Piezoelectric Cantilever Beam Research Articles

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.

Design of optimized cantilever form of a piezoelectric energy harvesting system for a wireless remote switch

A smart lighting system can be controlled using a smartphone and/or human activated wireless remote switches. We designed a wireless remote switch using a cantilever type piezoelectric energy harvester to make a battery-less IoT node device that has high output power but a small tip displacement through frequency up-conversion. The purpose of this design is to overcome the conventional volume problem of the piezoelectric cantilever beam. In order to apply the high resonance frequency to the model at constant displacement, we set the limiting conditions of maximum vertical displacement of the cantilever beam to be 1 mm and a human input pressing force of 5–8 N, the force generally required when a human presses a switch button. In these limiting conditions, different shapes of steel substrate were used to find the optimal harvester that meets the limiting conditions and generates about 65 μJ of energy at 5 kΩ resistive loads under free vibration. Using this harvester, we designed a wireless remote switch with an impact type mechanical mechanism with two cantilever type energy harvesters to generate 140 μJ of energy, requiring no impedance matching circuit. This energy was then used to power a microcontroller to transmit data packets using ZigBee Green Power communication. Three identical data packets were transmitted by the wireless remote control switch to ensure data reception by the smart LED bulb and to toggle the bulb on or off state. Finally, this study successfully contributed to elevating the possibility of commercialization of the piezoelectric harvester based wireless remote switch for IoT.

A Multi-Parameter Perturbation Solution for Functionally Graded Piezoelectric Cantilever Beams under Combined Loads.

In this study, we use a multi-parameter perturbation method to solve the problem of a functionally graded piezoelectric cantilever beam under combined loads, in which three piezoelectric coefficients are selected as the perturbation parameters. First, we derive the two basic equations concerning the Airy stress function and electric potential function. By expanding the unknown Airy stress function and electric potential function with respect to three perturbation parameters, the two basic equations were decoupled, thus obtaining the corresponding multi-parameter perturbation solution under boundary conditions. From the solution obtained, we can see clearly how the piezoelectric effects influence the behavior of the functionally graded piezoelectric cantilever beam. Based on a numerical example, the variations of the elastic stresses and displacements as well as the electric displacements of the cantilever beam under different gradient exponents were shown. The results indicate that if the pure functionally graded cantilever beam without a piezoelectric effect is regarded as an unperturbed system, the functionally graded piezoelectric cantilever beam can be looked upon as a perturbed system, thus opening the possibilities for perturbation solving. Besides, the proposed multi-parameter perturbation method provides a new idea for solving similar nonlinear differential equations.

A validated simulation of energy harvesting with piezoelectric cantilever beams on a vehicle suspension using Bond Graph approach

Nowadays, there is a combine effect of piezoelectric material performances and energy harvesting management strategy increase. As the same time, the energy consumption of electrical components and circuits decrease. Thus, this leads to a growing interest in recovering low energy level with piezoelectric cantilever beam in the suspensions of an automotive vehicle to perform predictive maintaining operations for example. For this purpose, a Bond Graph model of suspension with an embedded piezoelectric beam has been proposed since it gives the keys to find an optimal configuration for the energy harvester. The Bond Graph language is well adapted to translate multiphysics exchange of energy and power from mechanical to electrical conversion. In order to validate simulation results, a prototype of piezoelectric energy harvester has been built and tested in a laboratory environment. Furthermore, this study has been supplemented by measurements performed on a road and simulations are in good keeping with these proposed experimental tests. In view of an energy balance, small power but with a long duration harvesting has been obtained. Therefore, energy harvester may be interesting for a punctual use with a large period of electrical loading.

Hybrid piezoelectric-electromagnetic energy harvester for scavenging energy from low-frequency excitations

Capturing mechanical energy from our living environment is an effective approach for implementing self-sustained electronics. One of the key challenges is how to generate more electricity from the low-frequency and multi-directional excitations. To address this interesting issue, this paper reports a hybrid energy harvester (HEH) that consists of a piezoelectric energy harvester (PEH) and an electromagnetic energy harvester (EMEH), which can scavenge energy from both low-frequency and bi-directional excitations. The PEH is composed of two piezoelectric cantilever beams, each of which can deliver a peak power of approximately 0.13 mW when excited directly by a harmonic vibration of 0.8 g. A spherical magnet is utilized to not only trigger the PEH to function, which endows the PEH with bi-directional energy-harvesting capability, but also induce the coil to generate electricity, achieving the integration of EMEH with PEH. When the magnet is subjected to a sinusoidal excitation of 1.24 g, each beam of the PEH generates a peak power of 0.058 mW at 7 Hz and the coil outputs a peak power of 2.94 mW at 7.2 Hz. The HEH exhibits a better charging performance than the PEH or EMEH for charging a capacitor, and the fabricated HEH prototype can light up tens of light-emitting diodes (LEDs) when excited by hand-shaking vibrations.

Improving energy harvesting from random excitation by nonlinear flexible bi-stable energy harvester with a variable potential energy function

Abstract In this paper, aim at improving the performance of bi-stable energy harvester (BEH), we proposed a flexible bi-stable energy harvester (FBEH). The FBEH is composed of two elastic beams: one is the piezoelectric cantilever beam with a tip magnet and the other is the clamped-clamped beam with a mid-magnet. The dynamic behavior of FBEH was studied, and the results show that the FBEH owning a variable potential energy function is beneficial for snap-through. The governing equations of FBEH are derived by energy principles. Then its dynamic response under random excitation was studied. The results prove that the FBEH not only has a smaller threshold for snap-through, but also can generate a larger power output for the excitation intensity larger than the critical one. Validation experiments were designed and carried out. The experimental results are in good agreement with the simulation ones.

