Beam Harvester Research Articles

Multi-directional and multi-modal vortex-induced vibrations for wind energy harvesting

A conventional vortex-induced vibration (VIV)-based energy harvester is typically restricted to capturing wind energy from a very limited range of wind directions, making it inefficient in varying wind conditions. This Letter proposes a tri-section beam configuration for VIV-based piezoelectric energy harvester to enable harnessing wind energy from varying incident angle with different vibration modes being triggered. The finite element analysis investigates the tri-section beam harvester's mode shapes and natural frequencies. A wind tunnel experiment is conducted for a comparative study of the energy output performance of the harvesters with straight and tri-section beams. The findings show that the proposed harvester with the tri-section beam can efficiently capture wind energy from a much wider range of incident angles, as opposed to the specific limited directions of its counterpart with the straight beam. The proposed harvester can also widen the lock-in speed range with a higher bending mode being triggered and achieve the optimal output power of 1.388 mW when the proposed harvester works in the second mode at a higher natural frequency, superior to that of its counterpart (0.386 mW) that can only work in the first mode. The proposed configuration sheds light on developing multi-directional and multi-modal VIV-based energy harvesters adapted to wind conditions in natural environments.

A self-powered interface circuit for piezoelectric and photovoltaic energy extracting

This paper presents a high-efficiency multi-source energy harvesting system consisting of a piezoelectric rectifier, a photovoltaic maximum power point tracking circuit and a fast self-startup circuit for powering wireless sensor nodes. Synchronous electric charge extraction techniques (SECE) are utilized to extract the piezoelectric energy when the deflection of piezoelectric energy harvester beam reaches its peak. Compared with other circuits, the proposed SECE technique can achieve piezoelectric and photovoltaic extraction simultaneously with a concise flyback topology structure. A novel maximum power point tracking method is adopted to enhance the robustness of operation against changing operating condition and improve the photovoltaic extraction efficiency. To remove the need for a battery, a simple and efficient self-startup circuit is introduced. The energy harvesting circuit is fabricated in 180 nm CMOS process. Measurement results show a fast self-startup at a relatively low light intensity of 120 lux is realized. The energy harvesting circuit is capable of outputting 189 μW power at 3.3 V piezoelectric open circuit voltage and 0.6 V photovoltaic input voltage.

Branch spiral beam harvester for uni-directional ultra-low frequency excitations

In recent years, there has been a growing interest in piezoelectric energy harvesting systems, particularly for their potential to recharge or replace batteries in energy-efficient electronic devices and wireless sensor networks. Nonetheless, the conventional linear piezoelectric energy harvesters (PEH) face limitations in ultra-low frequency vibrations (1–10 Hz) due to their narrow operating bandwidth and higher resonance frequencies. To address this, researchers explored compact shaped geometries, with spiral PEH being one such design to lower resonance frequencies by reducing structural stiffness. While trying to achieve this lower resonance frequency, spiral designs overlooked that they were spreading the stress across the structure. This was a significant drawback because it reduced the structure's ability to stress the piezoelectric transducer. The issue remains unaddressed, limiting the power generation of spiral beam harvesters. Furthermore, spiral structures also fail to broaden the operating bandwidth, posing additional constraints on their effectiveness. This study introduces a novel solution – the “branch spiral beam harvester,” combining the benefits of both spiral and branch beam designs. The integration of the branch beam concept into the spiral structure aimed to broaden the effective frequency range and establish a concentrated stress area for the placement of the piezoelectric transducer. Finite Element Analysis (FEA) was employed to assess operating bandwidth and stress distribution, while experimental studies evaluated voltage and power generation. Once the workability was confirmed, a statistical optimisation method was introduced to tailor the harvester for specific frequencies in the ultra-low frequency range. Results indicated that the branch spiral beam harvester exhibits a wider operating bandwidth with six natural frequencies in the ultra-low frequency range. It harnessed significantly higher output voltages and power compared to conventional linear PEH. This innovation presents a promising advancement in piezoelectric energy harvesting, offering improved performance without the need for proof masses or additional accessories.

