Beam Energy Harvester Research Articles

A twist piezoelectric beam for multi-directional energy harvesting

This paper develops a twist beam for multi-directional energy harvesting using piezoelectric transduction. The working principle of the multi-directional ability is explained by the theory of a pre-twisted beam. A simulation study is performed for concept verification and revealing the potential advantages of the proposed twist-beam vibration energy harvester (VEH). A physical prototype is fabricated and an experimental study is conducted to evaluate the actual performance of the proposed twist-beam VEH for validation. The results show that for the excitation comes from any direction in the plane in parallel with the beam cross-section, the proposed twist-beam VEH can produce a substantial amount of power. The optimal resistance is independent of the excitation direction. Moreover, it is found that the relationships between the output voltage amplitude and the excitation direction are different for the cases around the first and second resonances of the twist-beam VEH. The underlying physics behind this phenomenon is that the dominant motion of the two resonant modes are contrarily different. In addition, the experimental study shows that the first two natural frequencies of the prototyped twist-beam VEH are 22.37 and 41.47 Hz, respectively, which are much closer to each other as compared with those of a conventional plain beam. This feature benefits multi-modal energy harvesting within a targeted frequency range. The prospects regarding further optimization of the proposed twist-beam VEH are discussed.

A piezoelectric beam model with geometric, material and damping nonlinearities for energy harvesting

To predict electrical generation in piezoelectric small-scale beam energy harvesting devices, it is important to have a complete mathematical model that captures the different associated phenomena. In the literature, some authors propose several alternatives of non-linear mathematical formulations, with non-linearities coming from different physical aspects. All these formulations present good aptitudes to predict the nonlinear behavior of the system under different values of accelerations, geometry and boundary conditions. At the same time, they do not represent a unified general proposal for modeling multimodal energy harvesting devices of any type of mode generation and boundary conditions at large excitations. In this sense, this paper presents a mathematical description of inextensional nonlinear Euler-Bernoulli piezoelectric beams that combines the best contributions of the literature to the voltage generation of multimodal nonlinear piezoelectric energy harvesters (geometric, material and damping non-linearities). The developed analytical model yields a total set of N+ 1 ordinary differential equations for the first N modes and for the output voltage. However, direct solution of this ordinary nonlinear differential system of N equations is computationally costly. Instead, a reduced algebraic system of 2() algebraic equations is proposed applying the method of averaging. Its main advantage is that it makes more suitable and computationally economical for the implementation of a parameter identification process involving any number of piezoelectric inserts (unimorph or bimorph) and mode of generation (d33 or d31). Two types of validations are presented for some selected physical systems to test the validity of the assumptions: a numerical one, by the direct integration of the equations of motion and an experimental one. A final comparison between the results demonstrates the importance of the having a unified nonlinear model to predict the generated voltage in multimodal energy harvesters.

A study on the optimal design and the performance evaluation of electromagnetic energy harvesting device for the rolling stock application

An electromagnetic energy harvesting device was studied based on the design parameters of an energy harvesting device for the power source of wireless sensors node on the rolling stock. The characteristics of the generated power by the energy harvesting device were tested using the laboratory equipment and a rolling stock (a high-speed train). First, a cantilever beam energy harvesting device, which allows for easy adjustment of the length according to the frequency and the power according to the cantilever beam materials, was researched. In addition, the new design for a practical resonant energy harvesting device for the railroad system was performed. To realize the performance of the practical resonant energy harvesting device, the generated power characteristics of the energy harvesting device were tested according to the moving displacement, the number of coil turns, and the initial coil displacement between the coil and magnet. The evaluation of the performance of the manufactured resonant energy harvesting device for the railroad system, which the parameters were determined based on the test results, was conducted under real driving conditions in the high-speed train, which was traveling at 300 km/h. Finally, this study analyzed whether the power generated could be applied to the wireless sensor nodes for the railroad system.

Enhancing Performance of a Piezoelectric Energy Harvester System for Concurrent Flutter and Vortex-Induced Vibration

This paper proposes a novel and efficient energy harvester (EH) system, for capturing simultaneously flutter and vortex-induced vibration. There exists a coupling effect between flexible spring energy harvester (FSEH) and cantilever beam energy harvester (CBEH) in aerodynamic response and output characteristic. Many prototypes of the harvester were manufactured to explore the coupling effect in a wind tunnel. The experimental results demonstrate that FSEH is mainly subjected to flutter-induced vibration and CBEH undergoes vortex-induced vibration. Disturbance of FSEH first takes place, a limited oscillation cycle then occurs, and chaos ultimately happens as airflow velocity increase. Root mean square voltages are more than 11 V for FSEH at beyond 10.52 m/s, which shows the better output performance over the existing harvesters. Vibration response and output voltage of various harvesters are mutually enhanced with each other. An enhancing ratio for FSEH-130-25 is up to 69.6% over FSEH-130-0, while the enhancing ratio for CBEH-130-30 is 198.3% compared to CBEH-0-30. Field application testing manifests that discharging time to power the pedometer is almost twice as long as the charging one for FSEH-130-25 at 14.48 m/s. The current research offers a suggestive guidance for promoting future practical application in micro airfoil aircrafts.