Large Deformation and Strain Gradient Fracture Analysis of Double Cantilever Beams with Piezoelectric Effect

AbstractThis paper examines the size-dependent fracture of a piezoelectric double cantilever beam (DCB) specimen based on large deformation–strain gradient theory. The governing equations with rele...

Y-type three-blade bluff body for wind energy harvesting

A three-blade bluff body for wind energy harvesting is proposed and designed. The bluff body with a Y-type cross-section is formed by three rigid thin blades and fixed at the free end of a piezoelectric cantilever beam. Simulations and experiments confirmed that this three-blade structure can achieve much higher energy output than a square prism. The output voltages of horizontal harvesters with different half-angles between the two front blades of the bluff body were measured first. The half-angle dramatically affected the performance of the energy harvester. Half-angles between 60° and 80° are found to be the optimal values for generating a high output voltage. In addition, the performance of the harvester can be enhanced when the length ratio of the rear blade to the front blade is in the range of 4/3–5/3. Interestingly, the output voltage of the vertical three-blade harvester was higher than that of the horizontal one and the optimal half-angle in this case was also between 60° and 80°.

Harvesting performance of quad-stable piezoelectric energy harvester: Modeling and experiment

Abstract To overcome the defects of bi-stable energy harvester (BEH) and improve the energy conversion ability under weak stochastic excitation, we developed a novel quad-stable energy harvester (QEH). This configuration is composed of a piezoelectric cantilever beam with a tip magnet and three external fixed magnets. By adjusting positions of the fixed magnets and altering the distances between the tip and the fixed magnets, four stable equilibrium positions (SEPs) can be realized in the static state of QEH. The diagram of potential energy illustrates that QEH has shallower and wider potential wells than BEH at the same separation distance, implying that it can execute jumping across the potential barrier easily. Validation experiment was carried out and the experimental results showed that QEH could create larger deflection and generate higher output voltage than BEH nearly over the whole range of excitation intensity. Furthermore, by controlling the gap and separation distances, the QEH can be optimized to reach the maximum output power for a certain excitation intensity.

A monostable piezoelectric energy harvester for broadband low-level excitations

This letter presents a monostable piezoelectric energy harvester (PEH) for achieving enhanced energy extraction from low-level excitations. The proposed PEH is realized by introducing symmetric magnetic attraction to a piezoelectric cantilever beam and a pair of stoppers to confine the maximum deflection of the beam. The lumped parameter model of such a system is presented and experimentally validated. Theoretical simulations and experimental measurements demonstrate that the proposed design can bring about a wider operating bandwidth and higher output voltage than the linear PEH. Under a sinusoidal vibration with an amplitude of 3 m/s2, a 54% increase in the operating bandwidth and a 253% increase in the magnitude of output power are achieved compared to its linear counterpart. Moreover, the proposed PEH exhibits rich dynamic features, including the tunable operating bandwidth, adjustable voltage and power levels, and softening hysteresis.

Self-adaptive piezoelectric ceramic vibration system based on asymmetric piezoelectric cantilever for energy harvesting

Micropower energy harvesting is one of key technologies for the micromation and practical development of wireless sensor and communication node networks. A self-adaptive piezoelectric vibration system based on modified homogeneous strain asymmetric PZT piezoelectric ceramic cantilever beam for the micropower energy harvesting was designed and prepared. A vertical cantilever was designed at the first time to obtain the homogeneous state of stress which can largely increase the power output and energy harvesting efficiency of piezoelectric cantilevers. In order to achieve the self-adaptive vibration, the asymmetric structure was adopted. Asymmetric cantilevers moved horizontally and changed the length of main cantilevers when affected by the variation in external frequency excitation, thus, the switching of resonant frequency was archived automatically without dissipating additional energy.

Scavenging energy from ultra-low frequency mechanical excitations through a bi-directional hybrid energy harvester

A bi-directional hybrid energy harvester (HEH) is presented in this paper to scavenge energy from ultra-low frequency mechanical excitations. The proposed HEH consists of two piezoelectric cantilever beams, a suspended magnet, and a set of coil. Specifically, the two piezoelectric beams work as a conventional piezoelectric energy harvester (PEH), whereas the suspended magnet and the coil constitute an electromagnetic energy harvester (EMEH). The two energy-harvesting units (PEH and EMEH), which are sensitive to excitations coming from different directions, are coupled by the suspended magnet, through which the PEH and EMEH are coherently integrated. The suspended magnet not only induces the coil to generate electricity but also actuates the PEH to work, achieving the simultaneous energy extraction from one excitation through two conversion mechanisms. The dynamic model of the HEH is established. Theoretical simulations and experimental measurements under the sinusoidal excitation indicate that the nonlinear interaction between the PEH and EMEH actuates the two energy-harvesting units to oscillate either chaotically or periodically with large amplitudes, which can improve both the PEH and the EMEH power outputs at ultra-low frequencies, not only expanding the HEH working bandwidth but also making the HEH suitable for ultra-low frequency energy harvesting. Moreover, the hand-shaking test shows that the HEH has a better charging performance than an individual energy-harvesting unit for charging a capacitor. Under the hand-shaking induced excitation, the fabricated HEH prototype can also light up tens of light-emitting diodes (LEDs), demonstrating its potential application for powering some portable electronics.