (from 70 % chance to 100 % chance to jump). Thanks to this orbit jump technique, the high orbits can be ensured for the considered bistable harvester on a continuous wide frequency range of 50 Hz (from 20 Hz to 70 Hz) on which the mean harvested power varies from 20 μ W to 500 μ W. Finally, it is shown that the energy consumed to ensure the orbit jump can be recovered within 2 s.

Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting

Abstract In this paper, we have studied the dynamical behaviour of a Leslie-Gower model with Holling type-IV functional response and nonlinear prey harvesting where target prey for harvesting are above a particular age which is called maturation delay. The model system has been studied using qualitative analysis, bifurcation theory, bionomic equilibrium, MSY and optimal harvesting policy. We explain that the interior equilibrium is delay dependent and locally asymptotically stable. The age-selective harvesting system under goes a Hopf-bifurcation with respect to the maturation delay. Conditions for the MSY and existence of bionomic equilibrium are analyzed and Pontryagin's maximum principle has been used to find the path of a singular control. Difficult analytical results are featured by numerical examples to better understand the system in a simple way.

A Nonlinear Electromagnetic Energy Harvesting System for Self-Powered Wireless Sensor Nodes

The Internet of things requires long-life wireless sensor nodes powered by the harvested energy from environments. This paper proposes a nonlinear electromagnetic energy harvesting system which may be used to construct fully self-powered wireless sensor nodes. Based on a nonlinear electromagnetic energy harvester (EMEH) with high output voltage, the model of a nonlinear interface circuit is derived and a power management circuit (PMC) is designed. The proposed PMC uses a buck–boost direct current-direct current (DC–DC) converter to match the load resistance of the nonlinear interface circuit. It includes two open-loop branches, which is beneficial to the optimization of the impedance matching. The circuit is able to work even if the stored energy is completely drained. The energy harvesting system successfully powered a wireless sensor node. Experimental results show that, under base excitations of 0.3 g and 0.4 g (where 1 g = 9.8 m·s−2) at 8 Hz, the charging efficiencies of the proposed circuit are 172% and 28.5% higher than that of the classic standard energy-harvesting (SEH) circuit. The experimental efficiency of the PMC is 41.7% under an excitation of 0.3 g at 8 Hz.

Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion

This study focuses on the spatial-temporal dynamics of predator–prey model with cross-diffusion where the intake rate of prey is per capita predator according to ratio-dependent functional response and the prey is harvested through nonlinear harvesting strategy. The permanence analysis and local stability analysis of the proposed model without cross-diffusion are analyzed. We derive the conditions for the appearance of diffusion-driven instability and global stability of the considered model. Also the parameter space for Turing region is specified by keeping the cross-diffusion coefficient as one of the crucial parameters. Numerical simulations are given to justify the proposed theoretical results and to show that the cross-diffusion term plays a significant role in the pattern formation.

A quasi-Gaussian approximation method for the Duffing oscillator with colored additive random excitation

Statistical analysis of stochastic dynamical systems is of considerable importance for engineers as well as scientists. Engineering applications require approximate statistical methods with a trade-off between accuracy and simplicity. Most exact and approximate methods available in the literature to study stochastic differential equations (SDEs) are best suited for linear or lightly nonlinear systems. When a system is highly nonlinear, e.g., a system with multiple equilibria, the accuracy of conventional methods degrades. This problem is addressed in this article, and a novel method is introduced for statistical analysis of special types of essentially nonlinear SDEs. In particular, second-order dynamical systems with nonlinear stiffness and additive random excitations are considered. The proposed approximate method can estimate second-order moments of the state vector (namely position and velocity), not only in the case of white noise excitation, but also when the excitation is a correlated noise. To illustrate the efficiency, a second-order dynamical system with bistable Duffing-type nonlinearity is considered as the case study. Results of the proposed method are compared with the Gaussian moment closure approximation for two types of colored noise excitations, one with first-order dynamics and the other with second-order dynamics. In the absence of exact closed-form solutions, Monte Carlo simulations are considered as the reference ideal solution. Results indicate that the proposed method gives proper approximations for the mean square value of position, for which the Gaussian moment closure method cannot provide good estimations. On the other hand, both methods provide acceptable estimations for the mean square value of velocity in terms of accuracy. Such nonlinear SDEs especially arise in energy-harvesting applications, when the ambient vibration can be modeled as a wideband random excitation. In such conditions, linear energy harvesters are no longer optimal designs, but nonlinear broadband harvesting techniques are hoped to show much better performance.

