Piezoelectric Cantilever Beam Research Articles

Modeling and power performance improvement of a piezoelectric energy harvester for low-frequency vibration environments

A novel oscillator structure consisting of a bimorph piezoelectric cantilever beam with two steps of different thicknesses is proposed to improve the energy harvesting performance of a vibration energy harvester (VEH) for use in low-frequency vibration environments. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler–Bernoulli beam assumptions, then the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the coupled electromechanical equations governing the piezoelectric energy harvester are introduced by means of the Lagrange equations. Furthermore, expressions for the steady-state response are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed, and the effects of the ratio of lengths, ratio of thicknesses, end thickness, and load resistance on the output voltage, harvested power, and power density are discussed. Moreover, to verify the analytical results, finite element method simulations are also conducted to analyze the performance of the proposed VEH, showing good agreement. All the results show that the present oscillator structure is more efficient than the conventional, uniform beam structure, specifically for vibration energy harvesting in low-frequency environments.

Design of a disk-swing driven piezoelectric energy harvester for slow rotary system application

This paper presents mathematical modelling of an energy harvester that converts slow mechanical rotation into piezoelectric vibration using a small disk and a pair of magnets, for large-scale machinery monitoring applications such as wind turbine blades. The harvester consists of a piezoelectric cantilevered beam, a gravity-induced disk, and magnets attached to both the beam and the disk. The energy method is used to derive the three coupled equations that describe the motion of the disk, the vibration of the beam, and the harvester voltage output. The equations are solved using ODE45 in MATLAB software and verified by the corresponding experimental study. The result shows varied energy harvesting performance by blade rotational speed. At low blade speed, the harvester generates power by regularized magnetic excitation per blade revolution. At high blade speed, however, the disk behavior becomes chaotic to increase excitation force and power generation. The results show that the model can quantify power as a function of blade speed, and the proposed harvester can generate a considerable amount of power for self-sustainable sensing and monitoring of wind turbine blades.

Performance Analysis for a Wave Energy Harvester of Piezoelectric Cantilever Beam

ABSTRACT Liu, M.; Liu, H.; Chen, H.; Chai, Y., and Wang, L., 2018. Performance analysis for a wave energy harvester of piezoelectric cantilever beam. In: Liu, Z.L. and Mi, C. (eds.), Advances in Sustainable Port and Ocean Engineering. Journal of Coastal Research, Special Issue No. 83, pp. 976–984. Coconut Creek (Florida), ISSN 0749-0208. In this paper, we present a convenient and economical wave energy harvester that consists of a large piezoelectric cantilever beam and a floating vertical axisymmetric buoy. A spring-mass-damper system is applied to simulate the heaving motion of a wave energy harvester and semi-analytical solutions based on the eigen-function are used to analysis hydrodynamic characteristics of buoy under potential flow theory. The numerical results show the influences of the different lumped and structural parameters for the energy harvesting efficiency. Theoretical analysis and numerical calculation reveal this kind of the wave energy harvester can provide adequate power for the large ...

Cochlear amplifier inspired two-channel active artificial hair cells

The mammalian auditory system exhibits rich characteristics that has inspired research for decades. Some of these key characteristics include frequency selectivity of the basilar membrane (BM), nonlinear amplification of low-level stimuli, and compressive nonlinearity that enables the ear to sense over a large range of sound pressure levels (0–120 dB in humans). Cochlear outer hair cells (OHCs) play a vital role in the nonlinear amplification and compression of input signals and this behavior is referred to as the cochlear amplifier. Damage to OHCs due to aging, diseases, and environmental conditions often results in a sensorineural hearing loss. As a result, there is a need to develop better hearing prosthesis that transduce sound-induced vibrations to electrical signals by mimicking OHCs. In the present work, active artificial hair cells (AHCs) made of piezoelectric cantilever beams are developed to mimic the nonlinear behavior of the OHCs. In literature, AHC based prosthesis operate over a spectrum by developing an array of AHCs with different fundamental frequencies. The present work extends the frequency bandwidth of each AHC to sense over multiple resonant frequencies, unlike conventional single-channel AHCs. Therefore, a single active multi-frequency resonant AHC is presented to minimize the need for more artificial hair cells to cover the desired bandwidth of interest in an array format. Herein, the response of a 26 mm AHC to a base excitation is controlled by applying a phenomenological feedback control law that tunes the system close to a Hopf bifurcation near the first and second natural frequencies. The experimental results show a power relation of about one-third, between the output and input of the AHC. This is very similar to the compressive nonlinearity seen in the mammalian cochlea. The present effort is a continuation of the authors’ previous studies in bio-inspired nonlinear control of AHCs, which can lead to an implantable cochlear device, acoustic, or flow sensor in future.