Piezoelectric breeze energy harvester with mechanical intelligence mechanism for smart agricultural monitoring systems

In this paper, a piezoelectric breeze energy harvester with a mechanical intelligence mechanism for smart agricultural monitoring systems (G-PBEH) is proposed. Different from the conventional magnetically coupled piezoelectric cantilever beam harvesters where the end magnet is mostly fixed, the G-PBEH has movable magnets in a fixed cylindrical channel. Which could achieve a mechanical intelligence mechanism with the tuned magnets on the shell, contributing to increasing voltage frequency and widening wind bandwidth. The effects of cylindrical channel length (L) and tuned magnet diameter (D) on performance were investigated. The experimental findings reveal that when L is 10 mm and D is 8 mm, the prototype starts at 2 m s−1, and the highest voltage and power are 17.9 V and 944.07 μW (150 kΩ) at 8 m s−1 . Compared to L is 5 mm (magnet fixed), the voltage waveform has a 28.6% increase in the quantity of peaks. Besides, the voltage is larger than 3 V occupying 91.6% of the experimental wind bandwidth. The application experiment demonstrates that the G-PBEH can be used as a reliable power supplier, which can facilitate the progress of smart monitoring systems for simplified greenhouses in remote areas.

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.

A Bidirectional T‐Shaped Energy Harvester: Modeling, Simulation, and Experiment

Piezoelectric cantilever beams are broadly implemented in energy harvesting. However, simple cantilever‐shaped harvesters are mostly unimodal. Herein, a T‐shaped cantilever beam harvester that can have a bimodal amplitude–frequency curve is developed. The modal of the system is designed in COMSOL finite‐element software and the dynamic behavior is carried out using the finite element simulation. Then, validation experiments are used to estimate the results of finite‐element analysis and it is concluded that the simulation results are in good agreement with the experimental data. Furthermore, the frequency response curves are plotted for various system parameters so as to discuss the influence of these parameters on the bandwidth of the harvester. It is found that there is an optimal resistance that can obtain the P = 2.87 mW maximum power. Finally, theoretical modeling is established and exact analytical solutions are derived, and the comparisons of theoretical, numerical, and experimental results are implemented. It is found that the results of these three methods are consistent. In addition, all of these predictions show that the bidirectional coupling induces the bandwidth increases.

Experimental study on the piezo-based energy harvester utilizing the ambient vibrations for smart applications

The proposed energy harvester has novel construction, its performance evaluated through frequency response, force response and power harvested under an optimum load, is presented. This harvester is more suitable for low power applications like IoT devices, Wireless sensor nodes and biomedical implants. The suggested harvester has two sections namely truncated cone and rectangular beam section (TCRB). The analytical model is formulated and natural frequencies are obtained using FEA tool. Simulations for natural frequencies and associated comprehensive parameters are done along with distribution of stress across the piezo patch. The tapered radius ratio of the truncated cone is analysed to obtain the optimal value. The simulated model is fabricated and verified experimentally. The result is compared with uniform cantilever beam harvester. The voltage produced by a TCRB harvester is 56.76 % higher than the harvester with a homogeneous rectangular cantilever beam. The rectangular harvester has a resonant frequency of 52.8 Hz, while the TCRB harvester has 39.4 Hz. Also, the TCRB type piezoelectric vibration energy harvester with optimum taper radius ratio provides greater power, than uniform and trapezoidal cantilever beams. The obtained experimental results match the simulation results, ascertains the validity of the proposed harvester.

