Broadband Energy Harvesting Research Articles

A piezoelectric acoustic black hole absorber for rail vibration reduction and energy harvesting: Semi-analytical model

Theoretically, vibration energy can be converted and harvested during the process of vibration reduction, thus enabling a self-powered supply for sensor nodes. However, little research was reported on rail absorbers that combine vibration reduction and energy harvesting. Accordingly, this study aims to design an absorber based on the acoustic black hole (ABH) effect, termed the P-ABH absorber, that can simultaneously achieve broadband vibration reduction and energy harvesting. Firstly, the P-ABH absorber was preliminarily designed, and the semi-analytical model of the track with the P-ABH absorber was established by the Rayleigh-Ritz method. Secondly, the semi-analytical model was verified by the 3D finite element method, and the vibration reduction and energy harvesting performance were initially evaluated. The dimensions of the ABH structure, along with the sizes of the piezoelectric patches, were then determined. Finally, the vibration reduction and energy harvesting performances of the P-ABH absorbers fully deployed between each fastener were evaluated. The results demonstrated that the P-ABH absorber exhibited a wider vibration reduction bandwidth than the uniform piezoelectric absorber and the piezoelectric patches, with an increase in energy harvesting power by 27.47 % and 115.26 %, respectively. The vibration reduction and energy harvesting performance were significantly affected by the number of piezoelectric patches but little affected by the thickness and total length. When the P-ABH absorbers were fully attached to the rail, the overall mean square velocities at the three resonant frequencies, which required emphatic control, were reduced by 36.77 %, 98.37 %, and 3.52 %, respectively. Meanwhile, the energy harvesting performance was excellent. The P-ABH absorber presents a promising solution for improving the sustainability and cost-effectiveness of track systems.

A novel cut-out piezoelectric beam with limiters for broadband energy harvesting

In this paper, we proposed a novel cut-out piezoelectric beam with two pairs of motion limiter for broadband operation. By means of the finite element simulation, a superior geometric structure of the corresponding linear model is designed and the model parameters are determined, then the simulation results are verified by experiments. The subsequent experiments mainly investigate the effect of the position of the limiter on the beam and the size of the limiting gap on the amplitude–frequency response of the system. The experimental results show that the frequency bandwidth of the first resonance peak can be significantly expanded from 2.45Hz to 6.28Hz by selecting suitable limiter parameters, which can increase of 256.33% compared with no limiter. Meanwhile, limiters also cause a maximum 171.79% increase in the primary resonance voltage amplitude, and the level of anti-resonance valley can be increased up to 5.35 times. Finally, the influence of external resistance load on the output power of the system is discussed through detailed parametric study, and the maximum power output of 370μW is achieved.

Broadband and high-efficiency acoustic energy harvesting with loudspeaker enhanced by sonic black hole

It is well-known that acoustic energy sources can be seen as a promising alternative energy resource by using acoustic energy harvester (AEH) which can transform sound energy into usable electrical power. However, the current AEHs have been restricted by their narrow bandwidths and low energy conversion efficiencies. In this study, a broadband and high efficient AEH is presented. The proposed AEH comprises an open-end sonic black hole (SBH) structure and an electrodynamic loudspeaker. The sound pressure is amplified through the open-end SBH structure, then the loudspeaker is used as electricity generator to convert acoustic energy into electric energy. The open-end SBH is a cylindrical tube with an array of regularly-spaced rigid-walled thin rings. The inner radii of the SBH rings are quadratically decreasing and the SBH effect can be obtained. The model for energy harvesting and sound absorption performance of the proposed AEH is then presented. Finally, the open-end SBH is fabricated by 3D printing apparatus. A prototype of the AEH is designed and tested by using an impedance tube. The energy conversion efficiency and absorption coefficient from calculation and experiment show a reasonable agreement. The proposed AEH can convert 11 % of total incident sound energy from 50 Hz to 800 Hz. The maximum energy conversion efficiency can achieve 65 % at 425 Hz under optimal resistance load. Furthermore, the broadband sound absorption can also be achieved by using the proposed AEH.

