Reconstructing the size of individual trees using log data from cut-to-length harvesters in Pinus radiata plantations: a case study in NSW, Australia

With their widespread utilization, cut-to-length harvesters have become a major source of ‘‘big data’’ for forest management as they constantly capture, and provide a daily flow of, information on log production and assortment over large operational areas. Harvester data afford the calculation of the total log length between the stump and the last cut but not the total height of trees. They also contain the length and end diameters of individual logs but not always the diameter at breast height overbark（DBHOB） of harvested stems largely because of time lapse, operating and processing issues and other system deficiencies. Even when DBHOB is extracted from harvester data, errors and/or bias of the machine measurements due to the variation in the stump height of harvested stems from that specified for the harvester head prior to harvesting and diameter measurement errors may need to be corrected. This study developed（1） a system of equations for estimating DBHOB of trees from diameter overbark（DOB） measured by a harvester head at any height up to 3 m above ground level and（2） an equation to predict the total height of harvested stems in P. radiata plantations from harvester data. To generate the data required for this purpose, cut-to-length simulations of more than 3000 trees with detailed taper measurements were carried out in the computer using the cutting patterns extracted from the harvester data and stump height survey data from clearfall operations. The equation predicted total tree height from DBHOB, total log length and the small end diameter of the top log. Prediction accuracy for total tree height was evaluated both globally over the entire data space and locally within partitioned subspaces through benchmarking statistics. These statistics were better than that of the conventional height-diameter equations for P. radiata found in the literature, even when they incorporated stand age and the average height and diameter of dominant trees in the stand as predictors. So this equation when used with harvester data would outperform the conventional equations in tree height prediction. Tree and stand reconstructions of the harvested forest is the necessary first step to provide the essential link of harvester data to conventional inventory, remote sensing imagery and Li DAR data. The equations developed in this study will provide such a linkage for the most effective combined use of harvester data in predicting the attributes of individual trees, stands and forests, and product recovery for the management and planning of P. radiata plantations in New South Wales, Australia.

Solar cell-based hybrid energy harvesters towards sustainability

Energy harvesting plays a crucial role in modern society.In the past years,solar energy,owing to its renewable,green,and infinite attributes,has attracted increasing attention across a broad range of applications from small-scale wearable electronics to large-scale energy powering.However,the utility of solar cells in providing a stable power supply for vari-ous electrical appliances in practical applications is restricted by weather conditions.To address this issue,researchers have made many efforts to integrate solar cells with other types of energy harvesters,thus developing hybrid energy har-vesters(HEHs),which can harvest energy from the ambient environment via different working mechanisms.In this re-view,four categories of energy harvesters including solar cells,triboelectric nanogenerators(TENGs),piezoelectric nanogenerators(PENGs),and thermoelectric generators(TEGs)are introduced.In addition,we systematically summar-ize the recent progress in solar cell-based hybrid energy harvesters(SCHEHs)with a focus on their structure designs and the corresponding applications.Three hybridization designs through unique combinations of TENG,PENG,and TEG with solar cells are elaborated in detail.Finally,the main challenges and perspectives for the future development of SCHEHs are discussed.

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.

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.

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.

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 new model for predicting the total tree height for stems cut-to-length by harvesters in Pinus radiata plantations

A new model for predicting the total tree height for harvested stems from cut-to-length(CTL)harvester data was constructed for Pinus radiata(D.Don)following a conceptual analysis of relative stem profi les,comparisons of candidate models forms and extensive selections of predictor variables.Stem profi les of more than 3000 trees in a taper data set were each processed 6 times through simulated log cutting to generate the data required for this purpose.The CTL simulations not only mimicked but also covered the full range of cutting patterns of nearly 0.45×106 stems harvested during both thinning and harvesting operations.The single-equation model was estimated through the multipleequation generalized method of moments estimator to obtain effi cient and consistent parameter estimates in the presence of error correlation and heteroscedasticity that were inherent to the systematic structure of the data.The predictive performances of our new model in its linear and nonlinear form were evaluated through a leave-one-tree-out cross validation process and compared against that of the only such existing model.The evaluations and comparisons were made through benchmarking statistics both globally over the entire data space and locally within specifi c subdivisions of the data space.These statistics indicated that the nonlinear form of our model was the best and its linear form ranked second.The prediction accuracy of our nonlinear model improved when the total log length represented more than 20%of the total tree height.The poorer performance of the existing model was partly attributed to the high degree of multicollinearity among its predictor variables,which led to highly variable and unstable parameter estimates.Our new model will facilitate and widen the utilization of harvester data far beyond the current limited use for monitoring and reporting log productions in P.radiata plantations.It will also facilitate the estimation of bark thickness and help make harvester data a potential source of taper data to reduce the intensity and cost of the conventional destructive taper sampling in the fi eld.Although developed for P.radiata,the mathematical form of our new model will be applicable to other tree species for which CTL harvester data are routinely captured during thinning and harvesting operations.

