Piezoelectric Cantilever Beam Research Articles

Parametric Analysis of Nonlinear Bi-Stable Piezoelectric Energy Harvester Based on Multi-Scale Method

Given the geometric nonlinearity of the piezoelectric cantilever beam, this study establishes a distributed parameter model of the nonlinear bi-stable cantilever piezoelectric energy harvester, following the generalized Hamilton variational principle. The analytical expressions of the dynamic response were obtained for the energy harvesting system using Galerkin modal decomposition and the multi-scale method. The investigation focuses on how the performance of the energy harvesting system is influenced by the gap distance between magnets, external excited amplitude, mechanical damping ratio and external load resistance. The calculation results were compared with those obtained neglecting the geometric nonlinearity of the beam. The results show that the system responses contain jump and multiple solutions. The consideration of the geometrical nonlinearity significantly amplified the peak displacement and peak output power of the intra-well and inter-well motions. There is an evident hardening effect of the inter-well motion frequency response curve. By reasonable adjusting the parameters, it is possible to improve the output power of the piezoelectric energy harvesting system and broaden the operating frequency of the system.

Needle selector failure detection based on piezoelectric sensor and driver co-location characteristics

Aiming at the problem of the malfunction of knitting machines caused by the unstable operation of the piezoelectric needle selector during the jacquard process, a state detection scheme for the piezoelectric needle selector that integrates the sensor and drive function co-located is proposed. The motion state of bimorph piezoelectric cantilever beam and its bi-directional piezoelectric effect in the jacquard process of piezoelectric needle selector are analyzed. Electrical and dynamic models were established for the electrical characteristics inside the bimorph piezoelectric cantilever beam and the dynamic characteristics of the cutter head and baffle of the needle selector. The signal detection circuit is designed to realize the real-time detection of the piezoelectric needle selector state by analyzing the time domain and frequency domain characteristics of the electrical signal. The results show that in the normal working state of the piezoelectric needle selector, the internal electric signal of the piezoelectric driver has two characteristic frequencies, which are between 155 and 180 and between 1630 and 1670 Hz, and the time for the piece to swing to the limit position is relatively long under abnormal working conditions.

Vortex-induced piezoelectric cantilever beam vibration for ocean wave energy harvesting via airflow from the orifice of oscillation water column chamber

Micro piezoelectric generators have attracted immense interest to convert mechanical vibrations into electric energy for ultralow power wireless sensors. Herein, an ocean wave vortex-induced vibration piezoelectric energy harvester(Wavee-VIVPEH) is proposed to extract wave energy. The renewable and sustainable ocean environment energy harvesting device consists of an oscillating water column(OWC) air chamber, wind tunnel, and piezoelectric energy converter. A fixed bluff body in the vent tunnel induces airflow vortexes and excites the piezoelectric cantilever vibration converting up the ultralow frequency of ocean waves. The novel Wave-VIVPEH is a complex multi-physics system requiring feasible methodologies to enhance its performance. The theoretical models are derived to systematically investigate and optimize the operation. The flume and wind tunnel experiments and the related fluid-solid electric coupling simulations are carried out to verify the concept's feasibility. The aerodynamic kinetic performance in the OWC chamber is characterized by the models. The instantaneous maximum exhalation airspeed reaches 16.55 m/s with the air pressure of 349.97 Pa and the wave period of T = 2.5 s. In this wave condition, the results are well agreed with the simulation values of wind speed of 17.96 m/s, and air pressure of 382.55 Pa. The output power characteristics of the piezoelectric energy harvester are analyzed for the distance of the vortex wake between the piezoelectric cantilever beam and the bluff body. With the bluff body diameter of 25 mm and distance of d/dD= 4, the theoretical results on the maximum peak voltage and output power are 10.46 V, 3.26 mW agree with the simulation optimized values of the maximum peak voltage of 10.85 V and the output power of 3.55 mW. When the wind speed is 15 m/s, the theoretical voltage of 8.62 V approaches the experimental result of 8.47 V. Especially, the comparisons of the theoretical power and voltage to experimental and simulational results indicate that the ingenious Wave-VIVPEH has great potential in ocean wave energy harvesting applications to supply power for intelligent buoys.

