Piezoelectric Cantilever Research Articles

A multi-stable ultra-low frequency energy harvester using a nonlinear pendulum and piezoelectric transduction for self-powered sensing

This paper presents the design, theoretical modelling and experimental validation of a quad-stable energy harvester for harnessing ultra-low frequency random motions using a nonlinear pendulum and piezoelectric transduction. The multi-stable pendulum is created by the magnetic forces between magnets on the pendulum and a tip magnet on a piezoelectric cantilever beam. Two attractive and one repulsive magnetic forces in combination with the gravitational force of the pendulum create multiple stable positions for the pendulum. The multi-stable dynamics allow the pendulum to effectively convert low-frequency random kinetic motions from the host, e.g. human motion or wind turbine tower oscillation into the pendulum oscillation, enabling effective plucking of the piezoelectric beam with enhanced output power. A theoretical model, including the magnetic interaction, piezoelectric conversion and pendulum dynamics, is established to describe the electromechanical dynamics of the whole harvester. A prototype is fabricated and tested on a linear shaker at ultra-low frequencies (1–3 Hz) to showcase the capability of the harvester and to validate the theoretical results. Around 8 μW Root-Mean-Square output power was obtained at 2.5 Hz and 0.8 g of excitation. Using the experimentally validated theoretical model, a parametric study was carried out to examine the influence of different structural and operating parameters, such as pendulum mass and length, magnetic coupling strength, excitation frequency and amplitude, on the output power and operating frequency range of the energy harvester. The operation frequency range and output power can be effectively adjusted by changing the above-mentioned parameters. The self-powered sensing capability is then illustrated by integrating the harvester with an off-the-shelf power management circuit and a 22 μF storage capacitor. The capacitor was charged from 2.8 V to 4 V in 90 s, showing its capability of implementing battery-free wireless sensing for different Internet of Things (IoT) applications.

Two-Dimensional Omnidirectional Wind Energy Harvester with a Cylindrical Piezoelectric Composite Cantilever.

To improve the response-ability of the energy harvester to multidirectional wind, this paper proposes a wind energy harvester to scavenge wind-induced vibration energy. The harvester comprises a cylindrical beam instead of conventional thin rectangular cantilevers, a bluff body (square prism or circle cylinder), and a piezoelectric tube bonded to the bottom side of the beam for energy conversion. Benefiting from the symmetry of the cylindrical structure, this harvester can respond to airflow from every direction of the two-dimensional plane. The performance of the harvester under a wind speed range of 1.5-8 m/s has been tested. The results demonstrate that the proposed harvester can respond to the wind from all directions of the two-dimensional plane. It provides a direction for the future in-depth study of multidirectional wind energy harvesting.

On the design of piezoelectric MEMS scanning mirror for large reflection area and wide scan angle

This study designs and implements the piezoelectric MEMS scanning mirror with large scan angle and reflection area for light beam manipulating applications. In this design, the scanning mirror has a large mirror plate (3 mm in diameter) supported by two T-shape torsional springs. The U-shape piezoelectric cantilever acts as the actuator to drive the scanning mirror through the transmission spring. The analytical model is established to provide the design guideline of transmission spring to increase the scan angle. In application, the proposed designs are fabricated on the SOI (silicon on insulator) wafer deposited with the PZT film. Measurements indicate the fabricated mirror could reach an optical scan angle of 140-degree (mechanical scan angle of ±35-degree) when driving at its resonant frequency of 1.5 kHz with a unipolar driving voltage of 42 V. Moreover, no vacuum environment is required for the presented scanning mirror to achieve the above scan angle. This is an extremely large optical scan angle for the MEMS scanner with a mirror plate of 3 mm in diameter. In addition, another U-shape piezoelectric cantilever serves as the position sensor to detect the scan angle of mirror plate. The sensing signals show good linearity with the scan angles and can be exploited as the feedback control. Measurements also demonstrate that the micro scanner could withstand 1500 g shock loading, and the deviation of scan angle is less than 10% after the cycling test under 10 V pp resonant driving in 95%RH and room temperature for 0.2 billion cycles.

