Bandwidth Of Energy Harvesters Research Articles

A piezoelectric and electromagnetic hybrid energy harvester based on two-stage magnetic coupling

Traditional piezoelectric energy harvesters cannot adapt to environmental energy with low frequency, wideband, and randomness because of the narrow working bandwidth. The introduction of magnetic coupling can improve the narrow-band characteristics of piezoelectric energy harvesting structures. To explore more efficient broadband methods, this paper designs a piezoelectric and electromagnetic hybrid energy harvester (PEEH) based on two-stage magnetic coupling to realize the expansion of piezoelectric energy harvesting bandwidth. In this paper, the magnetic pole alternating frequency is changed and the output of the structure is tested, and the operating frequency bands under different alternating frequencies are compared according to the test results. It can be seen from the experimental results that the output performance of the structure is obviously improved by increasing the AC frequency of the magnetic pole while reducing the optimal frequency point of the structure. When the number of magnets in the rotor magnet array is 6, increasing the pole alternating frequency can effectively improve the output performance of the electromagnetic unit when the rotor speed is low, and can also increase the maximum output voltage and energy harvest bandwidth of the piezoelectric unit by 189% and 150%, respectively. Therefore, by increasing the alternating frequency of magnetic poles, the output voltage of the structure can be improved, and the bandwidth of the structure can be broadened.

Fractal-inspired multifrequency piezoelectric energy harvesters

In this Letter, we propose fractal-based piezoelectric energy harvesters (PEHs) for broadband energy scavenging. The introduction of fractal topology into transducers significantly alleviates the inherent limitation of a narrow working bandwidth in commonly used cantilever PEHs. We conduct a finite element analysis and experiments to exploit the performance of fractal cantilever PEHs with different iteration times. Our findings reveal that the higher-order fractal structures generate an increased number of eigenfrequencies as well as modal patterns within a certain range of working bandwidth (i.e., <50 Hz). Experimental results indicate that the efficient energy harvesting bandwidth of the fractal PEHs of iterative levels 1 and 2 is 2.05 and 2.15 times, respectively, larger than the conventional PEHs (i.e., level 0). In addition, the harvested voltage and power of fractal PEHs can be enhanced by attaching a proof mass to compensate for the energy loss in producing iterations. This method exhibits superiority over capturing energy in low-frequency vibration environments, such as wave energy and human movement energy.

The effect of magnetic proof masses on the energy harvesting bandwidth of piezoelectric coupled cantilever array

In order to explore the ability of magnetic force in improving energy harvesting bandwidth, a novel energy harvester of piezoelectric coupled cantilever array (PCCA) was proposed which introduces nonlinear magnetic force (damping) to differentiate the natural frequencies of PCCs and widen energy harvesting bandwidth of PCCA. Meanwhile, the design of PCCA can increase the number of voltage peaks of each PCC at the cost of decreasing the voltage peaks of its neighbouring PCCs at resonance. The effect of some significant factors, such as PCC interval, PCS length, PCC number, and PCC substrate thickness, on PCC voltage, PCC natural frequency, and PCCA bandwidth are deeply studied and analyzed by experiments and simulations. The results demonstrate that the bandwidth for the proposed PCCA can achieve 73 Hz by the standard of >15 V pp. voltage in the excitation of 1 g acceleration amplitude. Based on the experiment and simulation results, a series of theoretical models are derived to compute PCC voltage, PCC natural frequency, and bandwidth of PCCA with different design parameters, these theoretical models give a reliable instruction for the design of PCCAs to match environmental vibration with different frequency such as machine, wind, wave, and so on.

