Piezoelectric Cantilever Beam Research Articles

Investigation on battery-less voltage of piezoelectric V-shape cantilever beam energy harvester using FEA method for pacemaker

AbstractThis paper presents an investigation on a battery-less voltage of Piezoelectric (PZT) V-shape cantilever beam Energy Harvester (EH) using human body vibration. The frequency ranges are walking (0–5 Hz), running (6–10 Hz) and motions (11–15 Hz) for human movement. Pacemaker devices typically require a lower resonant frequency with higher voltage which is powered by batteries. The battery has a limited duration during its working process and the battery is difficult to replace in the human body. To address the aforementioned issue, a V-shape cantilever beam EH has been developed as a solution to overcome these limitations. The cantilever beam was designed in COMSOL Multiphysics software 5.5 version using the Finite Element Analysis (FEA) method for experimental investigations followed by three categories of frequency ranges of the human body. The simulation results showed that the generated battery-less higher voltage was 269 mV (AC) at the resonant frequency of 14.37 Hz in the motion range of 11–15 Hz. Later, an Ultra Low Power (ULP) electronic circuits will be designed and simulated in the LTSPICE software to convert and boost-up from 269 mV (AC) to DC voltage attained. The estimated output power of the energy harvester system can be powered up (4.7 µW) for modern pacemaker applications.

Equivalent damping coefficient of a bistable piezoelectric cantilever beam energy harvester via experimental-analytical balanced energy method

This study shed light on the simultaneous effects of bistability and electrical resistor on the equivalent damping of a piezoelectric cantilever beam energy harvester. Damping coefficient has a direct effect on the frequency bandwidth of an oscillating system. This paper, extends the experimental-analytical balanced energy (BE) method to obtain the damping change due to bistability of a piezoelectric energy harvester. By using extended Hamilton principle and Euler-Lagrange formulation with nonlinear magnetic field relations, the governing equations of the system are derived. Then the equivalent BE viscous damping model was adopted and the equivalent damping term is achieved. In BE method, the test signals are registered into the proposed BE algorithm, then the equivalent viscous damping coefficient of the system will be obtained. In the end, the effects of bistability and electrical resistor of the power circuit of piezoelectric patch is discussed. According to the results, by increasing the bistability of the system, the equivalent damping of the system will also increase. Besides by escalation the value of electrical load in piezoelectric power circuit, the value of the equivalent damping coefficient reaches a maximum value. This behavior is originated from the extracted power of the system.

Hybrid piezo-triboelectric wind energy harvesting mechanism with flag-dragging the cantilever beam vibration

Hybrid power generators will improve the extraction of electrical energy from the wind to develop sustainable and eco-friendly self-powered wireless sensors. A novel piezo-triboelectric flag wind energy harvesting nanogenerator (P-FTENG) is proposed that consists of a piezoelectric cantilever beam and a triboelectric flag. The flag flutters in the wind, inducing vibration in the cantilever beam, thereby converting wind energy into electrical power with piezo and triboelectric effects. Based on the aerodynamic mechanism, a nonlinear flutter theoretical model is derived to evaluate the drag force and pressure of fluid separation on the piezo-triboelectric structure. Furthermore, this paper comprehensively elaborates on the transverse motion of the flag flutter caused by the airflow. The force from the transverse motion excites the cantilever beam. The power output of P-FTENG generation depends on various factors. The optimized flag-shaped configuration may activate the piezoelectric cantilever beam vibration and decrease the crucial flutter wind speed, according to test results. P-FTENG generates a voltage of around 17.8 V when the wind speed is 8.5 m/s. The cantilever beam energy harvester's PEH reaches 32 mW/m2, while Flag-TENG's output power density reaches 37 μW/m2, which charges capacitors and lights the array of LEDs. The hybrid piezo-triboelectric flag nanogenerator fluttering in the wind is promising for powering the function of a calculator or electronic thermometer/hygrometer sensor.