Enhanced flow induced vibration piezoelectric energy harvesting performance by optimizing tapered beam

This paper proposes a tapered cantilever beam flow induced vibration piezoelectric energy harvester, for optimizing the tapered beam and improving the output characteristics. The physical model of the tapered beam harvester is conceived, a two-dimensional CFD simulation model is established, and experimental validation as well as investigation is conducted. The output voltage and displacement response of the harvesters with various tapered beams are explored. The results show that the tapered beam possesses more uniform strain distribution and larger equivalent stiffness, and increasing the fixed end width results in enhancing output voltage and reducing vibration displacement. The optimal tapered beam with a tip width of 25 mm and fixed end width of 45 mm is obtained. The maximum output voltages of the tapered beam VIVPEH and GPEH are increased by 58.30% and 33.16% over the rectangular beam, respectively. The vibration displacements of the tapered beam VIVPEH and GPEH are reduced by 18.31% and 25.12% over the rectangular beam, respectively. The tapered effect in the flow field reduces the vortex shedding distance, increases the shedding frequency, enhances the aerodynamic forces, and thus improves the energy harvesting performance. This work lays the important foundation for exploring the cantilever beam flow induced vibration harvester system.

Experimental-numerical analyses on energy harvesting characteristics of non-conventional T-shaped beams with varied piezoelectric patch location and anchor position

Recently, researchers have studied innovative beam structures in a quest to maximize the energy conversion capability of piezoelectric (PZT) transducers coupled with the shims. A T-shaped beam is one of the structural elements used for harvester design owing to its exceptional geometrical advantage. While a number of research papers have reported its performance characteristics, its potential for harnessing the vibration energy at much lower resonance frequency and damping has not been explored. This paper presents non-conventional T-shaped beam harvesters, namely, the Uniform Tapered T-shaped Beam (UTB) and the Reversed Tapered T-shaped Beam (RTB), with the purpose of enhancing the T-shaped beam functionality. A performance analysis between the UTB, RTB and a conventional T-shaped beam (CTB) harvester of equal mass was conducted, where experimental results show that the RTB harvester has a lower fundamental resonance frequency of 12.3% and 28.3% when compared to the CTB and UTB, respectively. Also, a maximum terminal voltage of 82.8 V and an output peak power of 4.6 mW were produced by the RTB harvester when the PZT patch was placed near its clamped end. In addition, we investigated the effect of the anchor position of the beams on their energy harvesting performance using a finite element analysis (FEA) tool. The numerical results show that the position of the anchor has a considerable effect on the overall characteristics of the configurations.

Improving the Performance of a Post-Buckled Beam Harvester under Combined External and Parametrical Slow Excitations.

In this paper, we consider novel bursting energy harvesting under combined external and parametrical slow excitations, and a harvester is realized by employing an externally and parametrically excited post-buckled beam. Based on the method of fast-slow dynamics analysis, multiple-frequency oscillation, with two slow commensurate excitation frequencies, is used to observe complex bursting patterns, the behaviors of the bursting response are presented, and some novel one-parameter bifurcation patterns are observed. Furthermore, the bursting harvesting performances of the single and the two slow commensurate excitation frequencies are compared, and it was found that the two slow commensurate excitation frequencies can be used to improve the harvesting voltage.

Linear Segmented Arc-Shaped Piezoelectric Branch Beam Energy Harvester for Ultra-Low Frequency Vibrations.