Integrated a nonlinear energy sink and a piezoelectric energy harvester using simply-supported bi-stable piezoelectric composite laminate

A nonlinear device is presented for simultaneous vibration absorption and energy harvesting. This device is composed of a nonlinear energy sink and a piezoelectric energy harvester (NES-EH), and its core component is the simply-supported bi-stable piezoelectric composite laminate (BPCL). Its outstanding advantages are light weight, simple and reliable structure. The theoretical model is developed to model a harmonically excited linear oscillator coupled with NES-EH. The Runge–Kutta method and the harmonic balance method (HBM) are used to solve the theoretical model numerically and analytically. The vibration suppression efficiency is utilized to quantify the vibration absorption performance, while the energy harvesting performance is assessed by bandwidth for energy harvesting and maximum voltage within the bandwidth. The effects of the excitation amplitude, the concentrated mass of NES-EH, the length and width of BPCL, and the load resistance are considered on the performances of NES-EH. The vibration absorption and energy harvesting performances of NES-EH can be improved by adjusting these parameters. In addition, the proposed NES-EH can achieve the goal of higher power density and normalized power density under low-amplitude excitation and simultaneously have a good vibration absorption effect. Finally, approximate analytical solutions are obtained by using HBM to exhibit various bifurcations and singularities.

Parametric excitation analysis for system performance of piezoelectric energy harvesters

Capitalizing on the advantages of parametric excitation and real-life low frequency vibration, the steady-state response of piezoelectric energy harvesting system composing of a cantilever beam with a tip mass and horizontal excitation at the fixed end is investigated. By applying Hamilton's principle, the nonlinear partial differential equation of a cantilever bimorph piezoelectric energy harvesting system with an additional tip mass is derived and analyzed. The cantilever is modeled as an axially non-elongated Euler Bernoulli beam with geometric and damping nonlinearities. By using the Galerkin method, the nonlinear partial differential equation is reduced to an electromechanical coupling system that governs a cantilever piezoelectric energy harvesting system with a tip mass under parametric excitation. The first-order resonance response of this harvesting system is studied by using the method of multiple scales. The analytical response expressions and first-order amplitude functions for vertical displacement, output voltage and output power are derived and analyzed. The influence of different impedance and tip mass on the piezoelectric energy harvesting system performance is summarized and concluded. For the parametric excitation system, the load resistance shows significant influence on the initial threshold of the piezoelectric energy harvesters under parametric excitation. For a short circuit, the initial threshold increases with increasing load resistance. For an open circuit, the initial threshold decreases with increasing load resistance. For an open circuit resistance or a short circuit resistance under parametric excitation, an increase in the end block mass effectively reduces the resonance frequency of the piezoelectric energy harvesters. Consequently, the energy harvesting bandwidth is increased, and the harvesting effect of the piezoelectric energy harvesters is enhanced. In this paper, a more accurate and practical theoretical model is established to predict the electromechanical coupling behavior of cantilever piezoelectric energy harvester under parametric excitation. Using this approach, it is possible to complement parametric and direct excitation such that the advantages of parametric excitation can be achieved. It is also significant to improve the energy conversion efficiency of energy harvesting system.

Dynamic Design of a Quad-Stable Piezoelectric Energy Harvester via Bifurcation Theory

The parameter tuning of a multi-stable energy harvester is crucial to enhancing harvesting efficiency. In this paper, the bifurcation theory is applied to quantitatively reveal the effects of structural parameters on the statics and dynamics of a quad-stable energy harvester (QEH). Firstly, a novel QEH system utilizing the geometric nonlinearity of springs is proposed. Static bifurcation analysis is carried out to design quad-stable working conditions. To investigate the cross-well and high-energy vibration, the complex dynamic frequency (CDF) method, suitable for both weakly and strongly nonlinear dynamic problems, is then applied to deduce the primary response solution. By using the unfolding analysis in singularity theory, four steady-state properties and dozens of primary resonance modes are demonstrated. Based on the transition set, the effective bandwidth for energy harvesting can be customized to adapt well to various vibration environments by parametric adjustment. Finally, the experimental tests verify that the output power can reach up to 1 mW. The proposed QEH and its mechanics optimization can guide energy supply for next-generation wireless systems and low-power sensors under magnetic forbidding environments.

