Nonlinear Harvester Research Articles

Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator

This paper deals with the study of the stability and the bifurcation analysis of a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting. It is shown that the proposed model exhibits the bistability for certain parametric conditions. Dulac’s criterion has been adopted to obtain the sufficient conditions for the global stability of the model. Moreover, the model exhibits different kinds of bifurcations (e.g., the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcations, Bogdanov-Takens bifurcation, and the homoclinic bifurcation) whenever the values of parameters of the model vary. The analytical findings and numerical simulations reveal far richer and complex dynamics in comparison to the models with no harvesting and with constant-yield predator harvesting.

Bifurcation analysis in a prey–predator model with nonlinear predator harvesting

In this paper, the spatiotemporal dynamics of a delayed diffusive prey–predator model with nonlinear predator harvesting is investigated. Through mathematical analysis, we obtain the conditions for Turing and Hopf bifurcation. Numerical simulations display a variety of spatial patterns including spots, strips, mixture of spots and strips, spiral, patchy structure, and chaos. The delay is found to have significant influence on the emergent spatial patterns, such as changing arm length and direction of strips, and accelerating the transformation of spatial patterns.

Global stabilization of high-energy response of a nonlinear wideband electromagnetic energy harvester

This paper presents a resonance-type vibration energy harvester with a Duffing-type nonlinear oscillator which is designed to perform effectively in a wide frequency band. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. Introducing a Duffing-type nonlinearity can expand the resonance frequency band and enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator may have coexisting multiple steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to give global stability to the high-energy orbit by destabilizing other unexpected low-energy orbits by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this paper, an improved control law that switches the load resistance according to a frequency-dependent threshold is proposed to ensure the oscillator to respond in the high-energy orbit without ineffective power consumption. Numerical study shows that the steady-state responses of the harvester with the proposed control low are successfully kept on the high-energy orbit without repeating activation of the excitationmode.

Characterization of a nonlinear MEMS-based piezoelectric resonator for wideband micro power generation

Micro-scale piezoelectric unimorph beams with attached proof masses are the most prevalent structures in MEMS-based energy harvesters considering micro fabrication and natural frequency limitations. In doubly clamped beams a nonlinear stiffness is observed as a result of midplane stretching effect which leads to amplitude-stiffened Duffing resonance. In this study, a nonlinear model of a doubly clamped piezoelectric micro power generator, taking into account geometric nonlinearities including stretching and large curvatures, is investigated. The governing nonlinear coupled electromechanical partial differential equations of motion are determined by exploiting Hamilton's principle. A semi-analytical approach implementing the perturbation method of multiple scales is used to solve the nonlinear coupled differential equations and analyze the primary and superharmonic resonances. Results indicate that operational bandwidth of the nonlinear harvester is enhanced considerably with respect to linear models. Moreover considerable amount of power is generated due to occurrence of superharmonic resonances. This yields to extraction of energy at subharmonics of the natural frequency which is crucially important in MEMS-based harvesters.

Theoretical analysis and experimental verification for improving energy harvesting performance of nonlinear monostable energy harvesters

Theoretical analysis and experimental verification of nonlinear monostable energy harvesters are presented to enhance energy harvesting performance from low-level ambient vibrations. Harmonic balance analysis of these harvesters demonstrates that there are two stable orbits (high-branch orbit and low-branch orbit) in a specific multi-solution range when the excitation level is larger than a threshold. Under the same excitation, these nonlinear harvesters may finally vibrate at different orbits depending on different initial conditions or disturbances. The energy harvesting efficiency will be greatly improved if high-branch oscillations could be induced in the multi-solution range. Numerical investigations into the influence of a disturbance method and initial conditions on high-branch oscillations are performed for energy harvesting enhancement of nonlinear monostable energy harvesters. Experimental results verify the effectiveness of adding disturbances by using an impact method for improving energy harvesting performance and the capability of nonlinear monostable energy harvesters in maintaining high-branch oscillations at low-level vibrations.

