Broadband Piezoelectric Energy Harvester Research Articles

Increased mechanical robustness of piezoelectric magnetoelastic vibrational energy harvesters

This work presents a cantilever based broadband piezoelectric magnetoelastic vibration energy harvester with increased mechanical robustness. The energy harvester is fabricated using KOH etching to define the cantilever and the proof mass is made using micromachined Fe foils which together with a pair of miniature magnets provides the magnetoelastic properties. KOH etching leads to very sharp corners at the anchoring point of the cantilever which makes the cantilever fragile. The mechanical robustness of the energy harvesters is increased using a lithography-free two-step fabrication process where a thermal oxidation is used for corner rounding. The corner rounding at the anchoring point lowers the stress concentration and thereby increases the robustness of the device. The radius of curvature for the corner depends linearly on the thickness of the oxide. Both enhanced and non-enhanced beams are excited at increasing frame accelerations. The conventional beams break at frame accelerations of around 3 g while the enhanced break at almost twice as much, 5.7 g. The devices are characterized electrically by impedance measurements in both their linear and non linear regime. The magnetoelastic behaviour can be adjusted by varying the beam-magnet distance which allows for both spring softening and spring hardening.

Finite-element modeling of piezoelectric energy harvesters using lead-based and lead-free materials for voltage generation

ABSTRACTPiezoelectric energy harvesters are capable of sensing mechanical vibrations and converting them into usable energy to empower low-power microsystems. In this work, a novel seesaw cantilever structure-based broadband piezoelectric energy harvester has been designed using both lead-based and lead-free piezoelectric material. It has been observed that along with its structure dimensions and piezo material properties, a harvester’s load also determines its performance. An optimum load would yield maximum harvester power. The optimum value of a resistor generating peak power has been described in this work. The harvester is capable of producing a peak power of around 23 mW across a 0.14 MΩ load.

A Wideband Piezoelectric Energy Harvester Design by Using Multiple Non-Uniform Bimorphs

This paper presents an analytical approach for the development of a new wideband piezoelectric energy harvesting system. The proposed model is based on Adomian decomposition method to derive the dynamic response of the general non-uniform smart structures under external environmental excitations over a wide frequency domain efficiently harvesting the subsequent vibrational energy. The steady-state response of a nonlinearly tapered piezoelectric harvester subjected to harmonic base motion is obtained, and the higher potential electromechanical outputs compared with traditional uniform harvester are analytically derived. Afterward, a group of nonlinearly tapered cantilevers with the same volume and length but different taper ratios and surface bonded piezoelectric layers are assembled together in order to build a broadband piezoelectric energy harvester. Through numerical studies, it is proven that with the proposed non-uniform configuration, the new energy harvester design can function effectively and efficiently with high voltage output over a wide frequency range. The designed wideband harvester can automatically activate one of the non-uniform bimorphs to resonate at particular ambient vibration frequencies and eventually reach the maximum electromechanical output. Based on the proposed theoretical model, an optimum structural design for the wideband piezoelectric energy harvester in the required operational frequency range can be efficiently achieved.

An E-shape broadband piezoelectric energy harvester induced by magnets

We describe in this work a broadband magnetic E-shape piezoelectric energy harvester with wide frequency bandwidth. We develop first a nonlinear electromechanical model of the harvester based on the Hamilton variation principle that simulates the effect of the nonlinear magnetic restoring force at different spacing distances. The model is used to identify the distances existing between two different magnets that enable the system to perform with a specific nonlinearity. The performance of the E-shape piezoelectric energy harvester is also investigated through experiments, with E-shape energy harvesters at different spacing distances tested under several base acceleration excitations. We observe that the frequency domain output voltage of the system shows a general excellent controllable performance, with a widening of the frequency bandwidth. The half-power bandwidth of the linear energy harvester for a distance of 25 mm is 0.8 Hz only, which can be expanded to 2.67 Hz for the larger distance of 11 mm between magnets. The energy harvester presented in this work shows promising performances for broad-spectrum vibration excitations compared to conventional cantilever piezoelectric energy harvester systems with a tip mass.

Design and performance analysis of the low-frequency and broadband piezoelectric energy harvester

A novel type energy harvester composed with n masses and n beams was proposed to solve the problems of high-frequency and narrow band of cantilever energy harvester to improve its energy conversion efficiency, and broaden its application. Firstly, We taken micro beam as the research object, improved its dynamic model with size effect, then verified it by experiments. Secondly, the dynamic model was established based on the improved one, and its response and the output voltage of the external excitation was deduced formula. Finally, the performance was studied when n=2. The results show that resonance frequency was obvious reduced, and there are two frequency points less than 50Hz, 15.25 Hz and 23.08 Hz. Moreover, when the effective output voltage reached 80 mv, the effective frequency band was 20.32 Hz, which can make up for the energy conversion efficiency of single resonant frequency harvester.