Wind Energy Potential Ranking of Meteorological Stations of Iran and Its Energy Extraction by Piezoelectric Element

Piezoelectrics have been used in several recent works to extract energy from the environment. This study examines the average wind speed across Iran and evaluates the amount of extracted voltage from vortex-induced vibrations with the piezoelectric cantilever beam (Euler–Bernoulli beam). This study aims to compute the maximum extracted voltage from polyvinylidene fluoride piezoelectric cantilever beam at the resonance from vortex-induced vibration to supply wireless network sensors, self-powered systems, and actuators. This simulation is proposed for the first-ranked meteorological station at its mean velocity over six years (2015–2020), and the finite element method is used for this numerical computation. The wind data of 76 meteorological stations in Iran over the mentioned period at the elevation of 10 m are collected every three hours and analyzed. Based on the statistical data, it is indicated that Zabol, Siri Island, and Aligudarz stations had recorded the maximum mean wind speed over the period at 6.42, 4.73, and 4.42 m/s, respectively, and then energy harvesting at the mean wind speed of top-ranked station (Zabol) is simulated. The prevailing wind directions are also studied with WRPLOT view software, and the wind vector field of 15 top-ranked stations is plotted. For energy harvesting simulation, periodic vortex shedding behind the bluff body, known as vortex-induced vibration, is considered numerically (finite element method). The piezoelectric cantilever beam is at a millimeter-scale and has a natural frequency of 630 Hz in its mode shapes to experience resonance phenomenon, which leads to maximum extracted voltage. The maximum extracted voltages for three piezoelectric cantilever beams with the natural frequency of 630 Hz with the wind speed of 6 m/s are 1.17, 1.52, and 0.043 mV, which are suitable for remote sensing, supplying self-power electronic devices, wireless networks, actuators, charging batteries, and setting up smart homes or cities. To achieve this, several energy harvesters with various dimensions should be placed in different orientations to utilize most of the blown wind.

Vortex-based aggregation of micron particles in liquid using low-frequency vibration of a piezoelectric actuator

In this letter, we proposed a control method for microparticles aggregation by utilizing liquid vortices. The piezoelectric cantilever beam, equipped with a probe, caused fluid flow through low-frequency vibration and formed vortexes at the end of the probe to gather microparticles. The particle image velocimetry tests and the flow field simulation results revealed that the forming region of the liquid vortexes was consistent with the microparticle aggregation region. The control method proposed here has the merits of simple structures, no damage to the controlled objects and large control ranges.

Tunable Piezoelectric Vibration Energy Harvester With Supercapacitors for WSN in an Industrial Environment

This article presents the design strategy and experimental validation of a battery-free power supply for wireless sensor nodes (WSN) on an industrial study case. The power supply is based on the principle of vibration energy harvesting (VEH). The general architecture of the linear generator with electronic is presented. It is composed of commercially available components as a MIDE PPA 1014 piezoelectric cantilever beam and a LTC3588 circuit to extract and shape the electrical energy. The energy source comes from mechanical vibrations measured on the industrial environment in operation. A tunable mechanism of the resonance frequency is added in order to have a wider range of use than the natural range of a linear harvester. To adapt the VEH according with the source, it resonant frequency range can be tuned with a dedicated tip-mass. Then a fine adjustment within a range of about 20 Hz is set using both a moving clamping device and a temporarily wired electronic device working as a maximum power point finder (MPPF). To achieve a long lifetime, the storage is done using balanced supercapacitors. Two operational demonstrators are shown. The test benches as well as numerous experimental tests are presented. Shaped according to the industrial environment (49.0 Hz @ 2.7 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), the VEH is capable of delivering continuously 100mA@3.3V with 200 mA peaks. When the power harvested ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 2.9$ </tex-math></inline-formula> mW) is upper than the sensor average power, it offers the capability to store 17.5 J at 18.5 V. As a result, from this work, a WSN can successfully operate over a significantly long period of time despite fluctuations in the vibration source.