Piezoelectric energy harvesting systems have been drawing the attention of the research community over recent years due to their potential for recharging/replacing batteries embedded in low-power-consuming smart electronic devices and wireless sensor networks. However, conventional linear piezoelectric energy harvesters (PEH) are often not a viable solution in such advanced practices, as they suffer from a narrow operating bandwidth, having a single resonance peak present in the frequency spectrum and very low voltage generation, which limits their ability to function as a standalone energy harvester. Generally, the most common PEH is the conventional cantilever beam harvester (CBH) attached with a piezoelectric patch and a proof mass. This study investigated a novel multimode harvester design named the arc-shaped branch beam harvester (ASBBH), which combined the concepts of the curved beam and branch beam to improve the energy-harvesting capability of PEH in ultra-low-frequency applications, in particular, human motion. The key objectives of the study were to broaden the operating bandwidth and enhance the harvester's effectiveness in terms of voltage and power generation. The ASBBH was first studied using the finite element method (FEM) to understand the operating bandwidth of the harvester. Then, the ASBBH was experimentally assessed using a mechanical shaker and real-life human motion as excitation sources. It was found that ASBBH achieved six natural frequencies within the ultra-low frequency range (<10 Hz), in comparison with only one natural frequency achieved by CBH within the same frequency range. The proposed design significantly broadened the operating bandwidth, favouring ultra-low-frequency-based human motion applications. In addition, the proposed harvester achieved an average output power of 427 μW at its first resonance frequency under 0.5 g acceleration. The overall results of the study demonstrated that the ASBBH design can achieve a broader operating bandwidth and significantly higher effectiveness, in comparison with CBH.

An L-shaped and bending-torsion coupled beam for self-adaptive vibration energy harvesting

Vibration energy harvesting is promising for powering wireless sensor networks for mechanical equipment monitoring. Considering the broadband feature of ambient vibrations, a novel L-shaped self-adaptive piezoelectric energy harvester (LSA-PEH) with a slider is proposed. A linearized mathematical model of the LSA-PEH is established to obtain the relationship between its resonant frequency and the slider position. The maximum resonant frequency that can be achieved by the LSA-PEH is predicted based on the linearized model. The corresponding condition is to fix the slider at around 0.08 m, which is a nodal point. Moreover, the theoretical model explains why the slider moves back and forth when the excitation frequency is 40 Hz. Experimental results show that the slider of the proposed LSA-PEH can passively relocate its position to adjust its resonant frequency and maintain resonance. By the same criteria, the bandwidth of the proposed LSA-PEH is increased by 350% compared to a conventional L-shaped beam harvester.

Enhancing the Bandwidth and Energy Production of Piezoelectric Energy Harvester Using Novel Multimode Bent Branched Beam Design for Human Motion Application.

In recent years, harvesting energy from ubiquitous ultralow-frequency vibration sources, such as biomechanical motions using piezoelectric materials to power wearable devices and wireless sensors (e.g., personalized assistive tools for monitoring human locomotion and physiological signals), has drawn considerable interest from the renewable energy research community. Conventional linear piezoelectric energy harvesters (PEHs) generally consist of a cantilever beam with a piezoelectric patch and a proof mass, and they are often inefficient in such practical applications due to their narrow operating bandwidth and low voltage generation. Multimodal harvesters with multiple resonances appear to be a viable solution, but most of the previously proposed designs are unsuitable for ultralow-frequency vibration. This study investigated a novel multimode design, which included a bent branched beam harvester (BBBH) to enhance PEHs' bandwidth output voltage and output power for ultralow-frequency applications. The study was conducted using finite element method (FEM) analysis to optimize the geometrical design of the BBBH on the basis of the targeted frequency spectrum of human motion. The selected design was then experimentally studied using a mechanical shaker and human motion as excitation sources. The performance was also compared to the previously proposed V-shaped bent beam harvester (VBH) and conventional cantilever beam harvester (CBH) designs. The results prove that the proposed BBBH could harness considerably higher output voltages and power with lower idle time. Its operating bandwidth was also remarkably widened as it achieved three close resonances in the ultralow-frequency range. It was concluded that the proposed BBBH outperformed the conventional counterparts when used to harvest energy from ultralow-frequency sources, such as human motion.