Power enhancement of broadband piezoelectric energy harvesting using a proof mass and nonlinearities in curvature and inertia

This paper investigates the mechanical behavior of a unimorph piezoelectric cantilever beam with a tip mass subjected to a harmonic base excitation for energy harvesting. The energy harvester is modeled as an in-extensional beam with Euler–Bernoulli assumptions. The curvature and the inertia terms are assumed to be nonlinear due to large amplitude vibrations. The governing equations of motion are derived using the Euler–Lagrange equations. The reduced-order model equations (ROMs) are obtained based on the Galerkin method. A parametric study is performed to reveal the influence of different parameters such as proof mass, damping ratio and external resistance load on the scavenged power from the nonlinear energy harvester. It is shown that the addition of a sufficient large tip mass, significantly increases the power and the voltage. The effect of the tip mass on the Fast Fourier Transform (FFT) of the tip displacement and generated voltage is studied, and it is shown that in the presence of the tip mass two frequencies of the system are excited in contrast to the no tip mass case in which one frequency is excited. Furthermore, it is observed that the second excited frequency is three times of the first one, and due to the small amplitude ratios of the tip displacement of the second frequency to the first frequency, the second frequency can be neglected. Energy conservation is examined in the absence of the mechanical damping, and it is shown that energy harvesting annihilates the vibrations. In addition, the effect of the external resistance load on the average power is discussed in the presence and absence of the tip mass and the optimum value of the resistance load is obtained for each system. Some results obtained from MATLAB software were validated by using FE analysis with commercial software COMSOL, and a good accordance was shown between the results obtained from mentioned methods.

Broadband and tunable PZT energy harvesting utilizing local nonlinearity and tip mass effects

In this paper, a broadband piezoelectric energy harvester with an applied restoring force is studied. The restoring force is modeled as a spring in the boundary conditions of the system. The system is composed of a clamped-free beam with a tip mass which is supported by a spring at the free end. A piezoelectric layer is bounded to the upper surface of the beam and the system is exposed to an external harmonic base excitation. A nonlinear distributed parameter model of the harvester is derived using the Hamilton's principle utilizing the Euler–Bernoulli beam theory assumption. The nonlinear strain-displacement field is used to take the large transverse deflections effects into account. The reduced-order model is derived by implementing the Galerkin discretization method and the dimensionless form of the equations is used to analyze the system. The effect of the piezoelectric layer on the free vibrations of the structure is determined. Effects of tip mass and base acceleration on the frequency response of the system are investigated. The results show that, the tip mass can amplify the scavenged voltage and tune the resonance frequency. To study the influence of different types of the restoring force, linear, hardening, and pure nonlinear behavior are considered for the applied spring. The results demonstrate that by applying a pure nonlinear restoring force, the resonance bandwidth of the harvester increases which causes the harvester to generate energy in a larger frequency bandwidth and the output voltage increased remarkably in comparison to clamped-free energy harvester. This phenomenon enhances the harvester efficiency in the cases of the excitations with the time-varying frequency or the random excitations and the results in a broadband energy harvester. Finally, studying the frequency response curves for the different values of the spring location declares that, as the location of the attached spring changes, the nonlinear resonance frequency alters. The maximum increase in the bandwidth is accompanied by the case where spring is attached at the free end of the beam.

Optimization study on inductive-resistive circuit for broadband piezoelectric energy harvesters

The performance of cantilever-beam piezoelectric energy harvester is usually analyzed with pure resistive circuit. The optimal performance of such a vibration-based energy harvesting system is limited by narrow bandwidth around its modified natural frequency. For broadband piezoelectric energy harvesting, series and parallel inductive-resistive circuits are introduced. The electromechanical coupled distributed parameter models for such systems under harmonic base excitations are decoupled with modified natural frequency and electrical damping to consider the coupling effect. Analytical solutions of the harvested power and tip displacement for the electromechanical decoupled model are confirmed with numerical solutions for the coupled model. The optimal performance of piezoelectric energy harvesting with inductive-resistive circuits is revealed theoretically as constant maximal power at any excitation frequency. This is achieved by the scenarios of matching the modified natural frequency with the excitation frequency and equating the electrical damping to the mechanical damping. The inductance and load resistance should be simultaneously tuned to their optimal values, which may not be applicable for very high electromechanical coupling systems when the excitation frequency is higher than their natural frequencies. With identical optimal performance, the series inductive-resistive circuit is recommended for relatively small load resistance, while the parallel inductive-resistive circuit is suggested for relatively large load resistance. This study provides a simplified optimization method for broadband piezoelectric energy harvesters with inductive-resistive circuits.

