Performance improvement of the stochastic-resonance-based tri-stableenergy harvester under random rotational vibration

In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered.The stationary probability density function(SPDF)of the harvester is obtained by the improved stochastic averaging.Then,with the adiabatic approximation theory,the analytical expression of signal-to-noise ratio(SNR)for the TEH is deduced to characterize stochastic resonance(SR).To enhance direct current(DC)power delivery from a rotational TEH,the influences of system parameters on SR is discussed.The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system.The TEH has higher harvesting performance under the optimal SR.That is,the optimal parameter combinations can induce optimal SR and maximize harvesting performance.Thus,the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.

Disturbance rejection and performance enhancement of perturbed tri-stable energy harvesters by adaptive finite-time disturbance observer

Tristable energy harvesters(TEHs)have been proposed to achieve broad frequency bandwidth and superior low-frequency energy harvesting performance.However,due to the coexistence of three potential wells and the sensitivity to system conditions and external disturbances,the desired high-amplitude inter-well oscillation in the TEHs may be replaced by the chaotic or intra-well oscillations with inferior energy output.Specifically,the chaos has an unpredictable trajectory and may cause system damages,lessen the structural durability as well as require a more complicated circuit for power management.Therefore,in this paper,we firstly propose an adaptive finite-time disturbance observer(AFTDO)for performance enhancement of TEHs by detecting the external disturbances that induce the chaos,and reject them for the recovery of the desired inter-well motion.The proposed AFTDO eliminates the need to know in advance the upper bounds of imposed perturbations in conventional observers by means of the proposed adaptive protocols,leading to the higher efficacy of estimation.The mathematical model of the piezoelectric TEH system and the AFTDO is provided.To demonstrate the effectiveness of the AFTDO,a series of numerical simulations have been performed.Results show that for both cases with sinusoidal and impulsive disturbances,the AFTDO can successfully track the trajectories of the disturbance signals with the adaptive gain,and reject the disturbance to enable the TEH to sustain the periodic inter-well oscillation with effective energy harvesting performance.

A viscoelastic nonlinear energy sink with an electromagnetic energy harvester:Narrow-band random response

Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.

Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control

This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.

Output Voltage Model and Mechanical-Magnetic Design of Magnetostrictive Vibration Energy Harvester with a Rotating Up-Frequency Structure1

A vibration energy harvester can harvest vibration energy in the environment and convert it into electrical energy to power the sensors in the Internet of Things.Human walking contains high-quality vibration energy,which serves as the energy source for vibration energy harvesters due to its abundant availability,high energy conversion efficiency,and environmental friendliness.It is difficult to harvest human walking vibration due to its low frequency.Converting the low-frequency vibration of human walking into high-frequency vibration has attracted attention.In previous studies,vibration energy harvesters typically increase frequency by raising excitation frequency or inducing free vibration.When walking frequency changes,the up-frequency method of raising the excitation frequency changes the voltage frequency,resulting in the best load resistance change and reducing the output power.The up-frequency method of inducing free vibration does not increase the external excitation frequency,which has relatively low output power.This paper designs a magnetostrictive vibration energy harvester with a rotating up-frequency structure.It consists of a rotating up-frequency structure,a magnetostrictive structure,coils,and bias magnets.The main body of the rotating up-frequency structure comprises a torsion bar and a flywheel with a dumbbell-shaped hole.The magnetostrictive structure includes four magnetostrictive metal sheets spliced by Galfenol and steel sheets.The torsion bar and flywheel interact to convert low-frequency linear vibration into rotating high-frequency excitation vibration of the flywheel.The flywheel plucks the magnetostrictive metal sheet with a high excitation frequency to generate free vibration.The vibration energy harvester increases the excitation frequency while inducing free vibration,which can effectively improve the output power.To characterize the excitation vibration and free vibration,based on the theory of Euler-Bernoulli beam theory,the vibration equation of the magnetostrictive metal sheet after being excited is given.According to the classical machine-magnetic coupling model and the Jiles-Atherton physical model,the relationship between stress and magnetization strength is derived.Combined with Faraday's law of electromagnetic induction,the distributed dynamic output voltage model is established.This model can predict the output voltage at different excitation frequencies.Based on this model,the mechanical-magnetic structural parameter optimization design is carried out.The parameters of the magnetostrictive metal sheet,the bias magnet,and the rotating up-frequency structure are determined.A comprehensive experimental system is established to test the device.The peak-to-peak voltage and output voltage signal by the proposed model are compared.The average relative deviation of the peak-to-peak voltage and the output voltage signal is 4.9%and 8.2%,respectively.The experimental results show that the output power is proportional to the excitation frequency.The optimum load resistance is always 800Ωas the excitation frequency changes,simplifying the impedance-matching process.The maximum peak-to-peak voltage of the device is 58.60 V,the maximum root mean square(RMS)voltage is 9.53 V,and the maximum RMS power is 56.20 mW.The magnetostrictive vibration energy harvester with a rotating up-frequency structure solves the problem of impedance matching,which improves the output power.The proposed distributed dynamic output voltage model can effectively predict the output characteristics.This study can provide structural and theoretical guidance for up-frequency structure vibration energy harvesters for human walking vibration.