Modeling and Adaptive Parameter Estimation for a Piezoelectric Cantilever Beam

This paper proposes a new adaptive estimation approach to online estimate the model parameters of a piezoelectric cantilever beam. The beam behavior is firstly modeled using partial differential equations (PDE) considering the Kelvin-Voigt damping. To facilitate the estimation of unknown model parameters, the Galerkin’s method is introduced to extract desired vibration modes by separating the time and space variables of the PDE. Then, considering two major vibration modes, the corresponding system model can be represented by a fourth-order ordinary differential equation (ODE). Finally, by using measured input and output information, a novel adaptive parameter estimation strategy is introduced to estimate the unknown parameters of the derived ODE model in real time. For the purpose of driving the parameter updating law, the estimation error is extracted by using an auxiliary variable and a time-varying gain. Consequently, the convergence of the parameter estimation error is rigorously proved based on the Lyapunov theory. Simulations and experimental results show the validity and practicability of the proposed estimation method.

Broadband Piezoelectric Energy Harvester Based on Coupling Resonance Frequency Tuning.

The bandwidth of piezoelectric energy harvesters (PEHs) can be broadened by resonance-based frequency tuning approaches, including mechanical tuning and electrical tuning. In this work, a new coupling tuning mechanism for regulating the near-open-circuit resonance frequency by changing the effective electrode coverage (EEC) is presented. A linear model of a bimorph piezoelectric cantilever with segmented electrodes is used to evaluate the power harvesting behavior near the open-circuit resonance frequency when EEC changes from 0 to 100%. According to the theoretical analysis, it is found that the variation of EEC brings about the change in coupling strength, which is positively associated with the near-open-circuit resonance frequency of PEH. Two cantilever PEHs with segmented electrodes based on PZT and PZT-PT are constructed for validation of the coupling tuning mechanism. The analytical and experimental results illustrate remarkable improvements in both bandwidth and average power through the coupling resonance frequency tuning method. In addition, adopting extraordinary piezoelectric single crystals and optimizing the proof mass and piezoelectric layer dimensions were theoretically shown to be effective methods for further improvement of bandwidth.

Modeling of a Porous Piezoelectric Nano Energy Harvester Based on Timoshenko-Beam Theory

Collecting electric power from the vibration of piezoelectric beams is practical and has been widely used for decades. This paper investigates a porous piezoelectric cantilever Timoshenko-beam energy harvester at nanoscale. The aim is to propose an optimized Timoshenko beam in order to gain more power with the same working conditions. For this purpose, the width of the beam is assumed to be exponentially changing and pores are also introduced into the beam to relieve the inherent brittleness of piezoelectric materials. Based on Timoshenko beam theory and porous piezoelectric elasticity, the uncoupled motion equations of the porous piezoelectric nanoTimoshenko beam are deduced. The analytical solutions to the output voltage and power density are obtained. According to the numerical calculation, it can be concluded that the electrical output can be improved by increasing the section parameter. Moreover, the surface effects and pore properties on the energy harvesting characteristics are discussed. In addition, when there is a concentrated mass at the free end of the beam, the displacements and output power are studied.

Градиентная модель изгиба неоднородной пьезоэлектрической балки

The problem of bending a horizontally inhomogeneous piezoelectric cantilever beam is studied taking into account scale effects. The lower and upper surfaces of the beam are electroplated. Three types of loading are considered: load uniformly distributed along the length; transverse force at the other end of the beam; supply of electric potential to the upper electrode. The beam bending is modeled based on the Euler-Bernoulli hypotheses and the quadratic distribution of the electric potential. Based on the application of the variational principle of gradient electroelasticity, a system of differential equations of bending and electrostatics is obtained, as well as an extended range of boundary conditions. To find the bending moment and deflection of the middle line of a homogeneous beam, exact analytical expressions are obtained. In the case of an inhomogeneous beam at large values of the scale parameter, the solution is based on the shooting method. On specific examples, the calculations of moments and deflection are carried out, both in the case of a homogeneous and inhomogeneous beam. The influence of the mechanical and electrostatic gradient parameters, the electromechanical coupling coefficient, and the inhomogeneity parameter on the distribution of deflections has been clarified.