Array of resonant-type spin-torque diodes as a broadband rectifier: Numerical studies

In this paper, we propose a new approach for constructing broadband rectifiers from resonant-type in-plane spin-torque diodes (STDs). The intrinsic bandwidth of such STDs constrained by the ferromagnetic resonance linewidth of the corresponding magnetic tunnel junction’s is relatively narrow, which is a significant limitation. To address this issue, we propose the implementation of an array of these STDs, each with a distinct resonance frequency. By ensuring that the frequency difference between adjacent STDs is smaller than their individual bandwidths, we achieve a device capable of rectifying signals over a much wider frequency range. To verify the effectiveness of our approach, we have performed analytical calculations based on the Landau–Lifshitz–Gilbert equation with the Slonczewski term, complemented by macrospin modeling and full-scale micromagnetic simulations to account for thermal fluctuations and local magnetization inhomogeneities. Our results demonstrate that an STD array can effectively function as a broadband energy harvester, maintaining near-constant rectification efficiency across a broad frequency range. This research establishes the groundwork for the development of broadband energy harvesters based on STD arrays, with potential applications in various fields requiring efficient energy conversion across a wide frequency spectrum.

Effects of pendulum orientation and excitation type on the energy harvesting performance of a pendulum based wave energy converter

With global electricity requirements due to increase in the coming years and growing pressure to reduce dependence on fossil fuels, universal demand for renewable energy is projected to grow. Marine energy, including wave energy, is an active research area, with potential to meet future energy demands, due to its high energy density. With a view to using a pendulum system in a floating object to extract energy from ocean waves, this paper analyses the effects of pendulum orientation and excitation type on the system’s dynamics. Three excitation scenarios, surge, heave and dynamic tilt of the floating object, with various pendulum orientations, were analysed and simulated. Both linearised and nonlinear systems were investigated with the former providing insight into the nonlinear system’s behaviour. Effects of pendulum orientation on power output potential differs significantly with excitation type and pendulum properties. While expected peak power output is observed at the resonant frequency and twice the resonant frequency under direct and parametric excitations respectively for both systems, the linearised system also exhibits regions of instability. These instability regions under parametric excitations were investigated with consideration for energy harvesting applications. Theoretical and experimental findings revealed that dynamic tilt excitations can be utilised for broadband energy harvesting at the expense of the peak power output. While peak average power output for these excitations for the considered system parameters is relatively low, 1 W versus 12.5 W for heave excitation, the bandwidth is very broad and starts from 0 rad/s frequency if tilt excitation amplitude is above 1.1 rad.

A quad-stable nonlinear piezoelectric energy harvester with piecewise stiffness for broadband energy harvesting

A quad-stable nonlinear piezoelectric energy harvester with piecewise stiffness for broadband energy harvesting

Harvesting vibration energy by quad-stable piezoelectric cantilever beam: Modeling, fabrication and testing

The combination of beams with piezoelectric patches has become a prevalent energy harvesting tool due to its ease of use. Typical energy harvesting systems are usually linear, and their efficiency is not satisfying due to low-frequency bandwidth. In this paper, a quad-stable piezoelectric vibration energy harvester is analyzed both numerically and experimentally. The primary purpose of this investigation is to analyze the static and dynamic characteristics of a proposed quad-stable system to consider its potential for application in broadband energy harvesting comprehensively. The harvester system consists of a slotted cantilever beam, a piezoelectric patch, a pair of tip-mass blocks, and a double-sided clip. The cantilever beam is subjected to pre-displacement constraints made by a mutual self-constraint at the free end of it. The nonlinear behaviors of the harvester system, including snap-through and softening phenomena, are analyzed using the assumed modes and finite element method (FEM). The harvester's vibration equation is solved numerically and through an FE model which is made by an in-house finite element software. A prototype is designed and fabricated to validate the mathematical model and FE simulation. The experimental force-displacement diagram of the harvester displays distinct discontinuities, reflecting abrupt transitions occurring while switching its stable states. The prototype dynamics are analyzed by harmonic base excitation with different amplitude levels in two conditions, including the presence and absence of the piezoelectric patch. The results obtained from the mathematical and FEM model demonstrate a satisfactory correlation with the experimental data. Furthermore, the experimental data reveal the occurrence of the snap-through phenomenon, accompanied by a significant widening of the frequency bandwidth at relatively high amplitude levels. The system has the ability to provide an average output electrical power of 0.288 mW for an electrical resistance of 3.262 kΩ at the excitation frequency of 12.695 Hz and base acceleration amplitude of 3g.