Deployment optimization for target perpetual coverage in energy harvesting wireless sensor network

Energy limitation of traditional Wireless Sensor Networks(WSNs)greatly confines the network lifetime due to generating and processing massive sensing data with a limited battery.The energy harvesting WSN is a novel network architecture to address the limitation of traditional WSN.However,existing coverage and deployment schemes neglect the environmental correlation of sensor nodes and external energy with respect to physical space.Comprehensively considering the spatial correlation of the environment and the uneven distribution of energy in energy harvesting WSN,we investigate how to deploy a collection of sensor nodes to save the deployment cost while ensuring the target perpetual coverage.The Confident Information Coverage(CIC)model is adopted to formulate the CIC Minimum Deployment Cost Target Perpetual Coverage(CICMTP)problem to minimize the deployed sensor nodes.As the CICMTP is NP-hard,we devise two approximation algorithms named Local Greedy Threshold Algorithm based on CIC(LGTA-CIC)and Overall Greedy Search Algorithm based on CIC(OGSA-CIC).The LGTA-CIC has a low time complexity and the OGSA-CIC has a better approximation rate.Extensive simulation results demonstrate that the OGSA-CIC is able to achieve lower deployment cost and the performance of the proposed algorithms outperforms GRNP,TPNP and EENP algorithms.

Highly Flexible Graphene-Film-Based Rectenna for Wireless Energy Harvesting

Herein,we report the design,fabrication,and performance of two wireless energy harvesting devices based on highly flexible graphene macroscopic films(FGMFs).We first demonstrate that benefiting from the high conductivity of up to 1×10^(6)S m^(-1)and good resistive stability of FGMFs even under extensive bending,the FGMFs-based rectifying circuit(GRC)exhibits good flexibility and RF-to-DC efficiency of 53%at 2.1 GHz.Moreover,we further expand the application of FGMFs to a flexible wideband monopole rectenna and a 2.45 GHz wearable rectenna for harvesting wireless energy.The wideband rectenna at various bending conditions produces a maximum conversion efficiency of 52%,46%,and 44%at the 5th Generation(5G)2.1 GHz,Industrial Long-Term Evolution(LTE)2.3 GHz,and Scientific Medical(ISM)2.45 GHz,respectively.A 2.45 GHz GRC is optimized and integrated with an AMC-backed wearable antenna.The proposed 2.45 GHz wearable rectenna shows a maximum conversion efficiency of 55.7%.All the results indicate that the highly flexible graphene-film-based rectennas have great potential as a wireless power supplier for smart Internet of Things(loT)applications.

Integration of a nonlinear energy sink and a piezoelectric energy harvester

A mechanical-piezoelectric system is explored to reduce vibration and to harvest energy. The system consists of a piezoelectric device and a nonlinear energy sink （NES）, which is a nonlinear oscillator without linear stiffness. The NES-piezoelectric sys- tem is attached to a 2-degree-of-freedom primary system subjected to a shock load. This mechanical-piezoelectric system is investigated based on the concepts of the percentages of energy transition and energy transition measure. The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness. The plots of wavelet transforms are used to indicate that the nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the tran- sient vibration, and a 1：1 transient resonance capture occurs between two subsystems. The investigation demonstrates that the integrated NES-piezoelectric mechanism can re- duce vibration and harvest some vibration energy.