Recurrence Plot and Recurrence Quantification of the Dynamic Properties of Cross-Shaped Laminated Energy Harvester

The paper examines the dynamic properties of bistable cross-shaped laminate plates for broadband energy harvesting applications by converting mechanical vibration energy into the electrical power output. Bistable laminates plates coupled to piezoelectric transducers were excited by application of harmonic excitations and exhibited a range of vibration patterns. The vibration patterns included single-well oscillations and snap-through vibrations of both periodic and chaotic character; such vibration patterns led to a different power output. Classical spectral analysis of measured voltage, displacement and velocity time histories indicated the presence of a variety of nonlinear and chaotic phenomena. As a result, an analysis of the measured displacement and voltage time histories was carried out with the use of the Recurrence Plots and the Recurrence Quantification Analysis methods. The Recurrence Plots method was used for detection of qualitative changes in the dynamic behaviour of the non-linear harvesting system. In order to facilitate interpretation of piezoelectric voltage and laminate displacement, a detailed analysis using Recurrence Plots, Recurrence Quantification Analysis was employed.

Input-dependent performance study of a nonlinear piezoelectric energy harvester

This work reports an input-dependent performance study of a nonlinear piezoelectric energy harvester with introduced magnetic interaction. The performances of the novel harvester with two external magnet arrays (I and II) are compared. Array II that has symmetric magnetic force yields better voltage output under frequency sweep test. As such, the energy harvesting capacity with Array II is performed under two vibration inputs (I and II). Under excitation Input I with periodic varying frequency, experimental results show that the nonlinear piezoelectric harvester outperforms its linear counterpart (no magnetic interaction) at alternating input bandwidths. A 104.5% improvement of root mean square voltage output (318.2% of power output) is obtained under excitation of 0.334 g (root mean square) and bandwidth of 7 Hz. No advantage is observed under Input II consisting of one principal and finite non-principal components. However, detailed study indicates that the amplitude of the principal component and the amplitude ratio of the non-principal components to the principal component in Input II are essential to maintain large-amplitude periodic motion. Our work provides useful insights into the design, characterization, and application of nonlinear energy harvesters with external magnetic forces based on a priori knowledge of input.

Stability and bifurcation analysis in a predator–prey system with Michaelis–Menten type predator harvesting

The stability and bifurcation analysis for a predator–prey system with the nonlinear Michaelis–Menten type predator harvesting are taken into account. The existence and stability of possible equilibria are investigated. Specially, the stability of some positive equilibria is determined by using numerical simulation method due to the fact that the expressions of determinant and trace of the Jacobian matrix at these equilibria are very complex. The rigorous mathematical proofs of the existence of saddle–node bifurcation and transcritical bifurcation are derived with the help of Sotomayor’s theorem. Furthermore, in order to determine the stability of limit cycle of Hopf bifurcation, the first Lyapunov number is calculated and a numerical example is given to illustrate graphically. Choosing two parameters of the system as bifurcation parameters, we prove that the system exhibits Bogdanov–Takens bifurcation of codimension 2 by calculating a universal unfolding near the cusp. Numerical simulations are carried out to demonstrate the validity of theoretical results. Our research will be useful for understanding the dynamic complexity of ecosystems or physical systems when there is the nonlinear Michaelis–Menten type harvesting effect on predator population. This kind of nonlinear harvesting is more realistic and reasonable than the model with constant-yield harvesting and constant-effort harvesting. It can be thought as a supplement to existing literature on the dynamics of this system, since there is little literature involved in nonlinear type harvesting for the system up to now.

Internal resonance with commensurability induced by an auxiliary oscillator for broadband energy harvesting

An internal resonance based broadband vibration energy harvester is proposed by introducing an auxiliary oscillator to the main nonlinear harvesting oscillator. Compared to conventional nonlinear energy harvesters, the natural frequencies of this two-degree-of-freedom nonlinear system can be easily adjusted to be commensurable which will result in more resonant peaks and better wideband performance. Experimental measurements and equivalent circuit simulations demonstrate that this design outperforms its linear counterpart. In addition to the open-circuit voltage, the optimal resistance to obtain the maximum power is determined. Nearly 130% increase in the bandwidth is achieved compared to the linear counterpart at an excitation level of 2 m/s2. The findings provide insight for the design of a broadband energy harvester when there is nonlinearity and internal resonance.