A Piezoelectric Electromagnetic Composite Energy Harvester for Collecting Pedestrian Walking Energy

A piezoelectric‐electromagnetic composite energy harvester (PECEH) has been designed, to mainly study the relationship between the length and angle of piezoelectric cantilever beams and their power generation performance, and the analysis of dynamic models in magnetic levitation systems and the impact of magnet size on power generation performance. In this device, piezoelectric energy harvester (PEH) and electromagnetic harvester (EMH) are used as powered and sensing, respectively. The PEH collects vibration to generate electricity and supplies energy to the EMH, which then transmits the wireless signal. EMH adopts a magnetic levitation device with higher sensitivity, while PEH uses a direct contact strike piezoelectric plate to increase power generation. The paddles are made of flexible materials, which increase the durability of the device. The prototype was tested at different excitation frequencies. Research has shown that at a frequency of 1.4 Hz, the optimal voltage and power are 126.28, 4.04 V, and 4.9 mW and 0.57 μW. 60 light emitting diode can be lit when pedestrians are walking. Therefore, PECEH can be used to collect the vibration energy of pedestrians while walking, providing power to sensors and microstructure.

Active disturbance rejection control for piezoelectric cantilever beam with time delay

This Letter presents an active control method for the vibration of piezoelectric structures. First, a controller based on nonlinear extended state observer is designed to improve the disturbance rejection capability of the vibration structure. Additionally, an improved nonlinear active disturbance rejection control (IMNADRC) method is combined with Smith predictor for time delay compensation, resulting in Smith predictor-based IMNADRC. Finally, numerical simulations and experiments are carried out for active vibration suppression of piezoelectric beam under fixed harmonic excitation and variable harmonic excitation, respectively. The results show that the proposed method has good control effect on structural vibration suppression and is highly adaptable to various external excitations.

Harvesting vibration energy by quad-stable piezoelectric cantilever beam: Modeling, fabrication and testing

The combination of beams with piezoelectric patches has become a prevalent energy harvesting tool due to its ease of use. Typical energy harvesting systems are usually linear, and their efficiency is not satisfying due to low-frequency bandwidth. In this paper, a quad-stable piezoelectric vibration energy harvester is analyzed both numerically and experimentally. The primary purpose of this investigation is to analyze the static and dynamic characteristics of a proposed quad-stable system to consider its potential for application in broadband energy harvesting comprehensively. The harvester system consists of a slotted cantilever beam, a piezoelectric patch, a pair of tip-mass blocks, and a double-sided clip. The cantilever beam is subjected to pre-displacement constraints made by a mutual self-constraint at the free end of it. The nonlinear behaviors of the harvester system, including snap-through and softening phenomena, are analyzed using the assumed modes and finite element method (FEM). The harvester's vibration equation is solved numerically and through an FE model which is made by an in-house finite element software. A prototype is designed and fabricated to validate the mathematical model and FE simulation. The experimental force-displacement diagram of the harvester displays distinct discontinuities, reflecting abrupt transitions occurring while switching its stable states. The prototype dynamics are analyzed by harmonic base excitation with different amplitude levels in two conditions, including the presence and absence of the piezoelectric patch. The results obtained from the mathematical and FEM model demonstrate a satisfactory correlation with the experimental data. Furthermore, the experimental data reveal the occurrence of the snap-through phenomenon, accompanied by a significant widening of the frequency bandwidth at relatively high amplitude levels. The system has the ability to provide an average output electrical power of 0.288 mW for an electrical resistance of 3.262 kΩ at the excitation frequency of 12.695 Hz and base acceleration amplitude of 3g.