COUPLED ANALYSIS FOR THE HARVESTING STRUCTURE AND THE MODULATING CIRCUIT IN A PIEZOELECTRIC BIMORPH ENERGY HARVESTER

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio （length/thickness） and the non-dimensional end mass of the harvesting structure. The numerical results show that： （1） the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and （2） for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton＇s principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed- parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Low-frequency and broadband vibration energy harvester driven by mechanical impact based on layer-separated piezoelectric beam

Vibration energy harvesting is to transform the ambient mechanical energy to electricity. How to reduce the resonance frequency and improve the conversion efficiency is very important. In this paper, a layer-separated piezoelectric cantilever beam is proposed for the vibration energy harvester(VEH) for low-frequency and wide-bandwidth operation, which can transform the mechanical impact energy to electric energy. First,the electromechanical coupling equation is obtained by the Euler-Bernoulli beam theory.Based on the average method, the approximate analytical solution is derived and the voltage response is obtained. Furthermore, the physical prototype is fabricated, and the vibration experiment is conducted to validate the theoretical principle. The experimental results show that the maximum power of 0.445 μW of the layer-separated VEH is about3.11 times higher than that of the non-impact harvester when the excitation acceleration is 0.2 g. The operating frequency bandwidth can be widened by increasing the stiffness of the fundamental layer and decreasing the gap distance of the system. But the increasing of operating frequency bandwidth comes at the cost of reducing peak voltage. The theoretical simulation and the experimental results demonstrate good agreement which indicates that the proposed impact-driving VEH device has advantages for low-frequency and wide-bandwidth. The high performance provides great prospect to scavenge the vibration energy in environment.

Modeling and power performance improvement of a piezoelectric energy harvester for low-frequency vibration environment

A novel oscillator structure, bimorph piezoelectric cantilever beam with two-stepped variable thicknesses,is proposed to improve the energy harvestingperformance of the vibration energy harvester (VEH) under low-frequency vibration environment. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler-Bernoulli beam assumptions, and the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the electromechanical coupled governing equations for the piezoelectric energy harvesterareintroduced by means of the Lagrange equations. Furthermore, the steady state response expressions are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed and the effects ofthe lengths-ratio, thicknesses-ratio,end thicknessand load resistance on the output voltage, harvested power and power density are discussed. Moreover, to verify thecorrectness ofanalytical results, the finite element method (FEM)simulationis also conducted to analyze performance of the proposed VEH, where a good agreement is presented. All the results show thatthe present oscillator structureis moreefficient than the conventional uniform beam structure, specifically, for vibration energy harvesting in low-frequency environment.

Energy harvester array using piezoelectric circular diaphragm for rail vibration

Generating electric energy from mechanical vibration using a piezoelectric circular membrane array is presented in this paper.The electrical characteristics of the functional array consisted of three plates with varies tip masses are examined under dynamic conditions.With an optimal load resistor of 11 k,an output power of 21.4 m W was generated from the array in parallel connection at 150 Hz under a pre-stress of 0.8 N and a vibration acceleration of9.8 m/s2.Moreover,the broadband energy harvesting using this array still can be realized with different tip masses.Three obvious output power peaks can be obtained in a frequency spectra of 110 Hz to 260 Hz.The results show that using a piezoelectric circular diaphragm array can increase significantly the output of energy compared with the use of a single plate.And by optimizing combination of tip masses with piezoelectric elements in array,the frequency range can be tuned to meet the broadband vibration.This array may possibly be exploited to design the energy harvesting for practical applications such as future high speed rail.

Effect of oxygen partial pressure and transparent substrates on the structural and optical properties of ZnO thin films and their performance in energy harvesters

Zinc oxide(ZnO) thin films were deposited onto different substrates — tin-doped indium oxide(ITO)/glass, ITO/polyethylene naphthalate(PEN), ITO/polyethylene terephthalate(PET) — by the radio-frequency(RF) magnetron sputtering method. The effect of various O2/(Ar+O2) gas flow ratios(0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6) was studied in detail. ZnO layers deposited onto ITO/PEN and ITO/PET substrates exhibited a stronger c-axis preferred orientation along the(0002) direction compared to ZnO deposited onto ITO/glass. The transmittance spectra of ZnO films showed that the maximum transmittances of ZnO films deposited onto ITO/glass, ITO/PEN, and ITO/PET substrates were 89.2%, 65.0%, and 77.8%, respectively. Scanning electron microscopy(SEM) images of the film surfaces indicated that the grain was uniform. The cross-sectional SEM images showed that the ZnO films were columnar structures whose c-axis was perpendicular to the film surface. The test results for a fabricated ZnO thin film based energy harvester showed that its output voltage increased with increasing acceleration of external vibration.

Analysis on Output Power for Multi-direction Piezoelectric Vibration Energy Harvester

To predict the performance of multi-direction piezoelectric vibration energy harvester,an equation for calculating its output power is obtained based on elastic mechanics theory and piezoelectricity theory.Experiments are performed to verify theoretical analysis.When the excitation direction is along Y direction,a maximal output power about 0.139 mW can be harvested at a resistive load of 65kΩ and an excitation frequency of 136 Hz.Theoretical analysis agrees well with experimental results.Furthermore,the performance of multi-direction vibration energy harvester is experimentally tested.The results show that the multi-direction vibration energy harvester can harvest perfect energy as the excitation direction changes in XY plane,YZ plane,XZ plane and body diagonal plane of the harvester.