Dynamics of a vibrational energy harvester with a bistable beam: voltage response identification by multiscale entropy and “0-1” test

The use of bistable laminates is a potential approach to realize broadband piezoelectric-based energy harvesting by introducing elastic non-linearities to the system. In this paper the dynamic response of a piezoelectric material attached to a bistable laminate beam is examined based on the experimental measurement of the generated voltage-time series. The system was subjected to harmonic excitations and exhibited single-well and snap-through vibrations of both periodic and chaotic character. The ability to identify the vibration modes of the energy harvester is important since different levels of power are expected in each dynamic mode. We identify the dynamics of the selected system response using return maps, multiscale entropy, and “0-1” test. The potential of the approaches to identify periodic and chaotic modes and snap-through events in the non-linear bistable harvester is described.

Necessary and Sufficient Conditions for the Existence of Periodic Solutions of a Nicholson Type Delay System

We consider a Nicholson type system for two species with mutualism and nonlinear harvesting terms. We give sufficient conditions for the existence of a positive periodic solution. We also provide a necessary condition; more precisely, we prove that if the harvesting rate is large enough, then 0 is a global attractor for the positive solutions and, in particular, positive periodic solutions cannot exist.

Coupled static and dynamic FE analyses of a nonlinear electromechanical vibration energy harvester

Coupled static and dynamic FE analyses of a nonlinear electromechanical vibration energy harvester

Periodic Solutions of a Nonautonomous Leslie-Gower Predator-Prey Model with Non-Linear Type Prey Harvesting on Time Scales

In this paper, we investigate the existence of periodic solutions of modified version of the Leslie-Gower predator-prey model with Holling-type II functional response in the presence of Michaelis-Menten type prey harvesting over a time scale. Sufficient conditions for the existence of periodic solutions are derived by using the continuation theorem of coincidence degree theory. The condition we obtain is easily verifiable and not much restricted.

Stationary distribution and periodic solution for stochastic predator-prey systems with nonlinear predator harvesting

In this paper, we investigate the dynamics of the stochastic autonomous and non-autonomous predator-prey systems with nonlinear predator harvesting respectively. For the autonomous system, we first give the existence of the global positive solution. Then, in the case of persistence, we prove that there exists a unique stationary distribution and it has ergodicity by constructing a suitable Lyapunov function. The result shows that, the relatively weaker white noise will strengthen the stability of the system, but the stronger white noise will result in the extinction of one or two species. Particularly, for the non-autonomous periodic system, we show that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, numerical simulations illustrate our theoretical results.

Internal resonance for nonlinear vibration energy harvesting

The transformation of waste vibration energy into low-power electricity has been heavily researched over the last decade to enable self-sustained wireless electronic components. Monostable and bistable nonlinear oscillators have been explored by several research groups in an effort to enhance the frequency bandwidth of operation. Linear two-degree-of-freedom (2-DOF) configurations as well as the combination of a nonlinear single-DOF harvester with a linear oscillator to constitute a nonlinear 2-DOF harvester have also been explored to develop broadband energy harvesters. In the present work, the concept of nonlinear internal resonance in a continuous frame structure is explored for broadband energy harvesting. The L-shaped beam-mass structure with quadratic nonlinearity was formerly studied in the nonlinear dynamics literature to demonstrate modal energy exchange and the saturation phenomenon when carefully tuned for two-to-one internal resonance. In the current effort, piezoelectric coupling and an electrical load are introduced, and electromechanical equations of the L-shaped energy harvester are employed to explore primary resonance behaviors around the first and the second linear natural frequencies for bandwidth enhancement. Simulations using approximate analytical frequency response equations as well as numerical solutions reveal significant bandwidth enhancement as compared to a typical linear 2-DOF counterpart. Vibration and voltage responses are explored, and the effects of various system parameters on the overall dynamics of the internal resonance-based energy harvesting system are reported.

