Piezoelectric Vibration Energy Harvester Research Articles

Design and Modeling of Micro-Scale Piezoelectric Vibration Energy Harvester for Charging Pacemaker Battery

Design and Modeling of Micro-Scale Piezoelectric Vibration Energy Harvester for Charging Pacemaker Battery

Evaluating the efficacy of lead-free piezoelectric materials in microcantilever based vibration energy harvesters

Abstract The piezoelectric materials have been extensively utilized in various applications, such as sensors, actuators, and energy harvesters. This study evaluates the performance of six lead-free piezoelectric materials- aluminium nitride (AlN), barium titanate (BaTiO3), lithium niobate (LiNbO3), lithium tantalate (LiTaO3), polyvinylidene fluoride (PVDF), and zinc oxide (ZnO) in MEMS-based piezoelectric vibration energy harvesters (PVEHs) using cantilever configurations. Finite element analysis via COMSOL Multiphysics was employed to assess the deflection, voltage, and power outputs of these materials at their resonance frequencies, both with and without proof masses. The results indicate that BaTiO3 and PVDF cantilevers exhibited the highest voltage outputs, reaching 207.14 mV and 202.07 mV, respectively, with AlN also showing comparable performance at 184.72 mV. ZnO-based cantilevers demonstrated the highest power output of 1.35 nW without proof masses and 190.5 nW with proof masses, indicating its potential for high-power applications. The addition of proof masses generally reduced resonant frequencies but enhanced power outputs, like for ZnO. This comprehensive analysis underscores the critical impact of material selection and structural modifications on the efficiency of PVEHs, with BaTiO3, PVDF, and ZnO emerging as the most promising candidates for optimizing energy harvesting devices. This research lays a foundation for further advancements in piezoelectric MEMS technology, aiming for more efficient energy harvesting solutions.

Theoretical and experimental study on the combination internal resonance of L-shaped piezoelectric vibration energy harvester

In this work, the dynamic behaviors of L-shaped piezoelectric vibration energy harvester that result from the combination internal resonance are numerically, analytically and experimentally presented. The electromechanically coupled governing equations of the energy harvester were employed in accordence with our previous study. The multi-branch approximate responses of the system are derived by using the method of multiple scales. The stability of the system is determined by the eigenvalues of the Jacobi matrix. Parameterized analyses are conducted on the output response as the external excitation frequency approaches the differential combination frequency of the energy harvester. The effects of acceleration excitation and external resistance on the output performance of the system are analyzed. The nonlinear responses of the system under various initial conditions are numerically analyzed using time response curves, spectrograms, Poincaré maps, and bifurcation diagrams. The effects of external resistance and external excitation frequency on the attractor basin are investigated. The particular nonlinear phenomena identified in the theory are experimentally verified for the combination resonance. The broad frequency range of the LPEH ranges from 15 Hz to 16.82 Hz. The study of combination resonance and internal resonance of the piezoelectric energy harvester will help to understand its complex vibration characteristics and predict the dynamic behavior.

Performing Magnetic Boundary Modulation to Broaden the Operational Wind Speed Range of a Piezoelectric Cantilever-Type Wind Energy Harvester

Small piezoelectric wind-induced vibration energy harvesting systems have been widely studied to provide long-term sustainable green energy for a large number of wireless sensor network nodes. Piezoelectric materials are commonly utilized as transducers because of their ability to produce high output power density and their simple structure, but they are prone to material fracture under large deformation conditions. This paper proposes a magnetic boundary modulated stepped beam wind energy harvesting system. On the one hand, the design incorporates a composite stepped beam with both high- and low-stiffness components, allowing for efficient vibration and electrical energy output at low wind speeds. On the other hand, a magnetic boundary constraint mechanism is constructed to prevent the piezoelectric sheet from breaking due to excessive deformation. Experiments have confirmed that the effective operational wind speed range of the harvester with magnetic boundary constraints is doubled compared to that of the harvester without magnetic boundary constraints. Furthermore, by adjusting the magnetic pole spacing of the boundary, the harvesting system can generate sufficiently high output power under high-wind-speed conditions without damaging the piezoelectric sheet.