Modeling and analysis of magnetic spring enhanced lever-type electromagnetic energy harvesters

This study presents a novel enhanced monostable lever-type electromagnetic energy harvester(L-EEH).According to the positions of the coil and the lever pivot,four configurations are discussed to realize a better harvesting performance of the L-EEHs.On the basis of establishing the theoretical model of the L-EEH,the corresponding analytical solutions can be obtained by applying the harmonic balance method.The effects of the nonlinear coefficient,the lever ratio,the mass ratio,and the circuit parameters on the energy harvesting performance of L-EEHs are analyzed and discussed.The numerical and experimental efforts are carried out to verify the theoretical model and the energy harvesting performance.The results demonstrate that the maximum output voltage can be achieved with an appropriate lever ratio.Furthermore,the L-EEH possesses a considerable energy harvesting performance under a smaller lever ratio compared with the other three configurations.The output power can also be improved by adjusting the tip mass of the lever.The proposed L-EEH has a considerable operating bandwidth and an output power,which can reach 146.6 mW under the excitation amplitude of 0.3 g.

Theoretical Analysis of the Galloping Energy Harvesters under Bounded Random Parameter Excitation

In this paper,the response properties of galloping energy harvesters under bounded random parameter excitation are studied theoretically.The first-order approximate solution of the galloping energy harvester is derived by applying the multi-scales method.The expression for the largest Lyapunov exponent that determines the trivial solution is derived,and the corresponding simulation diagrams,including the largest Lyapunov exponent diagrams and time domain diagrams,verify our results.Then the steady-state response moments of the nontrivial solution are studied using the moment method,and the analytical expressions for the first-order and second-order moments of the voltage amplitude are obtained,respectively.The corresponding results show that wind speed enhances the steady-state response moments of the voltage amplitude.Meanwhile,the voltage output can be controlled by adjusting the cubic coefficient.To further verify the response characteristics of the galloping energy harvester,the stationary probability density functions of the displacement and velocity are obtained by the Monte-Carlo simulation method.The results show that the wind speed enhances the displacement of the bluff and the damping ratios should be reduced asmuch as possible to improve the performance.What’smore,the piezoelectric materials also impact the performance of the energy harvester.

Design and Analysis of MEMS Based Aluminum Nitride (AlN), Lithium Niobate (LiNbO₃) and Zinc Oxide (ZnO) Cantilever with Different Substrate Materials for Piezoelectric Vibration Energy Harvesters Using COMSOL Multiphysics Software

Interest in energy harvesters has grown rapidly over the last decade. The cantilever shaped piezoelectric energy harvesting beam is one of the most employed designs, due to its simplicity and flexibility for further performance enhancement. The research effort in the MEMS Piezoelectric vibration energy harvester designed using three types of cantilever materials, Lithium Niobate (LiNbO3), Aluminum Nitride (AlN) and Zinc Oxide (ZnO) with different substrate materials: aluminum, steel and silicon using COMSOL Multiphysics package were designed and analyzed. Voltage, mechanical power and electrical power versus frequency for different cantilever materials and substrates were modeled and simulated using Finite element method (FEM). The resonant frequencies of the LiNbO3/Al, AlN/Al and ZnO/Al systems were found to be 187.5 Hz, 279.5 Hz and 173.5 Hz, respectively. We found that ZnO/Al system yields optimum voltage and electrical power values of 8.2 V and 2.8 mW, respectively. For ZnO cantilever on aluminum, steel and silicon substrates, we found the resonant frequencies to be 173.5 Hz, 170 Hz and 175 Hz, respectively. Interestingly, ZnO/steel yields optimal voltage and electrical power values of 9.83 V and 4.02 mW, respectively. Furthermore, all systems were studied at different differentiate frequencies. We found that voltage and electrical power have increased as the acceleration has increased.