On the amplitude truncation effect in electromagnetic energy harvesters: Modeling and experimental validation

Energy harvesters based on a piecewise linear system make it possible to extract more energy from environment vibrations. The amplitude truncation effect is a phenomenon of an energy harvester with a piecewise linear system. It shows a wider energy harvesting bandwidth and a lower voltage response than the purely linear counterpart. This work investigates the influence of spring length on the amplitude truncation effect and power density of electromagnetic energy harvesters. We first establish an analytical model of the piecewise linear system. Then, we apply the averaging method to explore the voltage responses in the frequency domain and compare the influence of various parameters. Later, we conduct a finite element simulation to analyze the voltage response at a constant frequency. The results obtained by the finite element simulation and averaging method match well with the experimental measurements. The experimental results demonstrate that the amplitude truncation effect is more visible at the shorter spring. Spring length plays a key role in the power density of an electromagnetic energy harvester. The case of 40 mm yields a maximum average power of 45.13 mW. The case of 30 mm displays a maximum power density of 2.35 mW/cm 3.

Bi-objective optimal design of an electromagnetic shunt damper for energy harvesting and vibration control

Owing to the electromechanical energy conversion capacity, electromagnetic shunt dampers (EMSDs) are widely applied to vibration suppression or energy harvesting from vibrating structures. Either one of the two functions can be optimized in the designs of EMSD found in the literature. In this paper, a bi-objective optimization methodology of EMSD is proposed for the simultaneous maximization of energy harvesting from the damper and the suppression of resonant vibration of a dynamic structure. An EMSD with opposing magnet pairs configuration is designed to achieve the two design objectives simultaneously in a single-degree-of-freedom (SDOF) system and a dynamic vibration absorber (DVA). It is proved analytically and experimentally that maximum energy can be harvested by the EMSD when its internal impedance equals to the external electrical resistance of the electrical circuit. Minimum resonant vibration amplitude of the primary mass can be achieved at the same resistance ratio in the DVA system by selecting the suitable number of opposing magnet pairs of the EMSD without affecting the internal resistance. An EMSD with opposing magnet pairs configuration is designed and tested in a single-degree-of-freedom (SDOF) system and a dynamic vibration absorber. Following a proper procedure, the electromechanical transduction factor of the proposed EMSD can be tuned to achieve both objectives simultaneously. The harvested energy is higher when the EMSD is deployed in the SDOF system than in the DVA system, but the frequency bandwidth for energy harvesting is much wider in the DVA system. Analyses lead to a design guideline of the EMSD for achieving the bi-objective optimization.

Widening frequency bandwidth with parametric coupling in a wings-inspired low frequency MEMS energy harvester

Efficient energy harvesting with miniaturized harvesters for both low and random frequency vibrations remains a large challenge. This paper presents a wings-inspired design to implement a parametric coupling mechanism for widening the frequency bandwidth of a Micro-Electro-Mechanical System (MEMS) energy harvester (abbreviated as PCEH). The proposed PCEH is composed of two harvesting units, micro-fabricated by SU-8 with a serpentine geometry for decreasing working frequency, which like two wings, are placed at the bilateral of a flexible silicon middle support. When PCEH is excited, the flexible support can oscillate around its equilibrium position due to the lateral vibration of two wings. The parametric coupling is realized by alternately modulating the stiffness of each wing and verified by theoretical analysis, numerical simulation, and experimental measurements. Compared to those of non-parametric coupling energy harvesters (abbreviated as NPCEH), bandwidths and harvesting capacity of two wings in PCEH are increased by 55.4% and 73.7%, and by 3.3 and 2.5 times, respectively. The proposed PCEH opens a new way for widening the frequency bandwidth of energy harvesters at micro scale and lays a foundation for self-powered systems.