Jellyfish-inspired bistable piezoelectric-triboelectric hybrid generator for low-frequency vibration energy harvesting

In pursuit of enhancing the output power of energy harvesters, this paper introduces a novel jellyfish-inspired bistable piezoelectric-triboelectric hybrid generator (JIB-PTHG) with low potential energy barrier characteristics and low-frequency, broadband energy harvesting capabilities. The JIB-PTHG comprises two flexible beams, and two rigid links, connected via a spring. Utilizing the harmonic balance method and Runge-Kutta fourth-order algorithm, a comprehensive analysis of the mechanical properties of the low-barrier bistable structure is conducted. Static equilibrium bifurcation and dynamic response analysis are performed. Subsequently, an electromechanical coupling model incorporating piezoelectricity and triboelectricity is developed to theoretically predict the output voltage of the two modules, revealing a positive correlation between displacement and output voltage. Experiment validation demonstrated that adjusting the length of the rigid links can effectively increase the deformation of the piezoelectric beam and the relative displacement of the triboelectric layers, thus improving the generator's output performance. Specifically, the TENG module exhibited exceptional energy harvesting performance within the frequency range of 3.5–6.5 Hz, achieving a voltage of 1050 V, a power of 1.84 mW, and the ability to illuminate 70 LED lights under an excitation amplitude of 17.5 mm and a frequency of 5.5 Hz. The PEG module, displayed high output performance within the frequency range of 4-7 Hz, reaching a voltage of 6.2 Vs and a power of 12.8 μW at an excitation frequency of 7 Hz and an amplitude of 17.5 mm. Both theoretical and experimental findings indicate that the JIB-PTHG has achieved improved output power within the frequency range of 3.5–6.5 Hz. Furthermore, the JIB-PTHG has the potential to harness bridge vibration energy and convert it into useful electrical energy for powering wireless sensor nodes in bridge health monitoring systems.

Achieving transition between internal resonance and mode localization through coupling strength modulation

Nonlinear mode coupling phenomena are prevalent in a wide range of dynamic systems, offering intriguing insights into the rich complexities of vibrational behavior. Internal resonance (IR) and mode localization (ML) are two typical mode coupling phenomena that have been widely studied and applied for sensing and energy harvesting. In this work, the transition between IR and ML has been studied theoretically and experimentally utilizing a mechanically coupled resonator, as well as its potential application has been explored. Numerical results of amplitude–frequency curves, phase–frequency curves, and the frequency veering curves under different internal and external conditions all indicate that the vibration behavior of the coupled resonator will transition from 1:1 IR region to ML region as the coupling stiffness increases. An equivalent experiment has also been implemented for verification, and its results are consistent with the theoretical and simulation ones. Furthermore, a self-powered sensor with a tunable coupling has been proposed, which can combine the advantage of IR for broadband energy harvesting and that of ML for ultra-high sensitivity mass detection.