Vibration band gap analysis of a new periodic beam model using GDQR method

In this study, a new periodic beam model is introduced. This beam consists of the concentrated rigid masses and tapered beam elements with linearly variable width. The theoretical equations are derived by employing the Euler-Bernoulli beam and the Bloch–Floquet theorem and then solved using the generalized differential quadrature rule method to calculate the first two band gaps. The effects of the mass, mass moment of inertia and taper ratio on the widths and central frequencies of the first two band gaps are investigated. Results show that the wide band gaps at low frequency ranges can be obtained by changing the geometrical parameters. This is of interest for different applications of the band gap phenomenon such as broadband piezoelectric energy harvesting. Finally, the finite element simulation (ANSYS software) is used to validate the analytical method and good agreement is found.

Design of high output broadband piezoelectric energy harvester with double tapered cavity beam

Design of piezoelectric energy harvester for a wide operating frequency range is a challenging problem and is currently being investigated by many researchers. Widening the operating frequency is required, as the energy is harvested from ambient source of vibration which consists of spectrum of frequency. This paper presents a technique to increase the operating frequency range and to enhance the amplitude of the generated voltage in the operating frequency range. The wider operating frequency range is achieved by designing a harvester using propped cantilever beam with variable overhang and the amplitude of the generated voltage is enhanced by introducing a double tapered cavity. The proposed piezoelectric energy harvester is modeled analytically using Euler Bernoulli beam theory. The results from the modeling and analysis reveal that the maximum voltage is generated from the energy harvester designed with the double tapered cavity having the taper angle of α = 2.25°. Hence the experimental investigations are carried out with this energy harvester and the generated voltage measured is in close agreement with the results obtained from the model. The simulation and experimental results presented in this paper demonstrate that the proposed harvester design not only widens the operating frequency range but also it enhances the amplitude of the generated voltage in large extent.

MEMS Based Broadband Piezoelectric Ultrasonic Energy Harvester (PUEH) for Enabling Self-Powered Implantable Biomedical Devices.

Acoustic energy transfer is a promising energy harvesting technology candidate for implantable biomedical devices. However, it does not show competitive strength for enabling self-powered implantable biomedical devices due to two issues – large size of bulk piezoelectric ultrasound transducers and output power fluctuation with transferred distance due to standing wave. Here we report a microelectromechanical systems (MEMS) based broadband piezoelectric ultrasonic energy harvester (PUEH) to enable self-powered implantable biomedical devices. The PUEH is a microfabricated lead zirconate titanate (PZT) diaphragm array and has wide operation bandwidth. By adjusting frequency of the input ultrasound wave within the operation bandwidth, standing wave effect can be minimized for any given distances. For example, at 1 cm distance, power density can be increased from 0.59 μW/cm2 to 3.75 μW/cm2 at input ultrasound intensity of 1 mW/cm2 when frequency changes from 250 to 240 kHz. Due to the difference of human body and manual surgical process, distance fluctuation for implantable biomedical devices is unavoidable and it strongly affects the coupling efficiency. This issue can be overcome by performing frequency adjustment of the PUEH. The proposed PUEH shows great potential to be integrated on an implanted biomedical device chip as power source for various applications.

Experiments and Electromechanical Properties of a Broadband Piezoelectric Vibration Energy Harvester

A broadband piezoelectric energy harvester (BPEH), consisting of a conventional linear piezoelectric energy harvester (CPEH) and an elastic magnifier, was presented in this paper. The improved two-degree-of-freedom lumped-parameter electromechanical model of the BPEH was established and the optimal external resistances under short-circuit and open-circuit resonance conditions were investigated to maximize the output power of the BPEH. The output voltage and output power of the BPEH obtained from the theoretical model were verified and found to be in reasonable agreement with the experimental results. The obtained results have shown that the maximal output powers under short-circuit and open-circuit resonance conditions are both 24 times that generated by the CPEH without elastic magnifier. The frequency space between the two peaks of the frequency-response curve of the BPEH is 14 Hz which is 7 times that of CPEH.