Production of piezoelectric cantilever using MEMS-based layered manufacturing technology

Piezoelectric cantilever is widely preferred in many fields due to its small size, simple and perfect design, easy control process, easy integration with integrated circuits. The tip displacement is the most important character of piezoelectric cantilever and many models have been used for characterization. These models are only suitable for piezoelectric cantilever structures of the same length and layer thickness. In this study, a new model is proposed to estimate the tip displacement of a micro-electro-mechanical system (MEMS) based piezoelectric cantilever with layers of different lengths and thicknesses. Modeling was carried out in COMSOL Multiphysics software in 3D format with reference to the bimorph structure. The fabrication of the piezoelectric cantilever was made by Stereolithography (SLA), which is one of the additive manufacturing methods. Theoretical, simulated and real-time experiments were carried out to measure the tip displacement of the piezoelectric cantilever. An electrical characterization experiment was set up to measure tip displacement under constant voltage of the cantilever in real-time experiments. This setup includes an optical microscope and digital camera to observe displacements in the probe station. As a result of the characterization, it was found that the cantilever produced a maximum 14.98 µm tip displacement of 900 µm length, 225 µm width and 40 µm thickness under 10 V voltage. In addition, it has been determined that the tip displacement of the piezoelectric cantilever is directly proportional to the length and inversely proportional to the layer thickness. The results show that the model is in good agreement with the finite element method (FEM) simulation, theoretical and experimental measurements.

Improving energy harvesting by nonlinear dual-beam energy harvester with an annular potential energy function

In this paper, we develop a nonlinear dual-beam energy harvester for broadband energy harvesting. Two identical piezoelectric cantilevers are placed orthogonal to each other and coupled by repulsive magnetic force. Analytical and experimental studies indicate that the combination of the resonant motions of the two beams yields an annular potential energy function, where the oscillator can circumambulate around the potential barrier. The advantages of the design concerning a conventional bistable piezoelectric cantilever were examined. It is proved that the proposed harvester has a bandwidth of 3.4 Hz and a voltage output performance 298.7% better than that of a bistable one under excitations of 0.5 g.

Research on a novel non-linear magnetically coupled piezoelectric self-powered mouse

Based on the charging problem of wireless mouse, a magnetically coupled piezoelectric self-powered mouse is proposed in this paper. The piezoelectric self-powered mouse innovatively combines piezoelectric technology and scroll wheel structure into one. Moreover, the coupling in the structure deforms the piezoelectric element by magnetic force, avoiding damage to the piezoelectric element by direct contact. The introduction of non-linear forces improves the energy harvesting efficiency of the energy harvester. The distance between the piezoelectric cantilever beam and the rollers, and the number of magnets on the rollers are used as the study variables in this experiment. At a speed of 550 r/min, when the distance between the magnet attached to the free end of the piezoelectric cantilever beam and the mouse wheel is 17 mm and the number of magnets on the wheel is 4, the whole piezoelectric energy harvesting device has the maximum peak-to-peak voltage generated is 25.15 V. Through the design of the cantilever beam, greater deflection can be produced under the conditions of external force and size determination. The design of the structure is highly compatible with the actual mouse structure, which provides a great possibility to further combine the piezoelectric element with the mouse structure.