A piezoelectric cantilever-beam-spring-pendulum oscillator for multi-directional vibration energy harvesting

Harvesting energy from environmental vibrations holds significance for powering wireless sensors and transducers. However, the current vibration energy harvesting methods still have room for improvement, especially in the field of low-frequency vibration, where the performance of output voltage is relatively insufficient. This paper proposes a novel piezoelectric energy harvester consisting of a piezoelectric cantilever beam and a spring pendulum in order to address this challenge. Under external excitation, energy exchange is generated between the internal parts of the system, so that the swinging of the pendulum is interchanged with the extension and contraction motion of the spring and the bending motion of the cantilever beam to realize multidirectional energy harvesting. Firstly, the energy equation of system is obtained and the dynamics model of system is derived based on Lagrange's theorem. In addition, the response characteristics of system under harmonic excitation and the effects of different parameters on the system performance are investigated by simulation. With proper parameter selection, the system can produce higher output voltages. Compared to a piezoelectric cantilever-single-pendulum, the proposed structure demonstrates superior performance, especially in low-frequency vibration. The maximum voltage amplitudes in the x- and z-directions were 106.6% and 187.3% of those of the piezoelectric cantilever-single-pendulum, respectively. This paper proves the superior energy harvesting performance of the proposed structure.

Powering piezoelectric frequency up-converter with rotary magnetic forces for torque-sensing application

A piezoelectric frequency up-energy harvester (PFU-EH) utilizing an SECE circuit (synchronized electric charge extraction) is developed for torque-sensing application in rotating machinery. Development of an explicit theoretical model for the system with the PFU-EH, considering phase angle shifts and magnetic impulsive forces is proposed to formulate the frequency response equations for voltage and power outputs using Fourier analysis. In this study, harvesting electrical energy can be achieved through the magnetic force interaction between the cantilevered piezoelectric beam, which carries two attached magnets, and the compound rotating disk structure, also carrying two attached magnets. The compound rotating disk structure, composed of a metal ring (outer disk) and a flywheel (inner disk) connected by a spring system, can create a phase angle caused by an applied load. As a result, mechanical torque is formed for inducing magnetic excitation to the PFU-EH and subsequently generating an AC voltage signal. The functionality of the AC voltage harvested by the PFU-EH can be further leveraged for two primary benefits. First, it can be converted into DC voltage output using the SECE circuit, enhancing the effectiveness of the electric signal without requiring load matching under different modal vibrations. Second, the SECE harvesting voltage can simultaneously function as a sensing signal for detecting mechanical torque itself. The sensing signal detection process is further analyzed by applying feature extraction from the spectrogram and utilizing a 2D-CNN for auxiliary segment identification. Finally, the experimental results demonstrate reasonable agreement with the predicted outcomes.

Self-weight utilization harvester oriented to low-frequency gait for human health monitoring and assistive training

The mechanical energy generated during human daily activities holds the potential as a viable energy source for health monitoring and assistive devices. However, the vibrational energy generated from human walking is difficult to harvest due to the characteristics of low-frequency, especially considering the exemption of the additional walking burden. This work introduces an energy harvesting system incorporating an innovative spiral-spring and flywheel combination based on self-weight utilization strategy, alongside an excitation matching methodology to achieve efficient energy conversion. By utilizing a smart plucking structure with a piezoelectric cantilever beam to match the excitation displacement and force with the locomotion in the leg-stretching phase. The system can obtain a power output of 38.07mW, and 58.62mW at walking speeds of 1.0 m/s, and 3.0 m/s without imposing additional burden on the human by self-weight utilization strategy. Moreover, it can provide assistive force for gait movement due to the unique plucking structure realizing asymmetric loading style. The system showcases its potential as a lightweight, cost-effective, and ergonomic solution for the needs of adults requiring assistive training and health monitoring.

Enhanced energy harvesting from random excitations: A dynamic amplifier-augmented hybrid bistable piezoelectric energy harvester