Incident flow effects on the performance of piezoelectric energy harvesters from galloping vibrations

In this paper, we investigate experimentally the concept of energy har- vesting from galloping oscillations with a focus on wake and turbulence effects. The .harvester is composed of a unimorph piezoelectric cantilever beam with a square cross-section tip mass. In one case, the harvester is placed in the wake of another galloping harvester with the objective of determining the wake effects on the response of the harvester. In the second case, meshes were placed upstream of the harvester with the objective of investigating the effects of upstream turbulence on the response of the harvester. The results show that both wake effects and up- stream turbulence significantly affect the response of the harvester. Depending on the spacing between the two squares and the opening size of the mesh, wake and upstream turbulence can positively enhance the level of the harvested power.

A piezoelectric energy harvester based on internal resonance

A vibration-based energy harvester is essentially a resonator working in a limited frequency range.To increase the working frequency range is a challenging problem.This paper reveals a novel possibility for enhancing energy harvesting via internal resonance.An internal resonance energy harvester is proposed.The excitation is successively assumed as the Gaussian white noise,the colored noise defined by a second-order filter,the narrow-band noise,and exponentially correlated noise.The corresponding averaged root-meansquare output voltages are computed.Numerical results demonstrate that the internal resonance increases the operating bandwidth and the output voltage.

A comprehensive review of miniatured wind energy harvesters

Following the current rapid development of the Internet of Things(IoT)and wireless condition monitoring systems,energy harvesters which use ambient energy have become a key part of achieving an energy-autonomous system.Miniature wind energy harvesters have attracted widespread attention because of their great potential of power density as well as the rich availability of wind energy in many possible areas of application.This article provides readers with a glimpse into the state-of-the-art of miniature wind energy harvesters.The crucial factors for them to achieve high working efficiency under lower operational wind speed excitation are analyzed.Various potential energy coupling mechanisms are discussed in detail.Design approaches for broadening operational wind-speed-range given a variety of energy coupling mechanisms are also presented,as observed in the literature.Performance enhancement mechanisms including hydrodynamic configuration optimization,and non-linear vibration pick-up structure are reviewed.Conclusions are drawn and the outlook for each coupling mechanisms is presented.

Advances in Triboelectric Nanogenerators for Blue Energy Harvesting and Marine Environmental Monitoring

Blue energy,which includes rainfall,tidal current,wave,and water-flow energy,is a promising renewable resource,although its exploitation is limited by current technologies and thus remains low.This form of energy is mainly harvested by electromagnetic generators(EMGs),which generate electricity via Lorenz force-driven electron flows.Triboelectric nano genera tors(TENGs)and TENG networks exhibit superiority over EMGs in low-frequency and high-entropy energy harvesting as a new approach for blue energy harvesting.A TENG produces electrical outputs by adopting the mechanism of Maxwell’s displacement current.To date,a series of research efforts have been made to optimize the structure and performance of TENGs for effective blue energy harvesting and marine environmental applications.Despite the great progress that has been achieved in the use of TENGs in this context so far,continuous exploration is required in energy conversion,device durability,power management,and environmental applications.This review reports on advances in TENGs for blue energy harvesting and marine environmental monitoring.It introduces the theoretical foundations of TENGs and discusses advanced TENG prototypes for blue energy harvesting,including TENG structures that function in freestanding and contact-separation modes.Performance enhancement strategies for TENGs intended for blue energy harvesting are also summarized.Finally,marine environmental applications of TENGs based on blue energy harvesting are discussed.

Enhance limit cycle oscillation in a wind flow energy harvester system with fractional order derivatives

Advances in material science and mathematics in conjunction with tech- nological needs have triggered the use of material and electric components with fractional order physical properties. This paper considers the mathematical model of a piezoelectric wind flow energy harvester system for which the capacitance of the piezoelectric material has fractional order current-voltage characteristics. Additionally the mechanical element is assumed to have fractional order damping. The analysis is focused on the effects of order of derivatives on the appearance and characteristics of limit circle oscillations （LCO）. It is obtained that, the order of derivatives to enhance the amplitude of LCO and lower the threshold condition leading to LCO. The domains of efficiency of the system are illustrated in various parameters spaces.