Design and analysis of a hollow triangular piezoelectric cantilever beam harvester for vibration energy collection

The vibration of transportation infrastructure is random and of low frequency. The vibration energy can be collected and converted into electric energy by installing the piezoelectric cantilever beam (PCB) harvesters on the transportation infrastructure. The resonance frequency and the resonance number of the PCB harvesters within the low frequency range play critical roles. This paper presents an analysis of four types of PCB harvesters designed according to the characteristics mentioned above to evaluate the influence of three different shapes (rectangle, trapezoid and triangle) on the power generation capacity of the piezoelectric cantilever beams. The results show that the triangular PCB harvesters are more suitable for the low-frequency vibration environment of transportation infrastructure, and they usually have higher voltage outputs. In order to widen the resonant frequency of the triangular cantilever to better adapt to the random vibration environment of the transportation infrastructure, the performance of a hollow triangular piezoelectric cantilever beam (HTPCB) was also assessed. Through modeling and analysis, the resonant frequency of the HTPCB has a broader low frequency range. In practical applications, deployment of the HTPCB harvesters on transportation infrastructures such as pavements and bridges can collect more energy in the random and low-frequency vibration environment of the transportation infrastructures.

Taguchi Design of PZT-Based Piezoelectric Cantilever Beam with Maximum and Robust Voltage for Wide Frequency Range

Piezoelectric energy harvesting—an eco-friendly technology—is gaining more interest from researchers owing to its high power density. Among the various piezoelectric types, many studies have focused on the PZT-based piezoelectric cantilever beam because it can easily achieve the resonance effect compared to other types. In real applications, however, it is not easy to match the loading frequency with the resonance frequency owing to environmental factors. This prevents the application of piezoelectric energy harvesting to real life products because the efficiency of energy extraction decreases considerably outside the resonance frequency domain. In this research, the Taguchi design, which is an effective methodology used to improve product quality without controlling any noise factors, ensures that the PZT-based piezoelectric cantilever beam can obtain robust and high output voltage over a wide frequency range. The PZT-based piezoelectric cantilever beam should be implemented using the multi-response signal-to-noise ratio of the Taguchi design method because it has the two important responses, the output voltage and its deviation. Experiments are performed to measure the output voltage of various harvesters at the resonance frequency and several other frequencies. Based on the experimental results, the Taguchi design method is implemented considering the characteristics of the responses, and an optimal design combination is selected. As a result, the selected optimal combination results in a 9.86% output voltage reduction and an 18.14% decrease in voltage deviation.

A piezoelectric energy harvesting scheme based on stall flutter of airfoil section

Abstract The stall flutter of the airfoil section has the characteristics of self-excitation and violent vibration. As a new type of energy source, it could provide power for sensors and other devices. In this paper, a new energy harvesting scheme is proposed. A beam is fixed to the trailing edge of the airfoil section along the chord line and a piezoelectric transduction is stick to the appropriate position of the cantilever beam. When the airfoil section flies in stall flutter, the piezoelectric cantilever beam is excited to vibration and then drives the piezoelectric transduction to produce energy output. The system energy harvesting model consists of the dynamic model exported by the Lagrange Equation and the electromechanical coupling equation. The numerical simulation of the model shows that output voltage of a piezoelectric patch has stable amplitude of 1134.2 V and the output power has stable amplitude of 0.3233 W under the condition of resistance load R = 4 M Ω . The output voltage and power are greatly increased. The influence laws of load resistance, wind velocity, airfoil section torsion stiffness, sticking position of the piezoelectric patch, and wind gust are also analyzed by simulation. These analyses are conducive to the subsequent design of similar programs.