In the energy harvesting field, it is critical to efficiently convert ambient vibrations into usable electrical energy, especially under conditions characterized by low amplitude and random excitations. This study introduces a novel hybrid bistable piezoelectric energy harvester (HBPEH) designed to optimize energy conversion in challenging environmental conditions. The HBPEH features a unique piezoelectric cantilever beam integrated with a dynamic amplifier at the fixed end, significantly enhancing both rotational and lateral displacements of the beam. This innovation lowers the threshold for snap-through events, crucial for maximizing energy transfer in bistable systems, and enables superior energy harvesting capabilities. Furthermore, the HBPEH demonstrates significantly higher power outputs when subjected to excitation intensities beyond critical levels, outperforming conventional energy harvesters. Extensive numerical and theoretical analyses confirm that the HBPEH offers a promising solution for applications hindered by suboptimal energy conversion rates. Its ability to operate effectively under diverse and unpredictable excitation conditions underscores the HBPEH's robustness and superiority in advanced energy harvesting scenarios. The design improvements introduced in this study highlight the potential of the HBPEH to transform energy harvesting approaches. By addressing the limitations of traditional harvesters, the HBPEH provides enhanced efficiency and reliability, making it suitable for a broader range of practical applications in variable environmental conditions.

A novel asymmetric tri-stable piezoelectric vibration energy harvester for low-orbit vibration energy harvesting enhancement

This study introduces an innovative asymmetric tri-stable piezoelectric vibration energy harvester (ATPVEH) augmented with an elastic base (EB), aimed at optimizing energy capture from low-orbit vibrations. This design incorporates a uniquely configured asymmetric tri-stable piezoelectric cantilever beam, positioned within a U-shaped block that is further enhanced by an elastic base. A strategically placed spring (kf)–mass (Mf) system, situated between the U-shaped block and the constrained end of the beam, significantly boosts the vertical displacement of the beam during vibrational events. We developed a dynamic model for the ATPVEH+EB utilizing Lagrange’s equations, exploring the impact of various factors—including the asymmetry of the potential well, the stiffness of the elastic base, the mass of the spring–mass system, and the load resistance—on the system’s nonlinear dynamic responses. Our findings indicate that the ATPVEH+EB facilitates more efficient energy harvesting from low-orbit vibrations, demonstrating dual response peaks across its operational frequency spectrum. Notably, the displacement and output voltage amplitudes of the ATPVEH+EB can be enhanced by increasing mf or decreasing kb, whereas the peak output power transitions toward a lower frequency range as the load resistance escalates. Both theoretical analyses and numerical simulations corroborate the ATPVEH+EB’s superior performance in harvesting energy within low-orbit vibrational environments.

A pendulum based frequency-up conversion mechanism for vibrational energy harvesting in low-speed rotary structures

Motivated to run a self-powering monitoring sensor on a wind turbine blade, this paper proposes a pendulum based frequency-up converter that effectively captures a low-speed mechanical rotation into high-frequency vibration of a piezoelectric cantilever beam. A system of governing equations for the proposed concept is developed to describe the motion of the pendulum, the vibration of the beam, and the voltage output of the harvester. Design optimization is performed to improve the power generation performance, and the simulation results are verified experimentally. We demonstrate the improved power density from the proposed concept compared to the disk driven frequency-up converters.

Experiment and performance analysis of serpentine-shaped cantilever beam for pipeline vibration-based piezoelectric energy harvester prototype development

Abstract Pipelines produce vibrations during fluid or gas transportation. These vibrations are less likely to cause structural failure as they exist with a small magnitude and can be harvested into useful energy. This paper presents a study on the piezoelectric energy-harvesting method converting mechanical energy from pipeline vibration into electrical energy. The performance of the serpentine-shaped piezoelectric cantilever beam was observed to check whether the design can produce the highest output voltage within the allowable vibration region of the pipeline from 10 to 300 Hz through finite element analysis using COMSOL Multiphysics software (Supplementary Material). In addition, this study investigates the energy-harvesting potential of the proposed design under real pipeline vibration conditions through a lab vibration test. The harvested energy output is evaluated based on various vibration frequencies and amplitudes, which gives an idea of the device and its performance under different operating conditions. The experiment result shows that the energy harvester produced an open-circuit voltage of 10.28–15.45 V with 1 g of vibration acceleration. The results of this research will contribute to the development of efficient piezoelectric energy harvesters adapted for pipeline environments.