Design, fabrication, and characterization of a deformation-restricted piezoelectric vibration energy harvester triggered by a stopper

Vibration energy harvesting based on piezoelectric effect is emerging as a promising sustainable energy solution for micro-electromechanical systems and wireless sensor networks. Whereas, reliability issues stemming from excessive deformation-induced damage to piezoelectric materials have hindered the progress of piezoelectric vibration energy harvester development. Herein, an indirect triggering method involving a stopper has been implemented to design the deformation-restricted piezoelectric vibration energy harvester (D-RPVEH). This device utilizes the stopper to limit the maximum deformation of the piezoelectric beam, facilitating unidirectional deformation. Consequently, the D-RPVEH delivers enhanced reliability even under unexpected excessive impacts. The feasibility of the proposed principle and design are proved by finite element simulation and experimental test. Most importantly, the research results are found that the simulated end displacement and experimental voltage of PZT beam declined with the decrease of stopper height difference. Moreover, the efficacy of limiting the piezoelectric beam's maximum deformation by implementing the stopper structure is supported by both simulation and experimental findings. The D-RPVEH device can achieve a peak power output of 2.58 mW at frequencies as low as 5.5 Hz, utilizing an optimal load resistance of 30 kΩ. Furthermore, it can illuminate a minimum of 60 blue commercial LEDs connected in series. Therefore, the D-RPVEH not only has good power generation performance but also has high reliability. This design will provide a reference for the research on improving the reliability of PVEH.

A nonlinear and asymmetric monostable compliant ortho-planar spring piezoelectric vibrational energy harvester using a H-I structure

This paper proposes a compliant ortho-planar spring piezoelectric vibrational energy harvester (COPS-PVEH) using a H-I structure that exploits a nonlinearity and an asymmetric mono-stability to enhance the bandwidth of the device. The main structure is based on a double clamped beam (I-structure) coupled with four cantilever beams (H-structure) and an ortho-planar spring in the centre of the I-structure. Finite element analysis (FEA), analytical modelling, and experimentation were performed to analyse the dynamical and electrical behaviour of the harvester. The device was fabricated using polylactide (PLA). Six bimorph PZT-5H piezoelectric materials, electrically connected in parallel, were used as piezoelectric generators. The device was tested using an optimum load resistor of 90 kΩ under sinusoidal and sine sweep excitation in the gravity (vertical) direction. The pre-load (due to gravitation) causes a softening nonlinearity and an asymmetric mono-stability in the potential energy function. The results show that multiple peaks are observed in the output voltage of the harvester in the FEA, analytical modelling, and experimentation under harmonic excitation in the sub 15 Hz frequency range. Furthermore, analytical modelling and experimentation exhibit softening nonlinearity and chaotic behaviour, reaching a maximum amplitude power of 1.01 mW (at 8.3 Hz) and 1.07 mW (at 9.5 Hz) respectively under sine sweep excitation (amplitude of 0.6 g (g = 9.81 m/s2)). Experimentally, the harvester also generates an average power greater than 46 µW with a 6.8 Hz bandwidth under the same excitation. The softening nonlinearity and asymmetric mono-stability enhance the bandwidth of the harvester in the low frequency region where most broadband ambient vibrations are available in practical environments.

Coupled Thermo-Electric-Elastic Piezoelectric Vibration Energy Harvester With Axial Movement: Modeling, Verification, and Analysis