Piezoelectric energy harvester enhancement with graphene base layer

Traditional power source often becomes an obstacle for microelectromechanical systems (MEMs) from further miniaturization. Piezoelectric energy harvester serves as a perfect alternative power source which is clean and able to embed with MEMs. In this work, we replace silicon support layer in piezoelectric cantilever beam with nanocrystalline graphene (NCG) and compare their performance. By using finite element simulations, a cantilever beam piezoelectric energy harvester with nanocrystalline graphene as base layer with different thickness is modeled. For a better understanding on its performance, we had performed frequency response analysis for each design. The thickness of substrate layer and piezoelectric layer is varied from 50 nm to 400 nm. From the result, it is shown that higher thickness gives better Q-factor and figure of merit (FOM). Furthermore, graphene-based energy harvester had increase the operation bandwidth of energy harvester compared to silicon. For example, a 200 nm of ZnO layer and graphene layer gives a Q-factor & FOM of 3.4 times higher than silicon and a larger bandwidth by a factor of 1.1. In general, it is shown that the replacement of silicon with graphene had reduced energy loss by improving the efficiency of mechanical energy transfer in piezoelectric energy harvester.

Self-Sensing Vibration Suppression of Piezoelectric Cantilever Beam Based on Improved Mirror Circuit

The self-sensing technique allows a single piece of piezoelectric element to function simultaneously as an actuator and a sensor in a closed-loop system. This study proposes an improved vibration suppression system using the piezoelectric self-sensing technique whose usefulness is experimentally verified in a cantilever beam. A single piezoelectric element is bonded to the root of the beam and functions as an actuator and a sensor simultaneously. A mirror circuit constructed with two charge driver circuits is used to pick up the sensing signal from the driving voltage signal. Then, a closed-loop control strategy based on the proportion integration differentiation (PID) algorithm can adjust the sensing signal precisely to suppress the vibration of the cantilever beam quickly. The first mode of vibration is suppressed, and the amplitude of the vibration is actively dampened by a factor exceeding 96.4%. Moreover, the frequency sweep experiments demonstrate that with the PID feedback control circuit connected to the piezoelectric cantilever beam, the Q value of the system is greatly reduced, and the loss factor is increased from 0.053 to 0.288. The improved mirror circuit with PID control has a good suppression effect in the frequency range near the first order mode of the cantilever beam.

An Intelligent Self-Powered Pipeline Inner Spherical Detector With Piezoelectric Energy Harvesting

To break the limits of traditional pipeline inner spherical detector (PISD) application distances, this paper proposes a design of a piezoelectric energy harvester to develop an intelligent self-powered PISD. The harvester converts rotating mechanical energy into electrical energy. Due to restrictions in internal space and prohibition of magnet application, the harvester consists of a piezoelectric cantilever beam without any auxiliary structures. The fixed end of the harvester is fixed to the PISD shell and the free end extends in the direction of the center. A dynamic model was derived through the Euler-Lagrange method and an experiment platform with macro fiber composite was built. The harvester was designed in three schemes, and the longest harvester of 100 mm achieved optimum performance. After load optimization, 15.27 μW was obtained at 2.6 Hz, which is the rotational frequency of the PISD. A PISD prototype with a harvester was built and a pipeline experiment was conducted to analyze the output characteristics of the smooth operation and the passing weld operation. The results demonstrate that the proposed piezoelectric energy harvester has the potential to establish an intelligent self-powered PISD.

Micro-Piezoelectric Actuator Vibration Control using Electrorheological Fluid Active Support: Experimental Study

Abstract The paper investigated vibration control of micro piezoelectric actuator (MPA) using an electrorheological fluid (ERF) active support. In this era of micro-mechanical systems, technological advancement requires an effective way of damping these microstructures. MPA is used in micro air vehicles and micro-robotics in general. Utilization of piezoelectric cantilever beam and ERF as a damper presents a novel driving technique. The damping characteristics of the MPA by subjecting the system to unit excitations were investigated experimentally. The experimental results compared damping ratios of the free vibration of the MPA with and without ERF, MPA with non-activated ERF support and MPA with activated ERF support. It was concluded that when there is no electric field applied to the ERF the damping ratio is higher than when an electric field is applied.

Analysis of angular position, dimension and material of a cantilever piezoelectric energy harvester

The performance of an angular vibrating single piezoelectric cantilever beam energy harvester in a flexural mode was analyzed. In this research the approaches of theory, finite element, and experiment have been undertaken to study the effects of angular position, mechanical properties, and dimensions on the output power and resonance frequency of a piezoelectric cantilever beam. The phase shift is an important phenomenon observed in this system because of the angular position of the beam about its longitudinal axis. Frequency shift due to the angular position is usually observed in experiments. However, it has not been studied theoretically until now. The angular position not only affects the resonance frequency but also the amount of output power from the lead zirconate titanate ceramic bonded on it. Furthermore, beam and piezoelectric dimensions have a major effect on power output and resonance frequency. Another aspect considered in this research is the effect of materials on power and frequency which have been studied for aluminum, copper, and steel.