Piezoelectric breeze energy harvester with mechanical intelligence mechanism for smart agricultural monitoring systems

In this paper, a piezoelectric breeze energy harvester with a mechanical intelligence mechanism for smart agricultural monitoring systems (G-PBEH) is proposed. Different from the conventional magnetically coupled piezoelectric cantilever beam harvesters where the end magnet is mostly fixed, the G-PBEH has movable magnets in a fixed cylindrical channel. Which could achieve a mechanical intelligence mechanism with the tuned magnets on the shell, contributing to increasing voltage frequency and widening wind bandwidth. The effects of cylindrical channel length (L) and tuned magnet diameter (D) on performance were investigated. The experimental findings reveal that when L is 10 mm and D is 8 mm, the prototype starts at 2 m s−1, and the highest voltage and power are 17.9 V and 944.07 μW (150 kΩ) at 8 m s−1 . Compared to L is 5 mm (magnet fixed), the voltage waveform has a 28.6% increase in the quantity of peaks. Besides, the voltage is larger than 3 V occupying 91.6% of the experimental wind bandwidth. The application experiment demonstrates that the G-PBEH can be used as a reliable power supplier, which can facilitate the progress of smart monitoring systems for simplified greenhouses in remote areas.

A hybrid wave vibration energy harvester with electromagnetic double-speed and piezoelectric up-frequency driven by a rotating ball

The energy crisis and environmental pollution have driven the development of ambient energy harvesting technologies, and ocean waves usually contain abundant vibration energy, making the study of wave energy harvesting technology of profound value. This paper proposes a hybrid wave vibration energy harvester with electromagnetic double-speed and piezoelectric up-frequency driven by a rotating ball. For the electromagnetic generator (EMG), the excitation magnet and coil move simultaneously, resulting in double the flux variation rate compared with traditional structures, enhancing the output voltage. For the piezoelectric transducer (PZT), four piezoelectric cantilever beams are magnetically coupled with the EMG, generating power through bistable motion and broadening the working frequency band of the cantilever beam structure. The harvester is modeled and simulated, and its performance is tested on a simulated vibration platform, with simulation and experimental results in good agreement. Under external excitation at 0.8 Hz, the optimal load and maximum power for each EMG are 8.2 Ω and 207.2 mW, respectively, and the optimal load and maximum power for each PZT are 100 kΩ and 1.52 mW, respectively. The harvester can produce a maximum output power of 420.48 mW, demonstrating high efficiency in energy capture under low-frequency and multidirectional wave excitation.

Numerical investigation of smart material-based structures for vibration energy-harvesting applications

Abstract The present work deals with energy-harvesting devices, which are useful in scavenging power using piezoelectric materials. Utilizing classical beam theory and classical plate theory, finite element modelling has been carried out to optimize the performance of output power of a cantilever beam and a flexible rectangular plate. Harmonic oscillations and base excitation will be the two different forcing functions used to drive the system. Based on this, numerical investigations of the performance of output power for the piezoelectric cantilever beam and flexible rectangular plate with different cases are considered. The present work is also useful for designing the piezoelectric cantilever beams and plates to extract maximum output power within the frequency ranges from 0 to 200 Hz. Numerical investigations on the piezoelectric cantilever beam and flexible rectangular plate with different cases reveal that the performance of output power is influenced by factors like load resistance, applications of with and without host structures, and different design parameters like unimorph, bimorph, embedded, line- and cross-type piezoelectric patch arrangements.

Design and evaluation of a monostable symmetric piezoelectric energy harvester based on cantilever structure and magnetic excitation action.

This work proposes a monostable symmetric piezoelectric energy harvester based on the cantilever structure and magnetic excitation action (M-PEH). The governing equations of M-PEH are derived based on its kinematic properties. The intrinsic frequency of the piezoelectric cantilever beam was obtained by modal simulation. It has been demonstrated that the mode of arrangement of the magnetic poles has a significant effect on the output voltage of the energy harvester. The proposed M-PEH has four driving magnets with a mass of 6g and a radial driving distance of 15mm for more efficient energy harvesting. The experimental results show that the maximum voltage of the M-PEH with the double U-type rotor was 31.2V at 240rpm and 110 kΩ external resistance. The average power of the PEH with the double U-type rotor was 16.562 mW at a speed of 240rpm with an outer resistance of 20 kΩ. The energy harvester with a double U-type rotor can realize a voltage output of not less than 10V in the range of 60-300rpm when the same poles of the tip magnets are arranged outward. The M-PEH can also easily light up LEDs or miniature electronic watches with speeds of 120rpm and 240rpm. This further proves that the proposed piezoelectric energy harvester (M-PEH) has a better energy harvesting effect and great potential for practical applications.