Abstract In the field of rail transport and aerospace field, vibration energy harvesting is inevitably subjected to coupled excitations, including train wheel–track interaction induced friction heat and forced vibration, periodic thermal radiation, and vibration excitation. This paper investigates a coupled thermo-electric-elastic piezoelectric vibration energy harvester with axial movement under external heat flux and mechanical force load. The coupled forced vibration equation, coupled electric equation, and coupled thermoelastic heat conduction equation are derived and solved by Green's function theory. To analyze the effect of excitations on the response characteristics, the decoupled method is utilized to solve the coupled multi-field equations and obtain the displacement, electric, and temperature distribution closed-form solutions. The displacement coupling effect induced temperature distribution and the thermo-electric coupling effect triggered displacement are respectively decoupled and analyzed. The obtained closed-form temperature distribution and displacement solutions are verified by the finite element method. To further verify the obtained solutions, a numerical method is conducted by decoupling the coupled multi-field equations and comparing them with prior solutions. Additionally, the different height-to-length ratios, axially moving speeds, and external force load are analyzed in detail. The results indicate that the displacement, temperature distribution, and output voltage vary with external conditions due to the coupled multi-field effect. Overall, this work investigates the thermo-electric-elastic coupling effect on the axially moving piezoelectric energy harvesting, which is beneficial to promote theoretical investigations of the coupled multi-field energy harvesting system and accelerate the practical applications in the aerospace field.

Modified extended Rauch–Tung–Striebel smoother method for the dynamic external excitation identification of piezoelectric vibration energy harvesting systems

A vibration energy harvester can collect vibration energy from the environment to supply low-power devices, such as wireless sensor nodes. Reducing the size and power consumption of these devices is a challenging problem. A dual-function device, which includes energy harvesting and vibration measurement, may solve this problem. Therefore, studying inversion methods for identifying the external excitation of a harvester is meaningful. In this study, a modified inversion method that combines an extended Rauch–Tung–Striebel smoother (ERTSS) with the particle swarm optimization (PSO) algorithm, i.e., the ERTSS-PSO method, is proposed to identify the time domain signal of external excitation through the voltage response of a piezoelectric vibration energy harvester. A modified ERTSS approach with sliding windows is developed. The sliding windows are partially overlapped to eliminate identification errors between the two contiguous windows. Near real-time identification is achieved for the small sliding window. PSO is utilized to estimate state noise covariance and measurement noise covariance, improving identification accuracy compared with the L-curve approach. Under this proposed framework, prior knowledge regarding the statistical data of unknown external excitations is unnecessary, enabling a more comprehensive range of applications. To assess the performance of the proposed ERTSS-PSO method, numerical simulations, including two piezoelectric vibration energy harvesting systems with third-order and fifth-order nonlinear stiffness, are conducted to verify the effectiveness of the proposed method under harmonic, multifrequency, and random excitations. The method proposed in this study is also validated by a circular laminated piezoelectric plate harvester under harmonic and random excitations in an experiment. Results from the experimental studies demonstrate that the proposed method improves identification accuracy by at least 9% compared with the extended Kalman filter, at least 7% compared with the augmented Kalman filter (AKF) with Rauch–Tung–Striebel smoother (ARTSS), and at least 40% compared with AKF under random excitation. In addition, the proposed method is unaffected by initial conditions, and it is more stable and accurate than AKF and ARTSS. The proposed method lays the theoretical foundation for identifying the external excitation of a harvester. It is also a possible solution for the miniaturization and compactness of wireless monitoring devices.

Experimentally validated passive nonlinear capacitor in piezoelectric vibration applications

Abstract Piezoelectric vibration isolation and energy harvesting applications have been extensively studied in the literature. The studies include linear and nonlinear approaches. Linear methods are simpler but possess inherent limitations. On the other hand, nonlinear ones could perform better over a broader operating frequency range. Nonlinearity can be introduced in the mechanical domain or electrical domain actively or passively. Since electrical components can be on smaller scales compared to mechanical counterparts, inducing nonlinearity on the mechanical system through the electrical domain can be more practical. Moreover, passive structures require no energy supply and controller therefore they are simpler and more reliable than active ones. In this paper, a novel way to attain passive hardening stiffness was suggested by introducing an electrical component in a shunt circuit for passive nonlinear piezoelectric vibration isolation or energy harvesting applications and the induced structural non-linearity is demonstrated experimentally. A passive nonlinear component is suggested to be a hardening capacitor obtained by the P–N junction. An analytic model is derived for parallel connected macro-fiber composite (MFC) piezoelectric material attached bimorph configuration on a cantilever beam and the model is solved numerically. MFC integrated bimorph model, and P–N junction approximate model are presented. The frequency response of the coupled system is obtained by using numerical models and experiments. Both numerical analysis and experiments validated the hardening stiffness effect of the P–N junction. To the best of the authors’ knowledge, this study is the first study to demonstrate that nonlinear capacitance of P–N junctions can be used to attain nonlinearity in a mechanical system.