A broadband and multiband magnetism-plucked rotary piezoelectric energy harvester

This study introduces a broadband and multiband piezoelectric energy harvester characterized by an E-shaped structure based on the rotational magnetic excitation. The piezoelectric oscillator is comprised of a trio of piezoelectric beams, which is like the letter 'E'. To elucidate the harvester's performance, this work employs both finite element analysis and experimental methods to explore the effects of pivotal parameters. Length ratio (Lr) and mass ratio (Mr) can influence the first two modes of vibration of the E-shaped oscillator. Lr = 1.0 and Mr = 3.0 are the critical points for mode transition of the E-shaped oscillator. Changing the added mass can reduce the gap between the resonance speed regions of the inner and outer beams, thus achieving the purpose of broadband. When piezoelectric patches are arranged in a "品" shape on the inner and outer beams, the total output power of a single oscillator can reach 5.33 mW, with the inner and outer beams contributing 4.01 mW and 1.32 mW respectively. Besides, when rotating magnets are two, a single piezoelectric oscillator can have 9 effective working regions. These can enhance the efficacy of energy harvesters, particularly in the realm of autonomous and self-powered systems.

Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

The nonlinear energy sink (NES) and Galfenol material can achieve vibration suppression and energy harvesting of the structure, respectively. Compared with a linear structure, the geometric nonlinearity can affect the output performances of the cantilever beam structure. This investigation aims to present a coupled system consisting of a nonlinear energy sink (NES) and a cantilever Galfenol energy harvesting beam with geometric nonlinearity. Based on Hamilton’s principle, linear constitutive equations of magnetostrictive material, and Faraday’s law of electromagnetic induction, the theoretical dynamic model of the coupled system is proposed. Utilizing the Galliakin decomposition method and Runge–Kutta method, the harvested power of the external load resistance, and tip vibration displacements of the Galfenol energy harvesting model are analyzed. The influences of the external excitation, external resistance, and NES parameters on the output characteristic of the proposed coupling system have been investigated. Results reveal that introducing NES can reduce the cantilever beam’s vibration while considering the geometric nonlinearity of the cantilever beam can induce a nonlinear softening phenomenon for the output behaviors. Compared to the linear system without NES, the coupling model proposed in this work can achieve dual efficacy goals over a wide range of excitation frequencies when selecting appropriate parameters. In general, large excitation amplitude and NES stiffness, small external resistance, and small or large NES damping values can achieve the effect of broadband energy harvesting.

Design, modeling and experiments of bistable piezoelectric energy harvester with self-decreasing potential energy barrier effect

It is difficult for conventional bistable energy harvesters to undergo interwell motion in weak excitation environment. In this study, a bistable energy harvester with self-decreasing potential energy barrier effect is proposed, which innovatively turns a fixed end of S-shaped generator beam into the movable end with a spring oscillator, which effectively decreases the potential energy barrier and makes the harvester susceptible to interwell motion. Furthermore, a theoretical analysis of the nonlinear driving magnetic force and the system governing equations is carried out, then a numerical simulation of potential energy surface of harvester is performed to demonstrate the effect of the self-decreasing potential energy barrier in detail. The effect of spring pre-compression and stiffness of the moveable end on the system potential energy is analyzed by numerical simulation. Finally, the key parameters affecting the output performance, such as spring pre-compression, magnets distance, and external load resistance, are analyzed. The harvester has a maximum effective bandwidth of 6.62Hz (4.61–11.23Hz), a maximum peak-to-peak voltage of 10.2V, an RMS voltage of 1.3V, and a maximum output power of 2.91 μW. The proposed harvester achieves efficient broadband energy harvesting in low frequency environments.

Soft energy harvester with broadband based on piezoelectric composites

Over the past years, a variety of energy harvesters have been used to scavenge energy from ambient vibrations, but most harvesters work effectively only near the resonant frequency. This work presents a soft piezoelectric energy harvester with a wide bandwidth by compounding lead zirconate titanate particles and shape memory polyurethane. To clarify the relation between energy harvesting performances and frequency, the developed harvester was tested from 20 Hz to 1300 Hz. The results show a bandwidth of 330 Hz, which is benefit from the microstructures of particulate composites. This work supplies an alternative method to develop broadband energy harvesters.