A Hybrid Tri-Stable Piezoelectric Energy Harvester with Asymmetric Potential Wells for Rotational Motion Energy Harvesting Enhancement

This paper proposes an asymmetric hybrid tri-stable piezoelectric energy harvester for rotational motion (RHTPEH). The device features an asymmetric tri-stable piezoelectric cantilever beam positioned at the edge of a rotating disk. This beam is uniquely configured with an asymmetric arrangement of magnets. Additionally, an elastic amplifier composed of a vertical and a rotating spring connects the beam’s fixed end and the disk. This setup enhances both the rotational amplitude and vertical displacement of the beam during motion. A comprehensive dynamical model of the RHTPEH was developed using Lagrange’s equations. This model facilitated an in-depth analysis of the system’s behavior under various conditions, focusing on the influence of key parameters such as the asymmetry in the potential well, the stiffness ratio of the amplifier springs, the radius of the disk, and the disk’s rotational speed on the nonlinear dynamic response of the system. The results show that the asymmetric hybrid tri-stable piezoelectric energy harvester makes it easier to harvest the vibration energy in rotational motion and has excellent power output performance compared with the symmetric tri-stable piezoelectric energy harvester. The output power magnitude of the system at higher rotational speeds increases as the radius of rotation expands, but when the rotational speed is low, the steady-state output power magnitude of the system is not sensitive to changes in the radius of rotation. Theoretical analysis and numerical simulations validate the effectiveness of the proposed asymmetric RHTPEH for energy harvesting in low-frequency rotating environments.

Simulation and experimental study of notched cantilever beam for improved vibration energy harvesting

This research paper addresses the design and analysis of a Notched Cantilever Beam Energy Harvester (NCBEH) aimed at enhancing vibration energy harvesting. The voltage output from Lead Zirconate Titanate (PZT) piezoelectric material is directly related to the strain it experiences. Therefore, numerical simulations using ANSYS were conducted to investigate the variations in natural frequency and stress–strain distribution with respect to slot length in a slotted cantilever beam. Additionally, a notch was introduced into the beam to further enhance strain distribution. The study found that, with precise PZT placement, an NCBEH with a 55 mm slot length can generate 15% more voltage output at lower natural frequencies compared to existing Piezoelectric Cantilever Beam Energy Harvesters (PCEH) [1]. Experimental tests were also conducted to compare the voltage output response of the NCBEH and the PCEH, with the results showing good agreement with the numerical simulation findings.

A Bidirectional T‐Shaped Energy Harvester: Modeling, Simulation, and Experiment

Piezoelectric cantilever beams are broadly implemented in energy harvesting. However, simple cantilever‐shaped harvesters are mostly unimodal. Herein, a T‐shaped cantilever beam harvester that can have a bimodal amplitude–frequency curve is developed. The modal of the system is designed in COMSOL finite‐element software and the dynamic behavior is carried out using the finite element simulation. Then, validation experiments are used to estimate the results of finite‐element analysis and it is concluded that the simulation results are in good agreement with the experimental data. Furthermore, the frequency response curves are plotted for various system parameters so as to discuss the influence of these parameters on the bandwidth of the harvester. It is found that there is an optimal resistance that can obtain the P = 2.87 mW maximum power. Finally, theoretical modeling is established and exact analytical solutions are derived, and the comparisons of theoretical, numerical, and experimental results are implemented. It is found that the results of these three methods are consistent. In addition, all of these predictions show that the bidirectional coupling induces the bandwidth increases.