Tapered substrate thickness to enhance the performance of a piezoelectric energy harvester

In this paper, the improvement of the performance of a piezoelectric (PZ) cantilever beam using a non-uniform substrate thickness is presented. This reduces the resonant frequency, improves the stress distribution and generates more output voltage and power. Both analytical and finite-element method analyses were performed to investigate the effect of a tapered substrate thickness on a PZ cantilever beam. A tapered substrate thickness was used in rectangular and trapezoidal cantilever structures. All of the designed cantilever structures had the same fabrication area, and their performance was evaluated and compared using an excitation acceleration of 1g (9.8 m/s2). The tapered-down trapezoidal cantilever achieved a minimum resonant frequency of 62.41 Hz, which was 48.83% less than the resonant frequency of the uniform rectangular cantilever beam. The output peak voltage and average power of the proposed tapered-down trapezoidal cantilever beam were 12.36 V and 21 μW, respectively, which were improved by 44 and 74.48%, respectively, compared with those of the uniform rectangular cantilever structure.

Investigation of boundary flexibility on the performance of piezoelectric vibration energy harvesting beam systems by DTFM

The purpose of this paper is to investigate the effect of boundary flexibility on the performance of piezoelectric vibration energy harvester (PVEH) beam systems, which has not been studied comprehensively in the literature despite its importance. The coupled electromechanical equations of motion of a piezoelectric cantilever beam with a tip mass are established, with the base boundary constrained by translational and rotational springs. An exact closed-form solution of the frequency response function (FRF) of the PVEH is obtained by the distributed transfer function method (DTFM). The DTFM is a systematic powerful tool for the dynamic analysis of distributed parameter continua with non-classical boundary conditions, intermediate constraints, coupled fields, and non-proportional damping without adding much complexity to the solution formulation. Moreover, the DTFM computes the derivatives of the response, that is, the strains, which are required in the electromechanical coupling formulation, simultaneously without any differentiation. Numerical results showing the effects of boundary flexibility on energy harvesting efficiency are presented. A first-order rational function relating the boundary stiffness parameters and the harvesting efficiency is determined by nonlinear curve fitting of the calculated data. Physical insights and applicability of this analytical function for end-of-line quality check of the boundary of PVEH are discussed.

Vibration detection technology research based on piezoelectric cantilever

This paper studies the vibration detection technique based on the piezoelectric cantilever structure, and analyzes the relationship between the resonance frequency and the structure parameters. Although the output of the electrical signal is too small, it can be used to detect vibration during resonance with the maximum output voltage. A vibration testing device is designed based on piezoelectric cantilever structure, because in the vibration environment of the same frequency the vibration detection technology can obtain larger electrical signals. It can realize the automatic detection of real-time vibration state, and the vibration energy can charge the power supply through the energy storage circuit. Through the experimental method to verify relationship between the output voltage of piezoelectric cantilever beam, mass block, piezoelectric cantilever structure parameters and frequency, the experimental value of resonance frequency is very close with theoretical calculation value. The experimental resonant frequency of the designed piezoelectric cantilever beam is 16.5 Hz, which is slightly lower than the theoretical value of resonant frequency of 17.6 Hz, and the peak value of the piezoelectric output open-circuit voltage is 7.1 V.

Active vibration optimal control of piezoelectric cantilever beam with uncertainties

Considering the stiffness characteristics of piezoelectric layer, the bending stiffness of piezoelectric cantilever beam is obtained by applying the first-order shear deformation theory. The finite element model of piezoelectric cantilever beam is established by Hamilton variation principle, and the modal superposition method is employed to reduce the order of the finite element model. At the maximum strain point, the sensors/actuators are equipped in pairs. Based on the uncertain dynamic model of piezoelectric cantilever beam, the independent modal space control method based on LQR (linear quadratic regulator) control is employed for the active control of the smart beam structure, and the weighted matrices Q and R are selected according to the energy criterion. The numerical simulations and experiments verify the effectiveness of the proposed finite element model and the active vibration optimal control.