Influences of bluff body geometries upon performances of piezoelectric wind energy harvesters

Piezoelectric wind-induced vibration energy harvesters (PWVEHs) offer a promising solution for powering wireless sensor networks by converting wind energy into electrical energy. While conventional PWVEHs rely on vortex-induced vibration (VIV) and galloping to work, little has been done to investigate the coupling mechanisms between VIV and galloping and their influences upon energy harvesting performances of flow-induced vibration (FIV). To address this, we propose 36 bluff bodies (BBs) with various frontbody and afterbody shape combinations and conduct FIV experiments in a wind tunnel. The voltage output of each BB is recorded and analyzed based on whether pure VIV, pure galloping vibration, or concurrent VIV-galloping vibrations are involved. Hysteresis analyses are performed for BBs exhibiting concurrent VIV-galloping vibrations. The energy harvesting performances of all BBs are compared to circular and square cross-section BBs, revealing a BB shape that achieved 23.18% and 16. 57% higher maximum output than circular and square BBs, respectively. Computational analysis is conducted to investigate the flow field behind the given BBs. These findings provide valuable insights for developing efficient energy harvesters utilizing VIV and galloping by optimizing the involved BBs.

Current Research Status and Future Trends of Vibration Energy Harvesters.

The continuous worsening of the natural surroundings requires accelerating the exploration of green energy technology. Utilising ambient vibration to power electronic equipment constitutes an important measure to address the power crisis. Vibration power is widely dispersed in the surroundings, such as mechanical vibration, acoustic vibration, wind vibration, and water wave vibration. Collecting vibration energy is one of the research hotspots in the field of energy. Meanwhile, it is also an important way to solve the energy crisis. This paper illustrates the working principles and recent research progress of five known methods of vibrational energy harvesting, namely, electromagnetic, piezoelectric, friction electric, electrostatic, and magnetostrictive vibrational energy harvesters. The strengths and weaknesses of each method are summarised. At the end of the article, the future trends of micro-nano vibrational energy collectors are envisioned.

Bifurcation boundaries analysis of the thin-walled internal resonance energy harvester

The dynamic instability of the thin-walled 1: 2 internal resonant piezoelectric vibration energy harvester is investigated. Previously work (Nie et al., 2019) derived the nonlinear electromechanical-coupled governing equations and validated them experimentally. The modulation equations are performed by the method of multiple scales. The system stability is obtained from the eigenvalues of the Jacobi matrix. Then, three types of bifurcation boundaries of the system are determined analytically and simulated numerically via Routh–Hurwitz criterion. Results show that internal resonance complicates the dynamic properties of the bifurcation region. For a large external excitation, new saddle node bifurcation regions appear in the stability diagram. Moreover, the new saddle node and Hopf bifurcation regions may intertwine. Furthermore, as the acceleration excitation increases, the system can be observed to transition to stable–unstable–stable states. The system’s high and low branch responses are fed back by the system’s large and small initial conditions. The system’s periodic and quasi-periodic motions are characterized by time response, FFT, phase trajectory, and Poincaré map. The study of the stability boundary of the piezoelectric energy harvester contributes to the harvesting of energy from ambient vibrations over a broader frequency range.