Bifurcations and simulations of two predator–prey models with nonlinear harvesting

Abstract We propose and investigate a predator-prey model with selective nonlinear harvesting for the prey and predator, such harvesting increases smoothly to a limit value when the density of harvested population is large enough. The existence of nonlinear harvesting makes the dynamics of the model more complicated, including multiple equilibria, limit cycle, heteroclinic and homoclinic orbit, bistability, saddle-node bifurcation, transcritical bifurcation, subcritical and supercritical Hopf bifurcation and Bogdanov–Takens bifurcation. Furthermore, some numerical simulations are given to illustrate these results.

Bifurcation analysis in a singular Beddington-DeAngelis predator-prey model with two delays and nonlinear predator harvesting.

In this paper, a differential algebraic predator-prey model including two delays, Beddington-DeAngelis functional response and nonlinear predator harvesting is proposed. Without considering time delay, the existence of singularity induced bifurcation is analyzed by regarding economic interest as bifurcation parameter. In order to remove singularity induced bifurcation and stabilize the proposed system, state feedback controllers are designed in the case of zero and positive economic interest respectively. By the corresponding characteristic transcendental equation, the local stability of interior equilibrium and existence of Hopf bifurcation are discussed in the different case of two delays. By using normal form theory and center manifold theorem, properties of Hopf bifurcation are investigated. Numerical simulations are given to demonstrate our theoretical results.

Periodic Solution for Stochastic Predator-Prey Systems with Nonlinear Harvesting and Impulses

In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov function and using comparison theorem with an impulsive differential equation, we study that a positive periodic solution exists. Thirdly, we prove that system is globally attractive. Finally, numerical simulations are presented to show the feasibility of the obtained results.

DYNAMICS OF A MODIFIED LESLIE-GOWER MODEL WITH GESTATION EFFECT AND NONLINEAR HARVESTIN

This study focuses on the dynamics of a modified Leslie-Gower predator-prey model where the intake rate of prey is by per capita predator according to Crowley-Martin functional response and prey is harvested through nonlinear harvesting strategy. Further the time-delay $(\tau)$ is imposed to utilize gestation period of predations. We investigate the permanence analysis of proposed system. The local stability of non-delayed model at all possible equilibrium points is studied. It is shown that the given model undergoes Hopf bifurcation around positive equilibrium point with respect to delay parameter $\tau$. Subsequently the stability of Hopf bifurcation and its direction are explored through normal and center manifold theories. The derived theoretical results are justified with the help of numerical simulations.

Parametric study and optimization of linear and nonlinear vibration absorbers combined with piezoelectric energy harvester

In this work, a harmonically excited generalized two degree of freedom nonlinear system is used to manifest the functions of both the vibration absorber and energy harvester simultaneously. The generalized system has been reduced to a linear primary system with linear/nonlinear absorber and harvester or nonlinear primary system with linear/ nonlinear absorber and harvester. Multi harmonic balance method (MHBM) along with arc length continuation is used for generating frequency response plots for different absorber and energy harvester system parameters with constant primary system parameters and excitation amplitude. The frequency response plot shows multiple branches of stable periodic solutions and jump at certain frequency ranges for systems with nonlinearity. The absorber and energy harvester parameters are optimized using an optimization procedure based on genetic algorithm in combination with response surface methodology. The method is validated with analytical solutions available in the literature for a linear primary system with linear absorber and harvester and nonlinear primary system with nonlinear absorber alone. This study demonstrates that the proposed optimization framework along with MHBM is suitable for generating the optimal frequency response for multi functional energy harvesting systems or systems with nonlinear absorber. The frequency response plots with optimal parameter values reiterates the fact that the absorber system with nonlinear element perform better compared to its linear counterpart over a wider band of frequencies. This study also reports the comparison of the performance of a combined nonlinear absorber harvester system with that of a nonlinear energy sink (NES) absorber harvester system.