Synergistic composites energy harvester beams based on hybrid ZnO/PZT piezoelectric nanomaterials

This study aims at elucidating the synergistic effect of the hybridization of two piezoelectric materials: zinc oxide nanowires (ZnO NWs) and a thin film of lead zirconium titanate (PZT), on the mechanical and energy harvesting performance of carbon fiber reinforced polymer composites beams. Novel synthesis techniques were utilized to develop energy-harvesting composite beams with surface-grown ZnO NWs and sputtered PZT thin films. While not an extraordinarily strong piezoelectric material, ZnO NWs enhanced the strength and damping parameter of the composite due to the increased surface area and mechanical interlocking. The composite comprising two piezoelectric materials showed a substantial gain in stiffness, a 25.8% increase compared to plain composite without piezoelectric materials. The hybrid composite energy harvester based on PZT/ZnO NWs exhibited a significant electric power gain of 733.94% more than that for beams with ZnO NWs compared to 44% improvement for a beam utilizing only PZT. Using PZT thin films with ZnO NWs on carbon fiber could yield a high-performance hybrid composite with excellent mechanical properties and energy harvesting capabilities.

Nonlinear piezoelectric energy harvesting induced through the Duffing oscillator.

In this paper, nonlinear piezoelectric energy harvesting induced by a Duffing oscillator is studied, and the bifurcation trees of period-1 motions to chaos for such a piezoelectric energy-harvesting system are obtained analytically. Distributed-parameter electromechanical modeling of a piezoelectric energy harvester is presented first, and the electromechanically coupled circuit equation excited by infinitely many vibration modes is developed. The governing electromechanical equations are reduced to ordinary differential equations in modal coordinates, and eventually an infinite set of algebraic equations is obtained for the complex modal vibration responses and the complex voltage responses of the energy harvester beam. One single mode case is considered in this paper, and periodic motions with bifurcation trees are obtained through an implicit discrete mapping method. The frequency-amplitude characteristics of periodic motions are obtained for the nonlinear piezoelectric energy-harvesting systems, which provide a better understanding of where and how to achieve the best energy harvesting. This study describes about how the nonlinear oscillator induces piezoelectric energy harvesting through a beam system. The nonlinear piezoelectric energy harvesting is presented through a nonlinear oscillator. Due to the nonlinear oscillator, chaotic piezoelectric energy-harvesting states can get more energy compared to the linear piezoelectric energy-harvesting system.

Bifurcation behaviors and bursting regimes of a piezoelectric buckled beam harvester under fast–slow excitation

Bifurcation behaviors and bursting regimes of a piezoelectric buckled beam harvester under fast–slow excitation

Nonlinear Reduced Order Modeling of Structures Near Buckling and Application to an Energy Harvester

Abstract The focus of this investigation is first on assessing the validity to structures under in-plane forces, in particular near buckling, of the reduced order modeling approach for nonlinear geometric response that has been extensively developed in the last two decades. This focus is motivated by a class of piezoelectric energy harvesters that rely on strongly nonlinear behavior, such as large amplitude responses, to achieve broadband energy harvesting. A simple, two-rigid bars linkage that approximates a buckling beam is first considered to discover the features of the nonlinear force–displacement relationship induced by an in-plane loading. It is observed that the corresponding form of this relationship is not consistent with the one derived from a reduced order model (ROM) but can be closely approximated by it over a large displacement range. This analysis emphasizes in particular the role of a group of ROM coefficients that are usually considered unimportant. A similar study is performed next for the buckled harvester modeled within nastran and it is again found that a close match of the force–displacement relationship can be achieved. Based on that positive outlook, a six basis functions ROM of this beam harvester that includes piezoelectric effects is built and identified. It is found to provide a close match of nastran nonlinear predictions over a broad range of transverse and in-plane loadings in static and dynamic conditions. The ROM usefulness in predicting the open-circuit voltage is demonstrated.