A Multiple Direction Broad Frequency Band Piezoelectric Energy Harvester

A multiple direction broad frequency band piezoelectric energy harvester is proposed for harvesting ambient vibration energy with a variable frequency in different directions. The harvester is composed of eight cantilevers which point to different direction. The single cantilever consists of a base, two ceramic pieces and a proof mass which would be glued together. The finite element model of the harvester is constructed and the effects of structure parameters of the harvester on effective work frequency, electricity generating capability and maximal stress value are analyzed. The results indicate the effective work frequency scope of the harvester is about 13‐20Hz. The harvester can harvest relatively more energy in different excitation. The electric potential of a harvester is about 720.136V at the ambient load of 400Pa and the harvester is well suited for some wireless communication systems.

Nonlinear M-shaped broadband piezoelectric energy harvester for very low base accelerations: primary and secondary resonances

It has been well demonstrated over the past few years that vibration energy harvesters with intentionally designed nonlinear stiffness components can be used for frequency bandwidth enhancement under harmonic excitation for sufficiently high vibration amplitudes. In order to overcome the need for high excitation intensities that are required to exploit nonlinear dynamic phenomena, we have developed an M-shaped piezoelectric energy harvester configuration that can exhibit a nonlinear frequency response under very low vibration levels. This configuration is made from a continuous bent spring steel with piezoelectric laminates and a proof mass but no magnetic components. Careful design of this nonlinear architecture that minimizes piezoelectric softening further enables the possibility of achieving the jump phenomenon in hardening at few milli-g base acceleration levels. In the present work, such a design is explored for both primary and secondary resonance excitations at different vibration levels and load resistance values. Following the primary resonance excitation case that offers a 660% increase in the half-power bandwidth as compared to the linear system at a root-mean-square excitation level as low as 0.04g, secondary resonance behavior is investigated with a focus on 1:2 and 1:3 superharmonic resonance neighborhoods. A multi-term harmonic balance formulation is employed for a computationally effective yet high-fidelity analysis of this high-quality-factor system with quadratic and cubic nonlinearities. In addition to primary resonance and secondary (superharmonic) resonance cases, multi-harmonic excitation is modeled and experimentally validated.

Model and Experiments of a Broadband Piezoelectric Vibration Energy Harvester

In order to improve the energy transferring efficiency and the operating frequency bandwidth, focusing on a type of broadband piezoelectric cantilever vibration energy harvester(B-PCVEH) with an elastic magnifier(EM), an improved lumped parameter coupled electromechanical model of the B-PCVEH is proposed. The model equivalent parameters are determined though the energy conversion principle and the curve fitting method by considering a correction factor and the shape information of the cantilever, and then the governing equations of motion, the frequency function and the electrical output power of B-PCVEH are derived according to the mechanics and electronics equilibrium principles. The effects of the structural parameters(such as mass ratio, stiffness ration, and damping ratio and load resistance) on the frequency performance, the vibration performance and the electric output performance of the B-PCVEH are researched by numerical simulations. The prototype of the B-PCVEH and the experiment setup are developed, and the accuracy of the output performance in the numerical solutions is identified from the experimental results. A reasonable agreement is found between the numerical results and the experimental results. The results show that larger mass and stiffness ratios and smaller damping ratio of the EM and the cantilever piezoelectric beam are helpful to improve the energy transferring efficiency and the frequency bandwidth of the B-PCVEH.

Multiple patch–based broadband piezoelectric energy harvesting on plate-based structures

Several engineering systems, such as aircraft structures, are composed of load-bearing thin plates that undergo vibrations and employ wireless health, usage, and condition monitoring components, which can be made self-powered using vibrational energy harvesting technologies. Integrated piezoelectric patches can be implemented for enabling self-powered sensors in the neighborhood of plate-based structures. In this work, coupled electroelastic modeling and experimental validations of broadband energy harvesting from structurally integrated piezoelectric patches on a rectangular thin plate are presented. A distributed-parameter electroelastic model for multiple patch–based energy harvesters attached on a thin plate is developed. Closed-form structural and electrical response expressions are derived for multiple vibration modes of a fully clamped thin plate for the series and parallel connection configurations of multiple patch–based energy harvesters. Experimental and analytical case studies are then compared for validating the analytical models of structurally integrated multiple patch–based energy harvesters. It is shown that analytical electroelastic frequency response functions exhibit very good agreement with the experimental frequency response function measurements for the series and parallel connection cases. In addition to offering an effective interface for energy harvesting from two-dimensional thin structures, series and parallel multiple patch–based energy harvester configurations yield effective broadband energy harvesting by combining the electrical outputs of harvester patches for multiple vibration modes.