Lead-free silver niobate microparticles-loaded PDMS composite films for high-performance clip-like hybrid mechanical energy harvesters

A triboelectric nanogenerator(TENG)is a highly potential green energy harvesting technology to power small-scale electronic devices.Enhancing the overall electricity production capacity of TENGs is a primary concern for their utilization as an electricity generator in day-to-day life.Herein,we proposed a lead-free silver niobate(AgNbO_(3)(ANb))microparticles(MPs)-embedded polydimethylsiloxane(PDMS)composite film-based clip-like hybrid nanogenerator(HNG)device,producing an enhanced electrical output from the applied mechanical movements.The ANb MPs with a high dielectric constant were initially synthesized and embedded inside the PDMS polymer matrix.Various HNGs were fabricated utilizing ANb MPs/PDMS composite films/aluminum tape as negative/positive triboelectric films,respectively and operated in contact-separation mode.The electrical output from them was comparatively analyzed to investigate an optimum concentration of the ANb MPs inside the PDMS film.The robust HNG with 5 wt%ANb MPs/PDMS composite film produced the highest electrical output with promising stability.Thereafter,three similar optimized HNGs were fabricated and integrated within a 3D-printed clip-like structure and the electrical output was thoroughly evaluated while combining multiple HNGs as well as from each independent HNG.The clip-like HNG device exhibited an electrical output of 340 V and 20μA that can be further utilized to charge various capacitors and power portable electronics.Owing to the high resilience structure of the clip-like HNG device,it was also demonstrated to harvest biomechanical energy produced by human movements into electricity.The mechanical energy harvesting when the clip-like HNG device was attached to the accelerator pedal of the car and the pedal of a musical piano was successfully demonstrated.

Flexible multilayer MEMS coils and their application in energy harvesters

Electromagnetic vibration energy harvesters are promising for the power supply of wireless sensor nodes,small electronic devices,and wearable electronics.Conventional electromagnetic harvesters usually increase output by increasing the size of coils and magnets,limiting the improvement of energy conversion efficiency and power density.In this study,multilayer microelectromechanical system(MEMS)coils were prepared using flexible electronics,and their high integration performance in arbitrary space was utilized to greatly improve the utilization of the space magnetic field by the electromagnetic harvester.The core magnet of the generator was magnetically balanced to achieve levitation,which improved the sensitivity and reduced fatigue damage compared with traditional spring structures.The wound coils on the top and bottom of the magnet and the flexible coils on the sides worked together to improve the energy efficiency and output of the devices.The output performance of the device with different number distributions was simulated using mathematical models to obtain the optimal structural parameters.The results show that by introducing flexible multilayer MEMS coils on the side surface of the energy harvester,the open-circuit voltage of the energy generators increased from 7 to 10 V by more than 43%.Flexible multilayer MEMS coils can enhance energy conversion rates and possess compact dimensions,making them suitable for integration onto complex surfaces.After the vibration energy harvesting system testing,the maximum peak power of the harvester was 7.1 m W at an acceleration of1 g and a resonant frequency of 11 Hz with a resistor of 3.5 kΩinternal resistance.Moreover,a 470μF capacitor can be charged to 3.5 V within 10 s to drive a hygrothermograph to work for more than 80 s and can supply a light bulb continuously.This strategy shows the great potential of vibration-energy-driven electromagnetic generators for powering small electronics in limited spaces.

A machine learning-guided design and manufacturing of wearable nanofibrous acoustic energy harvesters