Rotational nonlinear double-beam energy harvesting

This paper presents an investigation of the performance of a coupled rotational double-beam energy harvester (DBEH) with magnetic nonlinearity. Two spring-connected cantilever beams are fixed on a rotating disc. Repelling magnets are attached to the frame and to the lower beam tip, and an equal-mass block is attached to the tip of the upper beam. To describe the dynamic response, a theoretical model related to the rotational motion of the coupled cantilever beam is derived from the Lagrange equations. In addition, the harmonic balance method, together with the arc-length continuation method, is applied to obtain the frequency response functions (FRFs). Parametric studies are then conducted to analyze the effect of varying the parameters on the energy harvesting performance, and numerical analysis is performed to validate the analytical solutions. Finally, the theoretical model is verified by forward- and reverse-frequency-sweeping experiments. The DBEH in rotational motion can perform effective energy harvesting over a wide range of rotational frequencies (10–35 rad s−1 ). The upper beam is found to exhibit better energy harvesting efficiency than the lower beam around the resonant frequency. This study effectively broadens the energy harvesting bandwidth and provides a theoretical model for the design of nonlinear magnet-coupled double-beam structure in rotational energy harvesting.

Simultaneous energy harvesting and vibration isolation via quasi-zero-stiffness support and radially distributed piezoelectric cantilever beams

Most of the existing energy harvesters are based on vibration amplification, which inevitably causes large disturbing force transmitted to the base. In this paper, a novel energy harvesting device is proposed based on vibration localization, through which the force transmitted to the base can be significantly reduced, thereby achieving simultaneous energy harvesting and vibration isolation. The proposed device is composed of a quasi-zero-stiffness (QZS) support which can greatly lower the beginning frequency of vibration isolation region, and several radially distributed piezoelectric cantilever beams by which the vibrational energy is localized and harvested. The electromechanical coupled equations are formulated starting from the most elementary mechanical and electrical knowledge. The harmonic balance method is employed to analyze the dynamic response and output voltage, accompanied by the verification through numerical simulations. The non-dimensional output power and the force transmissibility are comprehensively studied with tuning key parameters to investigate the crucial characteristics of the proposed system. The results indicate that the energy harvesting region does lie in the vibration isolation region and the former can be flexibly tuned within the latter by altering the mechanical parameters of the piezoelectric cantilever beam; the peak power and energy harvesting bandwidth can also be tuned by altering the electrical parameters; most importantly, the enhancement of the energy harvesting performance can be achieved with almost no sacrifice of the vibration isolation performance.

A hybrid wind energy harvester using a slotted cylinder bluff body

Harvesting energy from wind to supply low-power consumption devices has attracted numerous research interests in recent years. However, a traditional vortex-induced vibration energy harvester can only operate within a limited range of wind speed. Thus, how to broaden the effective wind speed range for energy harvesting is a challenging issue. In this paper, a slotted cylinder bluff body is proposed for being used in the design of a wind energy harvester. The physical prototype is manufactured and the wind tunnel test is performed for evaluating the actual performance of the prototyped energy harvester. The effect of the orientation of the slot on the performance of the proposed energy harvester is experimentally investigated. As compared to the traditional counterpart without the slot at the lateral side of the bluff body, the proposed energy harvester demonstrates the superiority for realizing broadband energy harvesting. Due to the introduction of the slot, and by carefully tuning the orientation of the slot, both the vortex-induced vibration and the galloping phenomena can be stimulated within two neighboring wind speed ranges, leading to the formation of an extremely broad bandwidth for energy harvesting.

Modeling and Simulation Analysis of a Two-degree-of-Freedom Nonlinear Piezoelectric Energy Harvester

In order to improve energy harvesting efficiency, this paper shows the design of a two-degree-of-freedom (2-DOF) nonlinear piezoelectric energy harvester. The proposed harvest is realized by introducing magnetic attraction to a 2-DOF piezoelectric cantilever beam in order to broaden the energy harvesting bandwidth. Electromechanical equations describing this nonlinear system are presented. The simulation results confirmed the advantage of this new 2-DOF nonlinear harvester. Performance comparison shows that the 2-DOF nonlinear harvester has much higher energy harvesting efficiency than a conventional one-degree-of-freedom (1-DOF) nonlinear one.