A low frequency and broadband piezoelectric energy harvester using asymmetrically serials connected double clamped–clamped beams

A novel structure of piezoelectric energy harvester was developed using double clamped–clamped beams serials connected by a rectangular frame, coupled with a proof mass and supporting mass near the center of upper and lower beams. The serials connection has a significant effect on reducing the resonance frequency, which is predicted by theoretical analysis and validated by experimental, and a reduction of 36.7% is achieved compared with the single clamped–clamped beam. More importantly, the bandwidth of the power spectrum is 36.4% wider, by introducing an asymmetry of 1 mm between the proof and supporting mass, than that of the symmetric setup. More than 0.8 mW ranging from 144 to 170 Hz is obtained near the two peaks of 0.992 mW at 150 Hz and 0.844 mW at 165 Hz, respectively. For its lower frequency, broader bandwidth and compact volume, the asymmetric harvester has promising application in wireless sensors networks.

극점-영점 상쇄 기법을 이용한 광대역 압전 진동 에너지 하베스터

이 논문에서는 기존 외팔보 빔 형상을 가진 진동 에너지 하베스터의 작동 주파수 범위를 공진 주파수 이후로 확장하기 위해 새로운 형태의 진동 에너지 하베스터가 제시되었다. 압전 재료를 사용한 기존 외팔보 빔 형상의 진동 에너지 하베스터에 레버형 반공진 시스템에서 발생하는 극점-영점 상쇄 기법을 적용하여 작동 주파수 영역을 확장하였다. 간단한 이론적 해석 및 실험을 통해 제안된 광역 압전 진동 에너지 하베스터의 실현 가능성을 검증하였다. This paper presents a new design for a piezoelectric energy harvester with the potential to harvest vibration energy over a wide range of excitation frequencies, particularly beyond the resonance frequency. The piezoelectric vibration energy harvester employs the concept of pole-zero cancellation occurring in a lever type anti-resonant system. The experimental results show that the proposed energy harvester can provide the potential possibility of a broadband piezoelectric vibration energy harvester.

Impedance matching for broadband piezoelectric energy harvesting

This paper presents a system design for broadband piezoelectric energy harvesting by means of impedance matching. An inductive load impedance is emulated by controlling the output current of the piezoelectric harvester with a bipolar boost converter. The reference current is derived from the low pass filtered voltage measured at the harvester terminals. In order to maximize the harvested power especially for nonresonant frequencies the filter parameters are adjusted by a simple optimization algorithm. However the amount of harvested power is limited by the efficiency of the bipolar boost converter. Therefore an additional switch in the bipolar boost converter is proposed to reduce the capacitive switching losses. The proposed system is simulated using numerical parameters of available discrete components. Using the additional switch, the harvested power is increased by 20%. The proposed system constantly harvests 80% of the theoretically available power over frequency. The usable frequency range of ±4Hz around the resonance frequency of the piezoelectric harvester is mainly limited due to the boost converter topology. This comparison does not include the power dissipation of the control circuit.

Broadband energy harvesting through a piezoelectric beam subjected to dynamic compressive loading

This paper investigates the design and analysis of a broadband piezoelectric energy harvester that uses a simply supported piezoelectric beam compressed by dynamic loading. The beam is restrained at one end and carries a moving mass at the other end where a magnetic force is applied axially. Taking advantage of the flexibility of the slender beam and the nonlinearity of the magnetic force, the design aims to enhance the harvester’s functionality with a broad frequency bandwidth. Both theoretical and experimental investigations are performed in this study over a range of excitation frequencies. Specifically, the electromechanical model of the harvester is analytically developed by means of the energy-based method and the extended Hamilton’s principle. Using the derived model, a parametric study is carried out to obtain the harvester’s voltage response under parametric excitations. Furthermore, the effects of various parameters on the harvester’s voltage response are examined. A prototype harvester is fabricated and experimentally tested. The theoretical model is validated against experimental data to confirm the harvester’s nonlinear response behaviors and enhanced capabilities. Both simulation and experiment illustrate that the harvester exhibits a softening nonlinearity and hence a broad frequency bandwidth with large-amplitude voltage response. It is also shown from numerical simulations that the harvester’s performance can be further improved by properly selecting the end mass and reducing the mechanical damping. The present findings demonstrate that dynamic compressive loadings can be successfully utilized to increase the harvester’s voltage output and frequency bandwidth.