Statistical linearization for random vibration energy harvesting with piezoelectric material nonlinearity

Due to piezoelectric softening and dissipative nonlinearities, the piezoelectric cantilever energy harvester exhibits nonlinear hysteresis when subjected to large excitation. These nonlinearities have brought significant challenges to the modeling and response prediction of randomly excited piezoelectric energy harvesting systems. In this study, the voltage responses of the nonlinear piezoelectric cantilever energy harvester under random excitation are initially assumed to follow the Gaussian distribution which is experimentally validated later. The equivalent linear transfer function are derived from the approximate linearization of the stiffness and damping using the statistical linearization (SL) technique. The mathematical expectations of the voltage responses are calculated from the multivariate normal distributions. Frequency sweep experiments are conducted to a cantilever energy harvester to identify the nonlinear piezoelectric material properties. The statistically linearized model was experimentally validated under random base acceleration excitation by comparing the probability density function of the predicted voltage responses and average power against the experimental measurements. The advantage of the SL technique lies in allowing one to use an iterative procedure to estimate the equivalent linear terms while the analytical expressions are unattainable because of the complex nonlinearity in the governing equations. The results show that the prediction of the SL model to the random base acceleration excitation agrees with experimental measurements with a broadband frequency range, although only the fundamental mode of the beam is considered.

Study on a Base-galloping Hybrid Excitation Piezoelectric Vibration Energy Harvester

Vibration response and performance of a piezoelectric energy harvester under the hybrid excitation of base vibration and galloping is studied. Based on the Euler-Bernoulli beam theory, the distributed-parameter model of a piezoelectric cantilever beam with base and galloping hybrid excitation is derived. Subsequently, the electromechanical coupled reduced order model and the decoupling model of the system is obtained. Thereafter, the analytical solution of the vibration response and the coupling relationship between the two hybrid excitations are analyzed. In the end, the impacts of the load resistance, the excitation acceleration and the wind speed on the power generation performance of the system are examined. Results indicated that the hybrid excitation can not only increase the energy harvester power of the system by 2.4W, but also effectively broaden the frequency band compared with the single foundation excitation. The research result is helpful to the dynamic design of a piezoelectric vibration energy harvesters under hybrid vibration excitation.

A single-degree-of-freedom mathematical model for energy harvesting from cavity flow oscillations

Flow-induced vibrations have proven to be a valuable power source for wireless sensors and MEMS devices. In this study, the energy harvesting aspects of an open cavity flow is explored and modelled as a single-degree-of-freedom system. Experiments with flow over a cavity of length-to-depth ratio of 3, with an incoming velocity of 30 m/s was taken as a case study to validate the model. It was observed in experiments that three distinct flow oscillation frequencies of significant amplitudes, corresponding to the different modes of oscillation were generated. To harvest this oscillatory power, a piezoelectric cantilever beam, mounted on the aft wall was subjected to unsteady pressure forces. To harvest efficiently, the natural frequency of the cantilever beam was tuned to lock in with the flow oscillation frequencies. The frequencies of cavity oscillations agreed well with Rossiter’s model in the experiments. A single-degree-of-freedom system assuming lumped parameters was used for modelling. The forcing term was described using a periodic function that uses empirical values for amplitude. The model was able to predict the overall trend and values of the average power and RMS voltage generated across a resistor load with reasonable accuracy. Using the model, the effects of cavity length, incoming velocity and resonant frequency were also studied.

Design and analysis of piezoelectric energy harvester for laser pointer

Obtaining energy from human body activities to power electronic equipment has broad application prospects. In this study, a piezoelectric energy harvesting system is designed to harvest energy from human finger rapping. The harvested energy can drive a laser lamp group to operate. The piezoelectric energy harvester uses a piezoelectric cantilever beam with a spring-mass block at the free end to obtain the kinetic energy of the finger operating a laser pen. The structure can produce considerable bending deformation under finger movement. At the same time, a dual-input synchronized switch harvesting on inductor circuit is designed to extract the charge generated by the piezoelectric beam when the spring-mass block at the free end is rapped and store it in the energy storage element. The charge and discharge of the energy storage element are controlled by a DC-DC management circuit. Experimental results show that the average harvesting power of the piezoelectric energy acquisition system is 169 μW, and its power density is 388.5 μW/cm3. When the spring-mass block is rapped for 8 s, the energy generated by the piezoelectric energy harvester lights the laser pen for 0.35 s.