Nanofibrous acoustic energy harvesters(NAEHs)have emerged as promising wearable platforms for efficient noise-to-electricity conversion in distributed power energy systems and wearable sound amplifiers for assistive listening devices.However,their reallife efficacy is hampered by low power output,particularly in the low-frequency range(<1 kHz).This study introduces a novel approach to enhance the performance of NAEHs by applying machine learning(ML)techniques to guide the synthesis of electrospun polyvinylidene fluoride(PVDF)/polyurethane(PU)nanofibers,optimizing their application in wearable NAEHs.We use a feed-forward neural network along with solving an optimization problem to find the optimal input values of the electrospinning(applied voltage,nozzle-collector distance,electrospinning time,and drum rotation speed)to generate maximum output performance(acoustic-to-electricity conversion efficiency).We first prepared a dataset to train the network to predict the output power given the input variables with high accuracy.Upon introducing the neural network,we fix the network and then solve an optimization problem using a genetic algorithm to search for the input values that lead to the maximum energy harvesting efficiency.Our ML-guided wearable PVDF/PU NAEH platform can deliver a maximal acoustoelectric power density output of 829μW/cm^(3) within the surrounding noise levels.In addition,our system can function stably in a broad frequency(0.1-2 kHz)with a high energy conversion efficiency of 66%.Sound recognition analysis reveals a robust correlation exceeding 0.85 among lexically akin terms with varying sound intensities,contrasting with a diminished correlation below 0.27 for words with disparate semantic connotations.Overall,this work provides a previously unexplored route to utilize ML in advancing wearable NAEHs with excellent practicability.

Experimental research on affecting factors of the cutting quality of sugarcane harvesters under complicated excitations

The sugarcane field excitation,cutting forces and the engine excitation constitute complicated excitations acting on sugarcane harvesters.In this study,the sugarcane cutting mechanism under complicated excitations was analyzed.The dynamics and the mathematical models of sugarcane harvesters were established and simulated.Based on theoretical analysis,sugarcane cutting experiments were done on a self-built sugarcane harvester test platform(SHTP),designed as single-factor and the orthogonal experiments.Effects of the sugarcane field excitation characterized by the sugarcane field excitation device(SFED)output frequency,the engine excitation characterized by the actuating engine output frequency,the cutter rotating speed,the sugarcane harvester travelling speed simulated through the sugarcane transporting speed of the SHTP and the cutter inclination angle on the cutting quality of sugarcane harvesters were studied.Effects of the axial cutter vibration on three-directional cutting forces and the sugarcane cutting quality(SCQ)as well as effects of three-directional cutting forces on the SCQ were further studied.It is shown that the sugarcane field excitation,the axial cutter vibration amplitude and frequency as well as the three-directional cutting forces have significantly negative monotonic correlated effects on the SCQ while the cutter rotating speed,the sugarcane harvester travelling speed and the cutter inclination angle have significantly positive monotonic correlated effects on the SCQ.Significance levels of effects on three-directional cutting forces and the SCQ form high to low are as follow,the axial cutter vibration,the sugarcane field excitation,the cutter rotating speed,the engine excitation,the cutter inclination angle,the sugarcane harvester travelling speed.The theoretical analysis results were verified through experiment and an optimal combination was obtained with the cutter rotating speed of 700 r/min,sugarcane harvester travelling speed of 0.6 m/s and cutter inclination angle of 8º.This study can provide a reference for setting cutting parameters of sugarcane harvesters with a good SCQ.

Optimizing bone marrow harvesting sites for enhanced mesenchymal stem cell yield and efficacy in knee osteoarthritis treatment

Knee osteoarthritis(OA)is a debilitating condition with limited long-term treatment options.The therapeutic potential of mesenchymal stem cells(MSCs),particularly those derived from bone marrow aspirate concentrate,has garnered attention for cartilage repair in OA.While the iliac crest is the traditional site for bone marrow harvesting(BMH),associated morbidity has prompted the exploration of alternative sites such as the proximal tibia,distal femur,and proximal humerus.This paper reviews the impact of different harvesting sites on mesenchymal stem cell(MSC)yield,viability,and regenerative potential,emphasizing their relevance in knee OA treatment.The iliac crest consistently offers the highest MSC yield,but alternative sites within the surgical field of knee procedures offer comparable MSC characteristics with reduced morbidity.The integration of harvesting techniques into existing knee surgeries,such as total knee arthroplasty,provides a less invasive approach while maintaining thera-peutic efficacy.However,variability in MSC yield from these alternative sites underscores the need for further research to standardize techniques and optimize clinical outcomes.Future directions include large-scale comparative studies,advanced characterization of MSCs,and the development of personalized harvesting strategies.Ultimately,the findings suggest that optimizing the site of BMH can significantly influence the quality of MSC-based therapies for knee OA,enhancing their clinical utility and patient outcomes.

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.