Self-powered SECE piezoelectric energy harvesting induced by shock excitations for sensor supply

The article studies the piezoelectric frequency up-converted energy harvester endowed with an SP-SECE (self-powered synchronized electric charge extraction) interface circuit. The harvester device comprises a piezoelectric cantilever beam whose tip magnet is impulsively excited by another magnet fixed on a rotating plate. Energy is therefore harvested by resonant vibration of a beam excited at certain discrete driving frequencies. Three aspects are discussed here, including the frequency up-conversion for conditionally resonant power, electrically induced damping for matching impedance and reducing power ripples, and SP-SECE’s implementation for power extraction under shock excitations. Precisely, a theoretical model based on the Fourier decomposition of magnetic force is developed for realizing the phenomenon of frequency up-conversion. The SECE electrically induced damping is derived by considering the conversion of energy to electricity in analogy to the dissipation process of a linear mechanical damper. In addition, a novel electronic breaker is implemented for reducing the switching delay effect and enhancing the range of operating voltage. Finally, two experiments are prepared for performance evaluation. The results show the good agreement between the theoretical predictions and the experimental observations. Further, the first one with parameters close to the impedance matching criterion confirms the SECE power outperforms that based on the standard interface. The second one with the SECE electrically induced damping larger than the mechanical damping, the power ripples observed in the SECE case are much more suppressed than that based on the standard interface. Thus, the properties of load-independence and low power fluctuations make the SECE-based frequency up-converted harvester superior in powering sensor nodes operated at around 2–5 volt.

Design and Optimization of Piezoelectric Cantilever Beam Vibration Energy Harvester.

Piezoelectric cantilever beams are commonly utilized to harvest energy from environmental vibrations due to their simple structures. This paper optimizes a single crystal trapezoidal hollow structure piezoelectric cantilever beam vibration energy harvester with a copper substrate to achieve high energy density at a low frequency. Finite element analysis (FEA) is adopted to optimize the size of the copper substrate at first, and the piezoelectric energy harvester (PEH) is further optimized with a trapezoidal hollow structure under the optimal size of the copper substrate. The developed PEH with a trapezoidal hollow structure (La = 20 mm, Lb = 15 mm, and Lh = 40 mm), with a copper substrate of 80 mm × 33 mm × 0.2 mm, can obtain the best output performance. Under the condition of 1 g acceleration, the resonance frequency and peak voltage output were 23.29 Hz and 40.4 V, respectively. Compared with the unhollowed PEH, the developed trapezoidal hollow structure PEH can reduce its resonant frequency by 12.18% and increase output voltage by 34.67%, while also supplying a power density of 7.24 mW/cm3. This study verified the feasibility of the optimized design through simulation and experimental comparison.

A robust resonant controller design for MEMS-based multi-layered prestressed piezoelectric cantilever beam

This paper presents the design and implementation of a robust resonant controller to damp the first resonant mode of a MEMS-based multi-layered prestressed piezoelectric (PZT) cantilever beam. The cantilever dynamics for control design are identified from experimentally measured data. The controller design is based on a mixed negative-imaginary, passivity, and a small-gain approach. Experimental results demonstrate that the designed resonant controller is able to effectively damp the first resonant mode of the cantilever, significantly reducing settling time from 528 ms to 32 ms. The controller is robust to changes in the cantilever dynamics due to the variation in residual stress in the PZT thin film or variation in driving voltage. This control design approach is useful for MEMS devices that are susceptible to residual stress variation or stress variation due to driving voltage.

Design and research of hybrid piezoelectric-electromagnetic energy harvester based on magnetic couple suction-repulsion motion and centrifugal action

In this paper, a hybrid piezoelectric-electromagnetic energy harvester (HEH) based on magnetic couple suction-repulsion motion and centrifugal action is proposed. Using a control variable approach, the effect of two variables on the output performance was investigated under different parameter conditions in order to maximize the output power. At a mounting angle of 60 degrees for the piezoelectric cantilever beam and a mass of 3.2 g for the rectangular magnet, the entire piezoelectric-electromagnetic harvester can produce 13.32 mW of power, which can successfully power low-power electronic devices such as light-emitting diodes (LEDs). The power generated by mixing piezoelectricity and electromagnetism is 1.16 times greater than the power generated by the piezoelectric generation unit alone and 70.1 times greater than the power generated by the electromagnetic generation unit alone. The composite piezoelectric-electromagnetic hybrid mechanism greatly increases the power output of the entire structure compared to the single generation mode. The suction-repulsion process is accomplished using magnetic coupling. This makes the piezoelectric cantilever beam deformed by the magnetic force and has power output. At the same time, the magnetic suction-repulsion makes the circular magnet complete cutting magnetic induction line motion at the same time, which cleverly combines piezoelectricity and electromagnetism. The form of reciprocating motion of the magnet in the coil frame using suction-repulsion is also proposed for the first time. In addition, compared with those structures that strike the piezoelectric cantilever to generate electricity, this paper uses magnetic coupling, which makes the piezoelectric cantilever beam more durable and longer in use. In summary, this structure has good prospects for application in the direction of powering wireless networks or low-power electronic devices.