Developing Ball Pulse Generator in Piezoelectric Transduction Designed on Wireless Sensing Devices

Progressing Ball pulse generator through piezoelectric transduction is designated in this paper directed on wireless recognizing procedures. A silver rolling ball is stimulated popular the original through method of an inertial proof mass motivated finished outside waves at random low frequency. Winning development of the metallic resistant mass, magnetic construction can be extended near motivate the piezoelectric cantilever finished awarding tip magnets near the acceptable completion. Prevalent accretion, self-synchronous switching is achieved via relating electrodes toward the path of the developing ball. An unique passive prebiasing instrument is familiar toward advance the presentation of the pulse producer. Together simulation also new results continued showed near determine the expansion. Experimental results rally supplementary energy container remains impassive through the prebias instrument associated near the impartial occasion. A announcement circuit founded decided a Colpitts oscillator stayed constructed toward examination the presentation of the capacitor-powered oscillator which remains calculated in way of the load of the pulse generator. Through addition a voltage regulator element, the transmission circuit is accomplished of software design an instrument signal via frequency intonation which controls the possibility of affecting a developing ball wireless sensing original founded decided the piezoelectric pulse generator.

Experimental and simulation research on the difference in motion technology levels based on nonlinear characteristics

Abstract Wearable and movable lodged health monitoring gadgets, micro-sensors, human system locating gadgets, and other gadgets started to appear as low-power communication mechanisms and microelectronics mechanisms grew in popularity. More people are interested in energy capture technology, which turns the energy created by motion technology into electric energy. To understand the difference in motor skill levels, a nonlinear feature-oriented method was proposed. A bi-stable magnetic-coupled piezoelectric cantilever was designed to detect the horizontal difference of motion technology. The horizontal difference was increased by the acceleration generated by the oscillation of the leg and the impression betwixt the leg and the ground during the movement. Based on the Hamiltonian principle and motion technique signal, a nonlinear dynamic model for energy capture in motion technique is established. According to the shaking features of human leg motion, a moveable nonlinear shaking energy-gaining system was the layout, which realized the dynamic characteristics of straight, nonlinear, mono-stable, and bi-stable. The experimental outcome shows that nonlinearity can effectively detect the difference of motion techniques. The experimental results of different human movement states confirm the benefits of the uncertain bi-stable human power capture mechanism and the effectiveness of the electromechanical combining design established. The nonlinear mono-stable beam moves in the same way as the straight mono-stable beam in the assessment, but owing to its higher stiffness, its frequency concentration range (13.85 Hz) is moved to the right compared to the linear mono-stable beam, and the displacement of the cantilever beam is reduced. If the velocity is 8 km/h, the mean energy of the bi-stable method extends to the utmost value of 23.2 μW. It is proved that the nonlinear method can understand the difference in the level of motion technique effectively.

Impact-driven frequency-up converter based on high flexibility quasi-concertina spring for vibration energy harvesting

In this paper, an impact-driven frequency-up converter for low-frequency vibration energy harvesting is proposed and investigated. Low-frequency vibration presents a significant challenge in vibration energy harvesting, and frequency-up conversion is one of several techniques used to tackle this concern. The proposed design is based on a high-flexibility Quasi-Concertina (QC)-based structure with a resonant frequency of ∼25 Hz, along with high-frequency piezoelectric cantilevers of a resonant frequency of ∼250 Hz. The mathematical model describing the operating sequence of the frequency-up conversion approach was initially developed. Experimental studies of the manufactured device were also conducted to validate the concept and to evaluate the performance and efficiency of the system under different frequencies, accelerations, and gaps between the QC structure and the piezoelectric cantilevers. The system achieved a peak voltage of 10 V (RMS voltage of 3.40 V) when subjected to vibrations of 2 g@25.5 Hz for an air gap of 2 mm. We also explored the possibility of using four piezoelectric cantilevers. Theoretically, the peak voltage dropped to 16 V; however, the RMS voltage increased to 8.44 V due to the slow damping of the generated output signal. The bandwidth was equal to 24–28 Hz for an acceleration of 1.8 g and 25–27.5 Hz for 1.4 g.