A Self-Powered Engine Health Monitoring System Based on L-Shaped Wideband Piezoelectric Energy Harvester.

Engine health monitoring is very important to maintain the life of engines, and the power supply to sensor nodes is a key issue that needs to be solved. The piezoelectric vibration energy harvester has attracted much attention due to its obvious advantages in configuration, electromechanical conversion efficiency, and output power. However, the narrow bandwidth has restricted its practical application. A self-powered engine health monitoring system was proposed in this paper, and an L-shaped wideband piezoelectric energy harvester was designed and implemented. The L-shaped beam-mass structure and the piezoelectric bimorph cantilever beam structure was combined to form the wideband piezoelectric energy harvester configuration, which realized effective output at both resonance points. The theoretical model and finite element simulation analysis of the wideband piezoelectric energy harvester were proposed and the parameters were optimized based on that to meet the requirement of the vibration frequency of the engine. The experimental results show that the proposed energy harvester can be applied into the automobile engine health monitoring system. Engine signal analysis results also demonstrate that the proposed system can be used for engine health monitoring.

Wireless power transfer system with center-clamped magneto-mechano-electric (MME) receiver: model validation and efficiency investigation

This paper presents a complete equivalent circuit model for a wireless power transfer concept utilizing a center-clamped piezoelectric cantilever beam with magnetic tip masses as a receiver. The analytical solution for the power delivered to a load resistance is given as a function of material properties, beam characteristics and external magnetic field strength. The lumped element model is experimentally verified. The efficiency of the system is thoroughly investigated and validated. The essential effect of the coil resistance is highlighted. The analyses show that optimization of transmitter coil size and geometry of the piezoelectric transducer has a significant impact on the transduction factor between the magnetic-mechanical-electrical domains, which greatly improves the transmission efficiency. Finally, the model for evaluating the efficiency is generalized for other similar structures.

New feedforward filtered-x least mean square algorithm with variable step size for active vibration control

The step size of least mean square (LMS) algorithm is significant for its performance. To be specific, small step size can get small excess mean square error but results in slow convergence. However, large step size may cause instability. Many variable step size least mean square (VSSLMS) algorithms have been developed to enhance the control performance. In this paper, a new VSSLMS was proposed based on Kwong’s algorithm to evaluate the robustness. The approximate analysis of dynamic and steady-state performance of this developed VSSLMS algorithm was given. An active vibration control system of piezoelectric cantilever beam was established to verify the performance of the VSSLMS algorithms. By comparing with the current VSSLMS algorithms, the proposed method has better performance in active vibration control applications.

Electrically rectified piezoelectric energy harvesting induced by rotary magnetic plucking

A theoretical framework together with an experimental validation is developed for the investigation of a rotational piezoelectric energy harvester attached to the standard interface circuit for AC–DC conversion. The energy harvester consists of an electrically rectified piezoelectric cantilever beam mounted on a stationary base with a magnet attached to its free end. Energy is harvested by vibration of beam induced by non-contact rotary magnetic plucking. A theoretical model accounting for magnetic coupling and rotary plucking is developed and the phenomenon of frequency up-conversion is realized by the Fourier analysis of the impulsive-like driving force. The analytic estimate of DC harvested power is derived showing that the electric response can be imitated to the case of rectilinear harmonic force vibration whereas the multiplication of the driving frequency and the integer value closely matches the device’s fundamental resonance. As a result, it exhibits broadband frequency response due to frequency up-conversion. In addition, the prediction on the crests and troughs of ripples in the DC power frequency response is remarkably found in excellent agreement with experiment. Finally, several design guidelines are proposed. These include power enhancement by lowering the ratio of perpendicular distance of magnetics to the radius of revolution, and the reduction of ripples by requiring larger mechanical damping.