Numerical modelling of micro energy harvesting systems based on piezoelectric composites polarized with interdigitated electrodes

This paper focuses on the numerical modelling of micro-energy harvesting systems(MEHSs) based on piezoelectric composites polarised with interdigitated electrodes (PCPIE). The system response and the harvested energy are numerically assessed using a multilayer piezoelectric shell finite element (FE) with a uniform fibre aligned electric field (UFAEF) in each active layer. Circuit and compatibility equations are included to take into account the presence of the electrical network. A state-space (SS) model is derived and used to evaluate the effect of electrical impedance on damping and natural frequencies, as well as dissipated energy/power. An energy harvester beam with a piezoelectric macro fibre composite (MFC) patch is first modelled with the developed tools. Numerical results are found to be in good agreement with experimental results reported in the literature. Finally, a MEHS consisting of a closed-box beam equipped with PCPIE devices bonded to its skin is analysed. The structural system is subjected to dynamic loading imposing oscillating displacements and deformations compatibles with those expected during service-life. Numerical results show the influence of the electrical impedance on system response, damping, natural frequencies, and electrical power.

Experimental study on broadband bistable energy harvester with L-shaped piezoelectric cantilever beam

This paper presents an experimental study of the broadband energy harvesting and dynamic responses of an L-shaped piezoelectric cantilever beam. Experimental results show that the L-shaped piezoelectric beam generates two optimal voltage peaks when the horizontal beam size is similar to the vertical beam size. Several optimized L-shaped piezoelectric cantilever beam structures are proposed. Power generation using the inverted bistable L-shaped beam is better. It is observed experimentally that the inverted bistable L-shaped beam structure shows obvious bistable characteristics and hard spring characteristics. Furthermore, the corresponding relationship between the bistable phase portrait and the potential energy curve is found in the experiment. This is the first time that a phase portrait for stiffness hardening of an L-shaped beam has been found experimentally. These results can be applied to analysis of new piezoelectric power generation structures.

Surface integrity and size dependent modeling and performance of non-uniform flexoelectric energy harvesters

Piezoelectric energy harvesters have recently been the focus of several researchers over several years due to their effectiveness at submicron scales by including the flexoelectric effect. Though the size-dependency of the flexoelectric effect had been examined at nanoscales, the size dependent effects of the material structure had been neglected; these nanoscale models do not accurately represent models at the nanoscale. A robust reduced-order model is introduced in this study that incorporates material structure size-dependency through the couple stress theory, the effects of the surface profile by examining the average roughness and slope of roughness and the impacts of the surface stress through the Gurtin–Murdoch surface elasticity theory on a non-uniform cantilever beam energy harvester. Couple stress considerations greatly impact all examined systems, harden the system, and increase the power bandwidth whereas surface roughness influences the expected harvestable power and optimal loading of the system, by reducing expected power output. This analysis shows the importance of considering the size dependent effects on the performance of flexoelectric energy harvesters in nanoscale.

Modeling and experiments on Galfenol energy harvester

Vibration energy harvesting can solve the energy supplying problem of systems like wireless sensors networks. The Galfenol cantilever beam energy harvester is suitable for this application. According to the electromechanical conversion principle, the constitutive relation of Galfenol is built. A magnetization model is also established, based on the hysteresis model of Galfenol. Combining the magneto-mechanical coupling model, the constitutive relation of Galfenol and the electromagnetic induction law, the mathematical model of Galfenol vibration energy harvester is established. A hyperbolic curve-shaped cantilever beam is designed and its performance is compared to three types of cantilever beams: rectangle, trapezoidal, and triangle. The stress distribution, modal analysis and frequency response of these four shapes of beams are compared. The hyperbolic beam is more suitable for low frequency vibration harvesting. The strain on the beams, output voltage and power output response to these energy harvesters, under different natural vibration frequencies, are determined by simulation. Finally, the simulation results are compared to experimental electric outputs of all four types of prototype beams. The comparative study showed consistency between the experimental and the simulation results, and also that the peak-to-peak induction voltage value of the hyperbolic beam is larger than other shapes of energy harvesters, whose average value is at 269.8 mV. The maximum power output of the hyperbolic beam is 403.8 μW when connected with a 50 Ω resistance.