A tunable pendulum-like piezoelectric energy harvester for multidirectional vibration

Harvesting energy from vibrations using piezoelectric mechanism has attracted much attention for powering wireless sensors over the past decade. This paper proposes a tunable pendulum-like piezoelectric energy harvester for multidirectional vibration (TP-PVEH) to enhance the power generation characteristic, durability, and environmental adaptability of energy harvester. Unlike traditional cantilevered piezoelectric vibration energy harvesters (PVEHs), which typically lowered working frequencies by adding the weight of proof mass at the end of beam or reshaping beam, TP-PVEH employed a pendulum to harness low-frequency vibrations. Moreover, in contrast to typical pendulum-like PVEHs, the pendulum in this design was not mounted at the end of beam but was attached to a radial spherical plain bearing (RSPB) structure, which avoided the irreversible beam damage caused by gravitational force. TP-PVEH utilized simple-pendulum-induced RSPB motion to smoothly pluck piezoelectric beams, subjecting the piezoelectric beams to unidirectional compressive stress only. Meanwhile, the RSPB structure's capability to facilitate multidirectional rotation enabled TP-PVEH to efficiently capture energy from various directions. Theoretical analysis, numerical analysis and experiment tests were conducted to validate the design and examine how excitation and structural parameters influenced on the output performance of TP-PVEH. The results demonstrated that the excitation amplitude, excitation angle, proof mass, and mass distance brought significant effects on the output characteristic of TP-PVEH. The working frequency, output voltage and power could be efficiently tuned by the abovementioned parameters. With an excitation amplitude of 3 mm, TP-PVEH achieved an optimal output power of 9.81 mW and an output power density of 11.37 μW/mm3, operating with a load resistance of 200 kΩ at a frequency of 12.5 Hz.TP-PVEH could power 100 blue LEDs and a calculator. Additionally, the ability of TP-PVEH to charge capacitors further demonstrated its practical power supply capabilities.

Piezoelectric Hinged Beam with Arc Mass Stopper for Vibration and Human Motion Energy Harvesting.

Compact reliable structure and strong electromechanical coupling are hot pursuits in piezoelectric vibration energy harvester (PVEH) design. PVEH with a static arc stopper makes piezoelectric stress uniformly distributed and widens the frequency band by collision but wastes space. This Article proposes a hinged PVEH with two arc mass stoppers (AS-H-PVEH). Two arc stoppers as movable masses increase the vibration energy and the effective electromechanical coupling coefficient to achieve strong electromechanical coupling. AS-H-PVEH generates a 4.1 mW power output at 11.6-12.0 Hz and 0.2 g. AS-H-PVEH sustains 4 g acceleration vibration for 10 min without attenuation. To offset the resonance frequency increase caused by arc contact, we discuss the magnetic coupling, and axial force effects are discussed. The design of the arc stopper radius, nonlinear electromechanical coupling model, and system parameter identification method are presented. The displacement varied mechanical quality factor and effective electromechanical coupling coefficient are considered in the modified model for the first time. The model obtained good agreement under experiments. The power generation and driven wireless sensor performance of AS-H-PVEH was verified. This research has important theoretical and application value for the performance optimization of PVEH with an arc stopper.

A Novel Design Strategy for Cantilever Based MEMS Piezoelectric Vibration Energy Harvesters: FEM Parametric Analysis and Modeling

Vibration-based energy-harvesting (VEH) technology is a viable alternative power source that addresses the issue of battery capacity constraints in portable electronic devices. A novel design strategy for developing a piezoelectric vibrational energy harvester (PVEH) based on a microelectromechanical system (MEMS) is proposed in this paper. Through FEM simulation and analysis, a correlation between the proof mass coverage (PMC) and piezoelectric coverage (PEC) for energy harvesters with different beam geometries is developed. The results show that the output power and resonant frequencies of the energy harvester are strongly dependent on the amount of PMC, PEC, and beam geometry. The optimum piezoelectric layer length for a PVEH depends on the amount of PMC and geometry of the beam. Moreover, as the PMC increases, the output power is found to be increasing. The structure with 80% PMC provides maximum output power. Also, a trapezoidal beam will give a lower resonant frequency than a rectangular beam. Thus the optimum design methodology for a cantilever-based MEMS PVEH in a given layout is to select the trapezoidal-shaped beam with a PMC of 60% to 80% and piezoelectric layer length equal to the beam length. This method would provide optimised resonant frequency and output power performance. Additionally, an analytical model is developed for the optimised cantilever PVEH based on trapezoidal geometry, and the simulation findings are validated with the analytical results.