Modelling of a Low Frequency Based Rectangular Shape Piezoelectric Cantilever Beam for Energy Harvesting Applications

<p>Harvesting few amount of charge from environmental ambient sources namely, wind, thermal, heat, vibration, solar utilizing micro scale energy harvesting devices, offers vast view of powering for numerous portable low power electronic devices. However, power harvesting using piezoelectric crystal from low power ambient source nowdays has increasing popularity with the advantages of low cost, long life time, stability and clean energy. Recent trends have shown that most researchers are interested in designing a low resonance frequency vibration based energy harvesting devices despite of its challenges ahead. In this paper, a low frequency based rectangular shape piezoelectric cantilever beam has been developed for energy harvesting applications. The proposed vibration based low frequency cantilever beam using piezoelectric element has been developed by finite element analysis (FEA) employing COMSOL Multiphysics platform. The main goal of the study is to analyze the outcome of geometric model of a piezoelectric cantilever beam and to calculate the resonance frequency of the structure according to its length. The material of PZT-5H, has been considered to enhance the efficiency of the low frequency based cantilever beam. Finally, the proposed result is compared with other existing works.</p>

Modeling and analysis of cantilever piezoelectric energy harvester with a new-type dynamic magnifier

An analytical concept of a new-type dynamic magnifier for a piezoelectric energy harvester is proposed. The new-type dynamic magnifier consists of the two-spring–mass system located between the constrained end of the piezoelectric beam and the vibrating base structure. The main function of the dynamic magnifier is capable of significantly widening the frequency bandwidth and increasing the power output from the ambient vibration. The mechanical system of the cantilever piezoelectric beam with the end mass offset and the translational and rotational springs attached to the magnifier mass offset has been modeled. The beam motions from the base (translational and rotational) and transverse relative system have been considered. A mathematical model of a cantilevered piezoelectric harvester with the new-type dynamic magnifier has been developed using the generalized Hamilton’s principle. The eigenfunction and natural frequency formulations of the cantilever beam with the new-type dynamic magnifier are presented. The orthogonal conditions of the mode shapes are derived. The reduced order electromechanical coupling dynamic equations are formulated by using the present eigenfunction and the modal Galerkin decomposition method. The effect of the spring stiffness and mass offset of magnifier, and the end mass offset on the performance of the harvester is investigated. Analytical results show that with the proper selection of the design parameters of the magnifier, the harvesting power can be dramatically enhanced and the effective bandwidth of the harvester system can be improved. It is observed that a small change for the end mass offset and two-spring stiffness ratio for widening the operational frequency and magnifying the mechanical system of the piezoelectric beam may result in a substantial change of energy harvester performance.

Detection of void and metallic inclusion in 2D piezoelectric cantilever beam using impedance measurements

The aim of current work is to improve the existing inverse methodology of void-detection based on a target impedance curve, leading to quick-prediction of the parameters of single circular void. In this work, mode-shape dependent shifting phenomenon of peaks of impedance curve with change in void location has been analyzed. A number of initial guesses followed by an iterative optimization algorithm based on univariate method has been used to solve the problem. In each iteration starting from each initial guess, the difference between the computationally obtained impedance curve and the target impedance curve has been reduced. This methodology has been extended to detect single circular metallic inclusion in 2D piezoelectric cantilever beam. A good accuracy level was observed for detection of flaw radius and flaw-location along beam-length, but not the precise location along beam-width.

Analysis of broadband characteristics of two degree of freedom bistable piezoelectric energy harvester

In order to broaden the working frequency band of the piezoelectric energy harvester and improve the energy harvesting efficiency, a new two degree of freedom bistable piezoelectric vibration energy harvester is designed in this paper. It consists of a basic cantilever beam, a mass, a piezoelectric cantilever beam and magnets. The equivalent model of the system is established using lumped parameter method, and the two degree of freedom bistable motion equation is established considering the influence of electromechanical coupling. Using Matlab, the motion equation is calculated, and the curve of the system voltage with time and frequency is obtained. The voltage output characteristics of the system under bistable vibration and the influence of the stiffness and the mass of the basic cantilever beam on the output performance of the system are analyzed. Under the excitation of 0.3 g simple harmonics, the two degree of freedom bistable piezoelectric energy harvester is experimented using one-way frequency-increasing sweep. The results show that the maximum output voltage of the two resonance band of the energy harvester is 26 V and 13 V. Compared with the single degree of freedom bistable structure, the frequency band is widened by 10 Hz. In addition, reducing the stiffness of the basic cantilever beam and increasing the mass of mass block are all beneficial to broadening the working band of the harvester.