Modeling and nonlinear analysis of stepped beam energy harvesting from galloping vibrations

This paper presents a nonlinear distributed-parameter model for harvesting energy from galloping oscillation. The stepped beam structure is beneficial to increase the stress and strain of the piezoelectric elements, thereby enhancing the power generation. The finite element analysis is used to verify the feasibility and effectiveness of the developed harvester. A nonlinear distributed-parameter model for the piezoelectric energy harvester with a stepped beam is developed. The instantaneous fluid force in the transverse direction is analyzed. Based on Euler-Bernoulli beam theory, a distributed-parameter model for undamped free vibration is derived, which can be used for the modal analysis. The electromechanical coupling model is established by using the piezoelectric effect theory. The forced vibration subjected to the galloping excitation load is analyzed by using the mode superposition method. The state vector and the fourth order Runge-Kutta algorithm are used to seek the numerical solution. The effects of the electrical load resistance, length, width and thickness of the piezoelectric beam, exposure area and mass of the bluff body on the output power are investigated. In order to find the optimal design of the energy harvester, optimization design is performed based on the established theoretical model. The particle swarm optimization algorithm is employed to search the optimal solution in multidimensional space. Finally, experimental work was carried out, the electrical output characteristics of the energy harvester prototypes were measured. The simulation results are validated with the experimental data. It is demonstrated that the optimal configuration of the energy harvester can improve the output power from galloping phenomenon effectively.

A Comprehensive Review on Vibration Analysis of Functionally Graded Beams

Beams and beam structures are structural components commonly used in mechanical, aerospace, nuclear, and civil engineering. To meet the different engineering design limitations such as operational conditions, weight, and vibrational characteristics, these components may be made of various materials such as functionally-graded materials (FGMs), composites, and homogeneous materials. Functionally-graded (FG) beams play a key role not only in classical structural applications, but also have vast applications in thermal, electric-structural and electric-thermal-structural systems, e.g. in the form of FG beam energy harvesters, sensors and actuators. In all these applications, using new materials like FGMs can greatly improve the efficiency of the structural components and systems. Since FG beams are mostly used as moving components in engineering structures, vibration analysis of these components has been studied by numerous researchers. In order to solve the governing equation and related boundary conditions of the FG beams, powerful numerical methods with a high level of accuracy and fast rate of convergence are often required. The differential quadrature method (DQM) is a powerful and reliable numerical method which has been extensively used by researchers to perform the vibration analyses of FG structures in the last decade. In this paper, firstly various mathematical models which have been used to express the material properties of FGMs are reviewed. Secondly different elasticity theories which have been applied in vibration analysis of FG beams are summarized. In addition, a review on the DQM and its applications is presented. At the next step, a comprehensive review on free vibration analyses of FG beams based on different elasticity theories and in particular those using the DQM is performed. In continue, a brief review on the application of other numerical methods in vibration analysis of FG beams is presented. Moreover, because of the importance of nonlinear vibration analysis of FG beams, a review on the application of various numerical methods and different elasticity theories on nonlinear vibration analysis of FG beams is performed. Finally, a brief review on linear and nonlinear vibration analysis of FG microbeams, as a special type of FG beams, is presented.

Thickness-variable composite beams for vibration energy harvesting

Researchers have recently focused on improving the efficiency of piezoelectric energy harvesters by redesigning their substrate beams. Two approaches have been explored, including changing the shape of the cross-section area, i.e., width variation, and changing the thickness of cantilever beams. The width changing approach suffers from the deduction of output power from the piezoelectric elements of the trimmed-off regions, while performance deterioration does not occur in the thickness-variable approach. The benefit of thickness-variable beams on energy harvesting has been analyzed theoretically, but its detailed experimental study is still absent. In this study, we for the first time fabricate a thickness-variable harvester based on the Garolite FR-4 epoxy laminate, and validate the superiority of the variable thickness beam on the harvester performance enhancement. A theoretical model is developed based on the Euler-Bernoulli beam theory and numerically solved via the Rayleigh-Ritz method. We compare the thickness-variable composite beam configuration with a conventional uniform-thickness counterpart and unveil the beneficial effect of evenly-distributed strain on performance enhancement. Experiments indicate that the thickness-variable method increases on the energy harvester efficiency by 78%.