Broadband energy harvesting by nonlinear magnetic rolling pendulum with subharmonic resonance

Nonlinear systems may exhibit secondary resonances, which can provide an additional and thus broadened bandwidth for energy harvesting. However, the secondary resonances of nonlinear energy harvesters reported in the literature suffer from low-power output and limited bandwidth. This work proposes a novel magnetic rolling pendulum (MRP) with a large bandwidth and high power output in both primary and secondary resonances for energy harvesting. The MRP employs the rolling motion of a magnetically levitated permanent magnet with minimal mechanical damping. A prototype was fabricated and characterised. An analytical model combined with finite element analysis was developed and validated by experiment. Both experiment and simulation show that the MRP has a linear resonance frequency of 4.6 Hz and peak power of 3.7 mW. It exhibits strong nonlinear behaviours and broadband characteristics with excitation amplitude as low as 2 m/s2 in the primary resonance. As the excitation amplitude is larger than 5 m/s2, the secondary resonance (1/2 order subharmonics) is excited. The responses of the MRP at the subharmonic resonance take the same form as the primary resonance in terms of displacement and power outputs. This helps the subharmonic resonance to produce the same power level as the primary resonance but with a larger bandwidth. When excited at 14 m/s2, the MRP shows 1-mW-bandwidth of 9.7 Hz, 2/3 of which is attributed to the subharmonic resonance.

Impacts of stopper type and material on the broadband characteristics and performance of energy harvesters

Exploiting nonlinear impact force induced by a stopper has been widely proposed to broaden the bandwidth of energy harvesters from mechanical vibrations, but the previous studies just directly employed the stopper and did not consider the effect of inherent factors of the stopper like its type and material. This letter devotes to efficiently utilize the stopper to broaden the resonance region of the energy harvester mainly from perspective of stopper type and material. Four stopper types are taken into account including the stopper with rigid and soft materials and the spring stopper. Experimental results show that two sides followed stopper type can greatly increase the bandwidth which is much better than other considered types. Importantly, using the stopper with soft materials or the spring stopper is followed by a wider resonance region and a higher output voltage of the energy harvester compared to that with rigid materials. Moreover, agreements between theoretical predictions and experimental measurements indicate the feasibility of using the trilinear spring model to describe the nonlinear impact force which is determined by stopper type and material. The present study delivers to essentially improve the output performance of energy harvesters by selecting the efficient stopper.

Resonance response interaction without internal resonance in vibratory energy harvesting

Abstract Resonance response interaction in nonlinear multiple degrees of freedom vibration systems has always involved internal resonance. In this article, bubble shaped response curve is uncovered without pre-designated resonances relationship that is a necessary condition for internal resonance. The objective of this article is twofold: first to explore the connection between the resonance response interaction and bubble shaped response curve that may appear in the forced response of a nonlinear magnetoelectric coupled system; and, second, to exploit resonance response interaction to enhance the vibratory energy harvesting bandwidth. A nonlinear magnetoelectric oscillator coupled linearly to an additional oscillator is used to demonstrate the phenomena and the enhanced performance. The lateral springs could produce the geometrical nonlinear stiffness and its stiffness to adjust the two resonance responses such that the bubble shaped response curve appears in the power-frequency response plot. The method of harmonic balance is well established method for the analysis of such the power-frequency response. The results are also validated by some numerical work. The power-frequency response curves are generated for distinct harvesting mass, manifesting the resonance response interaction could increase the bandwidth and output power. At last, the resonance response interaction designed energy harvesting from Gaussian white noise excitation is numerically addressed to illustrate positive effects of geometrical nonlinearity.