Enhancing power output of piezoelectric energy harvesting by gradient auxetic structures

In this Letter, a method is proposed to increase the power output of piezoelectric energy harvesting via gradient auxetic structures. This method is validated through a gradient auxetic piezoelectric energy harvester, which combines a cantilever beam and a gradient auxetic structure. Compared with the normal uniform auxetic structure, the gradient auxetic structure can contribute to a more uniform strain distribution of the piezoelectric cantilever beam; thus, the proposed gradient auxetic energy harvester can produce higher power than the uniform auxetic energy harvester without increasing the stress concentration at the same time. Finite element simulation is performed to analyze the characteristics of the gradient auxetic energy harvester. From the experimental results, under the base excitation of 1 m/s2, the power density of the gradient auxetic energy harvester is increased by 356% and 55%, respectively, compared with the conventional plain energy harvester without auxetic structure and the uniform auxetic energy harvester.

Design and Experimental Investigation of a Rotational Piezoelectric Energy Harvester with an Offset Distance from the Rotation Center.

Rotational energy harvesting technology has attracted more and more attention recently. This paper presents a piezoelectric rotational energy harvester that can be mounted with an offset distance from the rotation center. The piezoelectric energy harvester is designed to be dynamically excited by the force due to gravity, which causes the piezoelectric cantilever beams in the harvester to vibrate periodically as the harvester rotates. A novel design of the harvester structure with a hollow mass is proposed and analyzed in this paper. Experiments were performed to investigate the design and analysis. A power output of 106~2308 μW can be achieved at the rotating frequencies of 0.79~14 Hz with a piezoelectric cantilever beam in the prototyped energy harvester. Results showed that the prototyped harvester can be mounted on a rotating wheel hub and output sufficient power in a wide frequency range for wireless monitoring sensors.

Thin-Film PZT-Based Multi-Channel Acoustic MEMS Transducer for Cochlear Implant Applications

This paper presents a multi-channel acoustic transducer that works within the audible frequency range (250-5500 Hz) and mimics the operation of the cochlea by filtering incoming sound. The transducer is composed of eight thin film piezoelectric cantilever beams with different resonance frequencies. The transducer is well suited to be implanted in middle ear cavity with an active volume of 5 mm <inline-formula> <tex-math notation="LaTeX">$\times5$ </tex-math></inline-formula> mm <inline-formula> <tex-math notation="LaTeX">$\times0.62$ </tex-math></inline-formula> mm and mass of 4.8 mg. Resonance frequencies and piezoelectric outputs of the beams are modeled with Finite Element Method (FEM). Vibration experiments showed that the transducer is capable of generating up to 139.36 mV<inline-formula> <tex-math notation="LaTeX">$_{{\mathrm {pp}}}$ </tex-math></inline-formula> under 0.1 g excitation. Test results are consistent with the FEM model on frequency (97&#x0025;) and output voltage (89&#x0025;) values. Device was further tested with acoustic excitation on an artificial tympanic membrane and flexible substrate. Under acoustic excitation, 50.7 mV<inline-formula> <tex-math notation="LaTeX">$_{{\mathrm {pp}}}$ </tex-math></inline-formula> output voltage generated under 100 dB Sound Pressure Level (SPL). Output voltages observed in acoustical and mechanical characterizations are the highest values reported to the best of our knowledge. Finally, to assess the feasibility of the transducer in daily sound levels, it was excited with a speech sample and output signal was recovered. Time-domain waveforms of the recorded and recovered signals showed close patterns.