Shunted optimal vibration energy harvesting control of discontinuous smart beams

This paper presents an adaptive dynamic analysis of discontinuous smart beam energy harvester systems using a shunt vibration control. The smart structural systems, connected with the shunt and harvesting circuit interfaces, consist of the three types of non-homogeneous structural combinations with different piezoelectric materials. The constitutive coupled dynamic equations with full variational parameters are reduced using the charge type-based Hamiltonian mechanics and the Ritz method-based weak-form analytical approach. Unlike the conventional techniques, this study elaborates the appearance of the two resonances with a wider shift on a specific range of the optimal power output frequencies, using only the first mode of the smart structural systems. Moreover, the two-equal peak of the optimal response may potentially occur to appear not only at the first resonance, but also at the second resonance. This intrinsically represents strong electromechanical effect, depending on the properties and thicknesses of piezoelectric materials and the circuit parameters. The accuracy of the theoretical method is tested using the iterative computational process of the optimal frequency response with full coupled electromechanical system parameters. Further details of the parametric studies are discussed to show the prediction of the energy harvesting with the ability of tuning an adaptive frequency response.

Two-span piezoelectric beam energy harvesting

This paper reports an analytical study of nonlinear vibratory energy harvesting via a two-span piezoelectric beam. The distributed parameter electromechanical model is applied to explore the benefits of nonlinear interaction between buckled beam spans. The Galerkin truncation method and harmonic balance method are applied together to find forced responses of the energy harvesting system. The effects of axial pre-pressure on energy harvesting are also explored. The analytical results are supported by utilizing direct time integration of the equation of motion. The amplitude and voltage output frequency response functions (FRF) of single-span, buckled, and two-span piezoelectric beam configurations reveal some differences. For example, the voltage output FRF of the two-span buckled configuration is larger than that of the other two configurations at high frequencies, whereas at low frequencies, the voltage output FRF of two-span unbuckled configuration is larger than that of the other two configurations. Moreover, two-span buckled configuration has more natural frequencies lying at the concerned frequency range. Finally, a hybrid harvester is proposed, which combines harvested voltage from single-span buckled, two-span, and two-span buckled piezoelectric beam to cover a demand of broadband voltages output.

Electro-vibration modeling and response of 3D skeletal frame configuration for energy harvesters

3D skeletal frame configuration is introduced as a means for overcoming deficiencies encountered by conventional 1D beam energy harvesters (EHs). A composite finite element model based on 3D beam kinematics is further developed and tailor-made for this purpose. A comprehensive electro-vibration analysis is conducted using a MATLAB code for the 3D skeletal frame EH as an enhanced application of the theory and compared to the corresponding 1D beam harvester. The results obtained by the theory is then validated against numerical responses based on active solid elements. It is shown that the novel 3D skeletal frame configuration offers substantial benefits over the conventional 1D beam including higher strain areas, multi-directionality, and effectively higher extracted power levels. These are actually among the most significant deficiencies by 1D beam topologies. The internal volume of the novel EH along with the surfaces of the tip mass can be utilized for electronic components and circuit boards.

Lowering the resonance frequency of a two-dimensional high-power piezoelectric energy harvester with reducing the stiffness of the harvester

Generating more power in lower frequencies is one of the most challenging purposes in designing cantilever beam energy harvesters. Using geometrically symmetric two-dimensional beam shapes is one of the most effective ways that has been proposed to increase the output power of harvesters. With symmetry in the geometry, torsional forces on piezoelectric elements eliminate. Consequently, the output power of the harvester increases. However, the resonance frequency of these designed harvesters is still high for some applications. In this work, we demonstrate a strategy to decrease the stiffness of a two-dimensional harvester named Elephant type, without changing in its output power. The output power and the resonance frequency of our proposed harvester are calculated using a finite element simulation. The finite element model is in a good agreement with the analytical and experimental data for the Elephant type harvester. The finite element model predicts lower resonance frequency for our model compared to Elephant type, without a major drop in the output power. Finally, we propose a dimensionless parameter to evaluate the performance of piezoelectric harvesters which have a direct relation with the output power and an inverse relation with the resonance frequency of the harvester.

Analysis of bimorph piezoelectric beam energy harvesters using superconvergent element

Cantilever-based piezoelectric energy harvesters have been utilized as structures to extract mechanical energy from the ambient mechanical vibrations and transfer it into the electrical output. In this article, the performance of bimorph piezoelectric beam energy harvesters is investigated. The cantilever beam is modeled by using both Timoshenko and Euler–Bernoulli beam theories. The equations are discretized using the conventional finite element method and superconvergent element. Besides the high rate of convergence, easy switching between the above beam theories is enabled by such type of element. The current model is presented for a Timoshenko beam model, but it could as well be used for a Euler–Bernoulli beam model. In addition, voltage, current, and power frequency response functions for different ranges of load resistance varying from the short-circuit to open-circuit conditions are determined to reach the maximum values. Effects of the slenderness ratio and the required beam model based on the geometric properties of the piezoelectric energy harvesters are discussed in the final part of this study. The results show that only for smaller values of the slenderness ratio (below 5), it is necessary to model the beam using the Timoshenko assumptions; otherwise both beam theories provide approximately the same responses.