Energy harvester using two-phase flow conditions

Single-phase flow-induced vibration energy harvesting approaches, such as vortex-induced vibration, galloping, and flutter, have received considerable attention from researchers in recent years. However, the challenges and potential applications of multi-phase flow-induced vibration energy harvesting have rarely been explored. To bridge the research gap in the present energy harvesting studies based on two-phase flow, we investigated in detail the mechanism and potential benefits of the fluid–structure interaction between smart structures and two fluid phases (water and air) on the vibration energy harvesting performance. A piezoelectric energy harvester using air–water two-phase flow conditions is proposed for potential multifunctional applications. A T-shaped piezoelectric cantilever was used to harvest liquid sloshing energy in the proposed structure. A fluid–structure interaction containing two fluid phases (water and air) was theoretically modelled using the arbitrary Lagrangian-Eulerian technique. The experimental results showed that a prototype of the proposed structure can be used as a smart water bottle that simultaneously performs human-motion energy collection and acts as a drinking water bottle. The prototype achieved its maximum peak-to-peak voltage value (12.08 V) at 5 km/h for powering wireless IoT (Internet of Things) nodes. Furthermore, it can be used as an energy regenerative shock absorber to perform the dual functions of vibration damping and energy harvesting. Therefore, multi-phase flow-induced vibration energy harvesting shows great application potentials.

Performance Evaluation of Novel Piezoelectric Cantilever Beam Structure for Energy Harvesting

This study proposes an elastic compact Piezoelectric energy harvester (PEH) in multiple configurations, including a single cantilever beam, a single cantilever beam with a hole, two cantilever beams with a hole contributing towards a wider operating bandwidth. The cantilever beams are designed in multiple structural forms and section shapes, including symmetrical uniform section rectangle frames. Natural frequencies, vibration modes, and output voltages of PEH are estimated using Finite element software, with the frame acting as a rigid body and the cantilever plate acting as a deformed structure. A PEH with a rectangular cantilever plate surrounded by a rigid frame is designed and attached to the vibration platform with a customized fixture in the simulation software. The design meets the requirements of natural frequency and high output voltage in the low-frequency band. The PEH structure is simulated using a variety of piezoelectric materials, primarily PZT4 and PZT5H, barium titanate, lithium niobate, zinc oxide, and polyvinylidene difluoride (PVDF) using the finite element method. In the structural configuration of two cantilever beams with holes, PEH exhibited the maximum output voltage of 32.832 V for Zinc oxide compared to other materials. So, it can be concluded that insertion of hole and variation in the geometry of cantilever structure along with frame plays a vital role in achieving a large voltage from the vibrations in PEH. HIGHLIGHTS The finite element approach was used to develop and simulate the cantilever-based piezoelectric energy harvesting structure Multiple elastic compact Piezoelectric energy harvester (PEH) designs, including a single cantilever plate, a single cantilever plate with a hole, and two cantilever plates with a hole, are simulated using different materials The frame, hole insertion, and geometry modification of the cantilever structure all play important roles in generating a substantial voltage from the vibrations in PEH This study presents an Eigen frequency analysis of different PEH structures GRAPHICAL ABSTRACT

An accurate dew point sensor based on MEMS piezoelectric resonator and piecewise fitting method

Dew point sensors are widely used in various fields to provide accurate data of absolute humidity. In this paper, the dew point sensors based on MEMS piezoelectric circular resonator and cantilever are designed and fabricated. The previously reported MEMS dew point sensors suffer unavoidable errors by regarding dew point as the temperature corresponding to the maximum resonant frequency during cooling. Here, a piecewise function fitting dew point identification method is proposed, which considers the influence of relative humidity on resonant frequency and can detect dew point with small error. The results show that the piezoelectric resonant dew point sensor has good accuracy and stability, and the maximum relative error of the dew point is 0.30 °C DP. The proposed dew point sensors and method for identifying dew point have great potential in practices.