Analysis of Output Performance of a Novel Symmetrical T-Shaped Trapezoidal Micro Piezoelectric Energy Harvester Using a PZT-5H.

In recent years, low-power wireless sensors with high flexibility, portability and computing capability have been extensively applied in areas such as military, medicine and mechanical equipment condition monitoring. In this paper, a novel symmetrical T-shaped trapezoidal micro piezoelectric energy harvester (STTM-PEH) is proposed to supply energy for wireless sensors monitoring the vibrations of mechanical equipment. Firstly, the finite element model (FEM) of the STTM-PEH is established. Secondly, the modal analysis of the T-shaped trapezoidal piezoelectric cantilever beam is carried out by finite element software and its vibration modes are obtained. Additionally, the structural characteristics of the STTM-PEH and the composition of piezoelectric patches are described. Furthermore, the effects of resistance, acceleration coefficient, substrate materials and structural parameters of the output performance of the STTM-PEH are researched. The results indicate that the output power of the STTM-PEH rises first and then falls with a change in resistance, while the output voltage does not increase as resistance increases to a certain extent. Meanwhile, selecting copper as the piezoelectric material of the T-shaped trapezoidal piezoelectric cantilever beam can generate a higher energy output. Finally, how the structural parameters, including piezoelectric patch thickness, substrate thickness and cantilever head length, affect the output performance of the STTM-PEH is studied, which illustrates that the load range of the STTM-PEH can be appropriately broadened by adjusting the length of the cantilever beam head. This research is valuable for designing a novel high performance piezoelectric energy harvester.

Simulation Analysis and Experimental Study of Piezoelectric Power Generation Device Based on Shape Memory Alloy Drive.

In order to solve the problem of waste heat collection from energy consumption, a thermal energy generation device combining shape memory alloy and piezoelectric materials has been designed. The shape memory alloy is heated and deformed to drive the drive wheel continuously, and the impact wheel is deformed against the piezoelectric cantilever beam during the rotation of the drive wheel to generate electricity. In this paper, the impact force generated by the impact wheel and the output voltage of the piezoelectric cantilever beam during the rotation process are given. Finally, the experimental test shows that the larger the radius of the drive wheel, the lower the impact force of the wheel and the lower the output voltage of the piezoelectric cantilever beam; the larger the diameter of the shape memory alloy wire, the higher the impact force of the wheel and the higher the output voltage of the piezoelectric cantilever beam; the more teeth of the drive wheel, the higher the impact frequency of the piezoelectric cantilever beam and the higher the output voltage. The maximum output voltage of the thermoelectric converter is 14.2 V, when the drive wheel radius is 13 mm, the shape memory alloy wire diameter is 1 mm and the number of impact wheel teeth is 6. The new structural design provides a new structural model for waste heat recovery and thermal energy generation technology. The new structural design provides a new approach and idea for waste heat recovery and thermal energy generation technology.

Research and analysis of an energy harvester of piezoelectric cantilever beam based on nonlinear magnetic action.

In this paper, a nonlinear piezoelectric energy harvester is developed based on rotational motion applications. It consists of the pedestal, the piezoelectric beam, the connection mass, the tip magnetic mass, the revolving host, the support frame, and the bolts. This device drives the intermittent magnetic vibration between the magnet and the tip magnetic mass to generate electric energy, avoids mechanical collision and wear, and extends the service life of the device. The working principle and vibration model of the proposed energy harvester are studied theoretically. The displacement state of the piezoelectric beam under a magnetic force is simulated and analyzed. In addition, a series of experiments verify the simulation results. With two driving magnets, 5g tip magnetic mass, and 10mm radial excitation distances, a piezoelectric energy harvester can capture energy efficiently. The results demonstrate that the piezoelectric energy harvester produces four resonance frequencies of 4, 11, 15, and 19Hz. When the rotation frequency is 4Hz, the maximum open-circuit voltage of the piezoelectric energy harvester is 96.87V. The piezoelectric energy harvester gets the maximum average power of 8.97 mW when the external resistance is 300 kΩ. At this time, the voltage across the resistance is 51.87V.