Size-dependent behavior of micro piezoelectric VIV energy harvester: Parametric study and performance analysis

Implementation of self-powered MEMS units by converting wind and flow stream energy into electrical energy has gained substantial interest in recent years. A bluff body vortex induced vibrations (VIV) in combination with micro scale piezoelectric device can be designed to harvest the demanded power. In the present study, the mechanical performance of a piezoelectric micro energy harvester beam attached to a tip cylinder is numerically simulated. In order to increase the accuracy of the modeling, the elastic and piezoelectric micro-beam governing equations are derived based on strain gradient theory instead of the conventionally used classical theory. The actuating aerodynamic lift force due to the vortex shedding downstream of the cylinder, is simulated by the modified van der Pol wake oscillator equation. Using the mode summation and Galerkin method, the three coupled time dependent governing equations are solved. The accuracy of the van der Pol equation is examined by a moving object computational fluid dynamics (CFD) simulation on the basis of the cantilever beam tip deflection and great agreement is achieved. The effect of length scale parameter, beam length, cylinder diameter and mass, load resistance, piezoelectric thickness as well as the fluid velocity on the produced power density is studied. Findings revealed that increasing the length scale parameters, the device stiffness and frequency increases as well as the harvested power is increased at specific fluid velocities. In other words, increasing the length scale from 0 to 2μm, increases the power density up to 77%.

Investigation of boundary flexibility on the performance of piezoelectric vibration energy harvesting beam systems by DTFM

The purpose of this paper is to investigate the effect of boundary flexibility on the performance of piezoelectric vibration energy harvester (PVEH) beam systems, which has not been studied comprehensively in the literature despite its importance. The coupled electromechanical equations of motion of a piezoelectric cantilever beam with a tip mass are established, with the base boundary constrained by translational and rotational springs. An exact closed-form solution of the frequency response function (FRF) of the PVEH is obtained by the distributed transfer function method (DTFM). The DTFM is a systematic powerful tool for the dynamic analysis of distributed parameter continua with non-classical boundary conditions, intermediate constraints, coupled fields, and non-proportional damping without adding much complexity to the solution formulation. Moreover, the DTFM computes the derivatives of the response, that is, the strains, which are required in the electromechanical coupling formulation, simultaneously without any differentiation. Numerical results showing the effects of boundary flexibility on energy harvesting efficiency are presented. A first-order rational function relating the boundary stiffness parameters and the harvesting efficiency is determined by nonlinear curve fitting of the calculated data. Physical insights and applicability of this analytical function for end-of-line quality check of the boundary of PVEH are discussed.

Optimum network configuration design of a multi-beam vortex-induced vibration piezoelectric energy harvester

The focus of this study is on multi-beam piezoelectric energy harvester (MPEH) network optimization with respect to its configuration. Indeed, the harvested power in the single piezoelectric energy harvesters (SPEHs) may not meet the power level necessary to many applications. In case of constraint in the beam dimensions, the issue of sufficient power generation can be undertaken by arranging a definite number of those harvester units as an MPEH network. The versatility of network configurations presented in the literature, consisting of the harvester beams and their series/parallel interconnections, are limited to only two scenarios including all-series and all-parallel connections of the beams. As will be shown, these classic configurations are not necessarily the optimum ones for a given vortex shedding (VS) frequency. In fact, the harvested power as a function of VS frequency can be maximized by adopting a special network configuration, referred to as the optimum network configuration (ONC). In this study, the general form of the harvested power for each VS frequency is presented in a closed-form expression as a function of the network parameters. An optimization problem is formulated to maximize the harvested power and to obtain the ONC, which is solved through a proposed algorithm named the network configuration optimizer (NETCOOP). In the proposed MPEH structure, electrical switch blocks are used to implement the ONC and to reconfigure the network according to each VS frequency. The obtained VS frequency-dependent ONC enables the designers to develop the best configuration at each fluid flow velocity. To highlight the advantages of this proposed algorithm, the performance of the ONC is compared with other configurations like the all-series and the all-parallel configurations. In the simulation results, the optimum harvested power is obtained for different VS frequencies and load resistances by applying the brute-force approach. It is revealed that the harvested power obtained by the NTECOOP algorithm matches the optimum performance.