Self-sufficient electronic control for nonlinear, frequency tunable, piezoelectric vibration harvesters

Research in vibration energy harvesting focuses increasingly on nonlinear harvesters. In comparison to linear harvesters they show an inherent larger bandwidth through hardening or softening effects and higher conversion efficiency. A further increase of the bandwidth and thus a higher energy yield can be achieved by controlled tuning of such a nonlinear system. In this paper a self-sufficient tuning control electronic, which is directly powered by the harvester, is presented.

Experimental verificatio of load resistance switching for global stabilization of high-energy response of a nonlinear wideband electromagnetic vibration energy harvester

This paper presents an experimental verification of a self-excitation control of a resonance- type vibration energy harvester with a Duffing-type nonlinearity which is designed to perform effectively in a wide frequency range. For the conventional linear vibration energy harvester, the performance of the power generation at the resonance frequency and the bandwidth of the resonance peak are trade-off. The resonance frequency band can be expanded by introducing a Duffing-type nonlinear oscillator in order to enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator can have multiple stable steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to provide the global stability to the highest-energy solution by destabilizing other unexpected lower-energy solutions by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. It has been experimentally validated that this control law imparts the self-excitation capability to the oscillator to show an entrainment into the highest-energy solution.

Piezomagnetoelastic broadband energy harvester: Nonlinear modeling and characterization

Piezomagnetoelastic energy harvesters are one among the widely explored configurations to improve the broadband characteristics of vibration energy harvesters. Such nonlinear harvesters follow a Moon beam model with two magnets at the base and one at the tip of the beam. The present article develops a geometric nonlinear mathematical model for the broadband piezomagnetoelastic energy harvester. The electromechanical coupling and the nonlinear magnetic potential equations are developed from the dimensional system parameters to describe the nonlinear dynamics exhibited by the system. The developed model is capable of characterizing the monostable, bistable and tristable operating regimes of the piezomagnetoelastic energy harvester, which are not explicit in the Duffing representation of the system. Bifurcations and attractor motions are analyzed as nonlinear functions of the distance between base magnets and the field strength of the tip magnet. The model is further used to characterize the potential wells and stable states, with due focus on the performance of the system in broadband energy harvesting.

Axial Suspension Compliance and Compression for Enhancing Performance of a Nonlinear Vibration Energy Harvesting Beam System

Developing energy harvesting platforms that are strongly sensitive to the low and diffused frequency spectra of common environmental vibration sources is a research objective receiving great recent attention. It has been found that utilizing designs and incorporating structural influences that induce small values of linear stiffness may considerably enhance the power generation capabilities of energy harvesting systems. This research examines these two factors in new light toward the development of a biologically-inspired energy harvesting beam platform that exploits axial compressive effects and compliant suspensions. Through theory and experiments, it is found that the strategic exploitation of such characteristics promotes dramatic improvements in the average power that may be generated for the same excitation conditions. Examining the origin of these performance enhancements, it is seen that large compliance in the compressed axial suspensions facilitates a favorable redistribution of dynamic energy, which thereby enables greater bending of the harvester beam and increased electromechanical transduction.

Electric load optimization of a nonlinear mono-stable duffing harvester excited by white noise

This paper investigates the electric load optimization of a nonlinear mono-stable Duffing energy harvester under white noise excitations considering symmetric and asymmetric nonlinear restoring forces. Statistical linearization is utilized to obtain approximate analytical expressions for the statistical averages including the average output power, which is then optimized with respect to the electric load. It is shown that the optimal load is dependent on the nonlinearity unless the ratio between the period of the mechanical system and the time constant of the harvesting circuit is large. Furthermore, it is demonstrated that, under optimal electric loading, a mono-stable Duffing harvester with a symmetric nonlinear restoring force can never produce higher average power levels than an equivalent linear harvester regardless of the magnitude of the nonlinearity. On the other hand, asymmetries in the restoring force are shown to provide performance improvements over an equivalent linear harvester.