Non-linear dynamics of the Villari effect in the presence of a non-homogeneous magnetic field

Investigations of systems with an active magnetostrictive element generally assume the presence of an external homogeneous bias magnetic field. This article, however, presents the results of a study investigating a bimorph magnetostrictive-aluminium beam vibrating in a non-homogeneous bias field. By comparing results obtained under different operating conditions of the system, the combined effect of the non-linear beam stress and the non-homogeneous external magnetic field on the dynamics of the Villari phenomenon is determined. The preliminary results prove that the application of non-linear magnetic fields to the magnetostrictive devices ensures the extension of energy harvesting bandwidth of these devices and can be used to improve their control possibilities. A study of time series and hysteresis loops provides more detailed information about the non-linear magnetization and dynamics of the system.

A tunable nonlinear vibrational energy harvesting system with scissor-like structure

Vibrational energy harvesting systems with linear electromechanical generators have been largely studied, due to their simple structures and convenience in application. However, the ambient vibration characteristics such as random, time-varying or low-frequency properties make the linear electromagnetic devices cannot be excited at their resonances, which will greatly affect the energy harvesting efficiency. Some attempts to improve the efficiency of a vibration energy harvesting system involve both expand the operating bandwidth and enlarging the magnitude of power output. To this end, a scissor-like energy harvesting system with equivalent nonlinear damping and linear stiffness has been developed in this study. It has been shown that, due to the beneficial nonlinear damping effects provided by the scissor-like structure, the proposed system can greatly improve the vibration energy harvesting performance in terms of the magnitude of power output and energy harvesting bandwidth. On the other hand, the structure parameters of the proposed system can be modified to achieve more significant energy harvesting performance. Moreover, to achieve tunable resonant frequency of the energy harvesting system, the scissor-like structure has been updated by attaching a new lever-type system. In this way, the energy harvesting performance can be improved by tuning the proposed system according to the properties of the surrounding vibration sources. In this paper, both harmonic and random excitations have been adopted to verify the performance of the proposed energy harvesting system.

On Improvement of the Frequency Bandwidth of Nonlinear Vibration Energy Harvesters Using a Mechanical Motion Rectifier

This paper presents a broadband vibration energy harvester (VEH) which consists of a monostable Duffing oscillator connected to an electromagnetic generator via a mechanical motion rectifier. The mechanical motion rectifier converts the bidirectional vibratory motion of the oscillator induced by ambient environment vibrations into unidirectional rotation of the generator and causes the harvester to periodically switch between a large- and small-inertia system, resulting in nonlinearity in inertia. By means of analytical and numerical methods, this inertia nonlinearity is shown to have two advantages. First, it allows for more stiffness nonlinearity without inducing nonuniqueness of energy branches and enhances bandwidths of energy harvesting. The effect of mitigating nonuniqueness of energy branches occurs to steady-state and transient responses of the harvester and is experimentally verified by a prototype. The experimental results show a nearly 50% increase in the half power bandwidth via mechanical motion rectification (MMR). Second, it enlarges the basin of attraction of the high-energy branch when multiple energy branches are present. A numerical example shows that a more than 50% increase in the basin area can be achieved via MMR.

Analysis and experiment of magneto-mechanically coupled harvesters

Abstract Current trend in energy harvesting research is to increase the operating bandwidth of energy harvesters. Multiple harvesters, nonlinear harvesters and hybrid harvesters are suggested to address the issue. In this paper, a system consisting of two electromagnetic harvesters with magnetic and mechanical couplings subjected to harmonic support excitations is proposed. Two pendulums with close resonating frequencies are used to generate power over a broad range of frequencies. The pendulums behave nonlinearly under the influence of magnetic interaction. This nonlinear motion harvests power at broader bandwidth. A mathematical model of the proposed harvester is established. Experiments are performed to validate the theoretical results. It has been observed that the nonlinear responses due to both magnet and mechanical couplings improve individual harvester performance. This is advantageous over harvesters that have magnetically coupling only. Additionally, the dynamics of harvesting system is numerically studied where large amplitude chaotic motion, quasi-periodic oscillations and periodic motions are observed and reported.