All‐Polarized Elastic Wave Attenuation and Harvesting via Chiral Mechanical Metamaterials

AbstractManipulating elastic waves of all polarizations is highly challenging due to the complex behavior of elastic waves. To achieve simultaneous broadband vibration attenuation and energy harvesting across all polarizations of elastic waves at low‐frequency ranges, a chiral mechanical metamaterial‐based energy harvester is proposed in this study. The systematic development of a complete bandgap and defect structure is achieved through theoretical eigenfrequency analysis and numerical simulations. The defect structure is incorporated to induce defect modes for all wave polarizations within the complete bandgap region, ensuring their compatibility with the overall shape of the structure. The proposed chiral mechanical metamaterial with defect (CMMD) demonstrated significant performance improvements, achieving electrical output power enhancements that are 20.5 times for flexural waves and 511.4 times for longitudinal‐torsional waves compared to the defectless chiral mechanical metamaterial. This study accentuates the thoughtful design and multifaceted utility of chiral mechanical metamaterials, paving the way for their application not only in energy harvesting but also in wave attenuation for various polarizations.

Lightweight cellular multifunctional metamaterials with superior low-frequency sound absorption, broadband energy harvesting and high load-bearing capacity

Multifunctional materials are highly desired for the design of compact engineering structures, such as aircraft where weight reduction, sound absorption, load carrying, and energy harvesting are key considerations. However, design challenge remains in the balance of multiple functionalities. Here, we combine the sandwich structure with the neck-embedded cavities to design a cellular metamaterial having sound-absorption, compression/impact resistance and energy harvesting functionalities. For sound absorption, an autoencoder-like neural network is constructed to generate an instant design, after which a probabilistic module is inserted to optimize it by searching solutions in a slightly expanded design space. This inverse design has been experimentally validated, showing broadband sound absorption from 400 to 650 Hz merely with nine ultra-thin resonators. Beyond serving as absorber, the resonant cavities, once installed with well-tuned piezoelectric membranes, can gather broadband acoustic energy at low frequencies. Additionally, the cellular metamaterial inherits the excellent mechanical properties of honeycomb cores, having a low density of 0.64 g/cm3 yet displaying a high yield strength (21.2 MPa) in out-of-plane compression test and a superior energy absorption capability (8.6 J/cm3) in low-velocity impact tests. This work presents an effective approach to design lightweight metamaterials of superior mechanical and acoustic functionalities highly sought-after in practical engineering.

Design and optimization of quasi-zero-stiffness dual harvester-absorber system

The single quasi-zero-stiffness harvester-absorber system has shown its effectiveness in harvesting vibration energy and suppressing low-frequency vibrations simultaneously. Nevertheless, drawbacks of narrow frequency range of vibration suppression and low output power are still challenges. In this paper, a novel quasi-zero-stiffness dual harvester-absorber system (QZS DHAS) is proposed for broadband synergistic vibration suppression and energy harvesting at low frequency. The QZS feature is realized by mounting an equal-strength piezoelectric beam and a pair of magnet rings in parallel. Firstly, the restoring force of both the piezoelectric beam and the magnet rings are theoretically derived, respectively, which are verified by finite element simulations. Then, the governing equations of a host oscillator with QZS DHAS are derived based on Newton's law and Kirchhoff's law, which are solved by the harmonic balanced method combined with the pseudo arc-length continuation method. Moreover, the effects of mass ratios, frequency ratios and damping ratios on the performance of the QZS DHAS are investigated in details. Finally, the parameters of the QZS DHAS are optimized to improve the performance of vibration suppression and energy harvesting by using the multi-objectives genetic algorithm in combination with the technique of establishing order preference by similarity to the ideal solution. The results show that the peak response of the host oscillator is reduced by 33.48 % and the peak power is increased by 531.38 % after optimization, which indicates that the dual objectives of broadband vibration absorption and high-efficiency energy harvesting are fulfilled.