Role of inertial nonlinearity and coupling stiffness on a series of coupled harvesters

This study investigates the effect of coupling configuration on a state-of-the-art harvesting system consisting of a series of spring-coupled piezoelectric nonlinear monostable tip-loaded cantilever-based vibration energy harvesters (VEHs). The investigation finds favorable coupling configurations that exploit complex nonlinear interaction for improving system performance. The system model incorporates the beam's geometric nonlinearities in the governing equation using inertial and stiffness nonlinear terms. The study first analytically investigates the effect of grounding stiffness on a single harvester's performance. Then, it numerically investigates the effect of increasing array size and changing stiffness distribution. The study discovers a novel hardening/softening transition phenomenon at a critical grounding stiffness value induced by the inertial nonlinear effect. This critical event also maximizes peak output power near the largest eigenfrequency at an optimum grounding stiffness value. At larger arrays, the peak power shows a complex bifurcation behavior, hinting at the presence of multiple attractors. The numerical study of different stiffness configurations and linearized eigenanalysis reveals the necessity of a multilevel optimization strategy focused on both the stiffness ratio between the coupling springs' and their overall stiffness level. This study bridges the gap between previous studies on spring-coupled linear and bistable arrays, offering new insights into coupled nonlinear interactions and proposing novel optimization strategies.

A piezoelectric and electromagnetic vibration energy harvesting system based on spring pendulum structure and MPPT control

A piezoelectric and electromagnetic vibration energy harvesting system based on spring pendulum structure and MPPT control

Theoretical and experiment optimization research of a frequency up-converted piezoelectric energy harvester based on impact and magnetic force

Harvesting environmental vibrations to power electronic components is an essential approach for addressing the power supply challenge in MEMS. However, conventional vibration energy harvesting systems frequently suffer from limited frequency bandwidth and high-frequency deficiencies. This paper proposes a novel up-frequency structure for piezoelectric vibration energy harvesting (VEH) that relies on both nonlinear magnetic force and piecewise linear force. The proposed VEH’s nonlinear dynamic characteristics are analyzed theoretically, and an experimental prototype machining and vibration test platform are constructed. Theoretical and experimental results are compared and analyzed by conducting basic experiments and key parameter optimization experiments. The research results demonstrate that the proposed VEH can efficiently harvest vibration energy in low-frequency and wide-band environments. Regarding the system parameters, higher vibration acceleration results in increased output voltage and wider working frequency bandwidth. Reducing the gap distance enhances piecewise linear vibration, which broadens the working frequency bandwidth. Furthermore, the proposed VEH’s ability to harvest low-frequency vibrations can be enhanced by reducing the magnet distance, thereby reducing the linear resonance frequency of the system. The findings of this study offer valuable insights for advancing the engineering application of MEMS self-power supply technology.

A load impedance emulation active interface for piezoelectric vibration energy harvesters

A single stage active AC/DC electronic interface able to emulate the optimal load impedance of a Resonant Piezoelectric Vibration Energy Harvester (RPVEH) is proposed. As theoretically shown, unlike an electronic interface that emulates an optimal load generator, an interface that emulates an optimal load impedance does not require adaptation to the acceleration of input vibrations. This allows the use of a very simple control, avoiding the implementation of Maximum Power Point Tracking algorithms that require lossy microcontrollers. Thus, the proposed interface is equipped with a simple analog controller allowing the RPVEH to work in its Maximum Power Point in both steady-state and variable conditions of vibrations, without recurring to multivariable perturbative approaches, as it happens for the most of single stage AC/DC interfaces proposed in the literature. The absence of perturbative techniques allows a significant improvement of both stationary and dynamic performances. Experimental tests of a prototype of the proposed interface confirm the theoretical findings and the predicted behavior.

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.