Modeling and experimental characterization of a multi-point loaded piezocomposite beam for actuation and energy harvesting

This article proposes a multi-point support and inertial loading for beam-like piezocomposite vibration energy harvesters as an alternative to the common cantilevered beam configuration. In the proposed configuration, symmetrical overhanging free segments extend beyond two interior pinned supports, and tip masses are attached to the free ends for inertial tip-loading. The dynamic response of this multi-point loaded beam can be significantly altered by varying two configuration parameters: the support location and tip-loading. In this article, the transverse vibration due to harmonic excitation of a piezocomposite beam in this multi-point configuration is analyzed. The effects of configuration parameters on the natural frequency and curvature shapes of the beam are shown. Results from experimental testing of several support locations and tip masses are compared with analytical predictions, and it is demonstrated that the fundamental frequency of this system can be tuned by adjusting the support location and tip-loading. Comparisons of the output-to-input power ratios for the different configurations during vibration energy harvesting are also made, which demonstrate increased strain-normalized transduction for the multi-point configurations over a reference cantilevered beam. This article concludes with a discussion of the potential application of this configuration as a vibration energy harvester.

Intelligent Metasurfaces with Continuously Tunable Local Surface Impedance for Multiple Reconfigurable Functions

Electromagnetic metasurfaces can be characterized as intelligent if they are able to perform multiple tunable functions, with the desired response being controlled by a computer influencing the individual electromagnetic properties of each metasurface inclusion. In this paper, we present an example of an intelligent metasurface which operates in the reflection mode in the microwave frequency range. We numerically show that without changing the main body of the metasurface we can achieve tunable perfect absorption and tunable anomalous reflection. The tunability features can be implemented using mixed-signal integrated circuits (ICs), which can independently vary both the resistance and reactance, offering complete local control over the complex surface impedance. The ICs are embedded in the unit cells by connecting two metal patches over a thin grounded substrate and the reflection property of the intelligent metasurface can be readily controlled by a computer. Our intelligent metasurface can have significant influence on future space-time modulated metasurfaces and a multitude of applications, such as beam steering, energy harvesting, and communications.

Modeling and characterization of permendur cantilever beam for energy harvesting

This article presents the development of a cantilever harvester made of permendur with tip excitation. In the beginning, the dynamic behavior of the tip-mass beam harvester subjected to a harmonic bending force at the free-end has been studied. Also, the magneto-mechanical model, rotating unbalance equations and Faraday's Law have been combined to present the general model for generated power. Furthermore, damping coefficients have been elaborately measured and considered in the modeling of magnetostrictive harvester and prediction of optimum load to generate the maximum power. Good agreement between analytical and experimental results shows that the model is able to predict the behavior of harvester under the vibration with tip excitation and can find the optimum external load to have maximum power. Experiment results show that the maximum output power is 6.81 μW/cm3 and this power happens when the harvester is connected to a 0.63 Ω external load. Compared to other magnetostrictive harvesters, Permendur shows lower power density. However, its harvested power is enough to energize μW electrical devices at a reasonable cost. The presented results in this paper can be utilized as a design guideline for future investigations to optimize vibration-based magnetostrictive energy harvesters with tip excitation.

Design and Test of the MEMS Coupled Piezoelectric–Electromagnetic Energy Harvester

This paper researches on the design and test of the output performance of double-end clamped MEMS coupled piezoelectric–electromagnetic energy harvester. It establishes the theoretical output model of the double-end clamped rectangular beam and trapezoidal beam piezoelectric–electromagnetic energy harvester, and optimizes the structure parameters of piezoelectric and electromagnetic unit with simulation analysis. It also respectively realizes the processing of piezoelectric and electromagnetic unit by MEMS and flexible PCB technology, and completes the performance test of structure prototype through the experimental system. The result showed that the capacity of MEMS coupled piezoelectric–electromagnetic energy harvester, which taked four coil piezoelectric with integrated electromagnetic in series, was 12.23 times higher than that of piezoelectric energy harvester. Also the output voltage and power of coupled trapezoidal beam energy harvester were respectively increased 18.89% and 2.26%, compared with coupled rectangular beam energy harvester.