A Novel Tri-Magnet Levitating Bistable Electromagnetic Energy Harvester with Variable Potential Wells to Promote Snap-Through Behavior

To achieve broadband energy harvesting under weak excitations, this paper comprehensively investigates a novel tri-magnet levitating bistable electromagnetic energy harvester with variable potential wells (BEEH-VP). The bistable nonlinear mechanism is realized using the single-sided bipolarity of the ring magnets. Auxiliary springs are integrated into the ring magnets to dynamically self-adjust the spacing of the ring magnets, causing variable potential wells. The analytical model of BEEH-VP is derived and verified experimentally. The performance of the proposed BEEH-VP is compared with that of the bistable electromagnetic energy harvester with featuring fixed potential wells (BEEH-FP). The comparative results clearly demonstrate that the BEEH-VP exhibits superior capabilities in terms of energy output under weak excitation and possesses a broader frequency bandwidth. Bifurcation analysis for the excitation conditions reveals that the proposed structure features complex dynamic behaviors, such as intra-well, chaotic, harmonic inter-well and subharmonic inter-well vibrations. In comparison to BEEH-FP, BEEH-VP requires lower acceleration to perform the snap-through and has a larger vibration amplitude, facilitating improved output performance.

Dynamic Characteristics of Bistable Vibration Energy Harvester Incorporating Electromagnetic Generator

Although various vibration energy harvesters have been designed over the past few decades, efforts to develop efficient, broadband energy harvesters continue. This work provides a detailed insight into a bistable vibration harvester subjected to correlated Gaussian white noise, with the friction between the rack and pinion described by the slip-stick model. Using the harmonic balance method, the frequency response curve of the amplitude under different mass ratios is discussed. The system response will be enhanced with an increased mass ratio for sinusoidal excitation, but not in the case of random excitation. By employing the stochastic average of the energy envelope, the dynamical governing equation of the harvester is solved, and the probability density functions (PDFs) under different damping coefficients, nonlinear stiffness of the restoring force, and excitation intensities are derived. The results are compared with those from Monte Carlo simulations (MCS) and show good accuracy. The results reveal the presence of P-bifurcations. When the nonlinear stiffness and damping coefficient vary, the number of peaks in the PDFs of system displacement and velocity changes. By adjusting the system parameters, the motion of the system can be significantly enhanced.

A novel M-shaped 2-DOF piezoelectric energy harvester with built-in outer-inner magnetic tri-stable oscillators for energy converting enhancement and applications

Tri-stable oscillators have been widely used to develop various nonlinear broadband energy harvesters. Focusing on further achieving high-performance piezoelectric energy harvester under broadband vibrations, a novel M-shaped 2-DOF piezoelectric energy harvester (M-PEH) with built-in outer-inner magnetic tri-stable oscillators is proposed, in which an inner magnetic tri-stable oscillator is built-in into a U-shaped outer magnetic tri-stable oscillator using its cut-out cantilever beam, assisted by the coupling interface to further enhance the dynamic responses. A complete physical model by considering the nonlinear coupling interaction between the outer-inner magnetic tri-stable oscillators is established to describe the dynamic performances under different system parameters. The theoretical model is well validated by experiments, which show that the proposed M-PEH has more compact size, wider operating frequency and higher power generation, offering an effective bandwidth of 20.1 Hz (5.1–25.2 Hz) at base excitation A = 5 m/s2, and achieving maximum output voltage 8.5 V and total peak power 26.7 μW. Compared to the original magnetic-coupling nonlinear tri-stable PEH, the effective bandwidth and total power have increased by 300 % and 662 % respectively, and the average power density is increased by 917 %. In addition, four main coupling interaction modes between the outer and inner built-in tri-stable oscillator are observed, in which the nonlinear synchronous coupling interaction is conducive to generating inter-well motion, leading to more mechanical energy being transferred from the outer tri-stable oscillator to the inner built-in tri-stable oscillator, thereby improving power generation capacity. Besides, the coupling interaction between these two tri-stable oscillators produces two close resonances which can be easily tuned to form a wide operating bandwidth. Practical applications prove that the proposed M-PEH has the ability to power low-powered electronic products, meeting the power supplying requirements of engineering community.

Single-crystalline silicon quantum well embedded in SiO2 thin layer for broadband photodetection and energy harvesting

Single-crystalline silicon quantum well embedded in SiO2 thin layer for broadband photodetection and energy harvesting