Typical dampers and energy harvesters based on characteristics of ferrofluids

Ferrofluids are a type of nanometer-scale functional material with fluidity and superparamagnetism.They are composed of ferromagnetic particles,surfactants,and base liquids.The main characteristics of ferrofluids include magnetization,the magnetoviscous effect,and levitation characteristics.There are many mature commercial ferrofluid damping applications based on these characteristics that are widely used in numerous fields.Furthermore,some ferrofluid damping studies such as those related to vibration energy harvesters and biomedical devices are still in the laboratory stage.This review paper summarizes typical ferrofluid dampers and energy harvesting systems from the 1960s to the present,including ferrofluid viscous dampers,ferrofluid inertia dampers,tuned magnetic fluid dampers(TMFDs),and vibration energy harvesters.In particular,it focuses on TMFDs and vibration energy harvesters because they have been the hottest research topics in the ferrofluid damping field in recent years.This review also proposes a novel magnetic fluid damper that achieves energy conversion and improves the efficiency of vibration attenuation.Finally,we discuss the potential challenges and development of ferrofluid damping in future research.

Development and application of mechanized maize harvesters

Maize harvesting is one of the most important filed operations of maize production.As the accelerating development of maize industry,mechanized maize harvesting is widely accepted and used by farmers in the world.According to the harvesting methods,maize harvesters could be classified into two types,one is maize-for-grain harvesters,including pickers and grain harvesters,the other is whole plant harvesters,including forage harvesters and combined grain-stover harvesters.Structure characteristics,appropriate areas and relative technologies of those harvesters are described in this paper,i.e.,pickers are suitable for multi-crop areas,Grain harvesters are mainly for one-crop areas when grain moisture content is lower than 25%,combined grain-stover harvesters are applicable in agro-pastoral ecotone,and forage harvesters are capable in large-scaled animal husbandry farming areas where large amount of silage are required.Meanwhile,the future development trend of the different harvesters is predicted.Big horsepower engines,enhanced working efficiency,automation and intelligence are required by large scaled farms.As maize breeding development,more varieties that are suitable for grain harvesting are put into practice,so grain combine harvesters will be popular in future.

Development of uncut crop edge detection system based on laser rangefinder for combine harvesters

The objective of this research was to develop an uncut crop edge detection system for a combine harvester.A laser rangefinder(LF)was selected as a primary sensor,combined with a pan-tilt unit(PTU)and an inertial measurement unit(IMU).Three-dimensional field information can be obtained when the PTU rotates the laser rangefinder in the vertical plane.A field profile was modeled by analyzing range data.Otsu’s method was used to detect the crop edge position on each scanning profile,and the least squares method was applied to fit the uncut crop edge.Fundamental performance of the system was first evaluated under laboratory conditions.Then,validation experiments were conducted under both static and dynamic conditions in a wheat field during harvesting season.To verify the error of the detection system,the real position of the edge was measured by GPS for accuracy evaluation.The results showed an average lateral error of±12 cm,with a Root-Mean-Square Error(RMSE)of 3.01 cm for the static test,and an average lateral error of±25 cm,with an RMSE of 10.15 cm for the dynamic test.The proposed laser rangefinder-based uncut crop edge detection system exhibited a satisfactory performance for edge detection under different conditions in the field,and can provide reliable information for further study.

Response regimes of nonlinear energy harvesters with a resistorinductor resonant circuit by complexification-averaging method

In this paper, the steady-state response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit are theoretically investigated. The complexification averaging(CA) method is used to theoretically analyze the energy harvesting performance and reduce the motion equations into a set of first-order differential equations. The amplitudes and phases of both the response displacement and the output voltage are derived, and the corresponding stability conditions are determined. The response regimes are studied with the variation of nonlinear stiffness coefficients and coupling parameters, which are verified by the time domain analysis. The frequency island phenomenon is found and analyzed. Additionally, the backbone curve for deducing the extreme vibration frequency and amplitude is derived. Simultaneously, the analytical expressions of the switching points(critical amplitude and frequency) to identify the hardening and softening properties are established. Accordingly, a criterion is given to determine the occurrence of the jump phenomenon, and its effectiveness is verified. Overall, this paper presents an in-depth theoretical analysis of nonlinear energy harvesters with a resistor-inductor resonant circuit. It presents the theoretical framework and guidance for more extensive evaluations and understanding the theoretical analysis of nonlinear energy harvesters with external circuits.