Cantilever Piezoelectric Energy Harvester Research Articles

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.

Performance Correction and Parameters Identification Considering Non-Uniform Electric Field in Cantilevered Piezoelectric Energy Harvesters.

In the current electromechanical model of cantilevered piezoelectric energy harvesters, the assumption of uniform electric field strength within the piezoelectric layer is commonly made. This uniform electric field assumption seems reasonable since the piezoelectric layer looks like a parallel-plate capacitor. However, for a piezoelectric bender, the strain distribution along the thickness direction is not uniform, which means the internal electric field generated by the spontaneous polarization cannot be uniform. In the present study, a non-uniform electric field in the piezoelectric layer is resolved using electrostatic equilibrium equations. Based on these, the traditional distributed parameter electromechanical model is corrected and simplified to a practical single mode one. Compared with a traditional model adopting a uniform electric field, the bending stiffness term involved in the electromechanical governing equations is explicitly corrected. Through comparisons of predicted power output with two-dimensional finite element analysis, the results show that the present model can better predict the power output performance compared with the traditional model. It is found that the relative corrections to traditional model have nothing to do with the absolute dimensions of the harvesters, but only relate to three dimensionless parameters, i.e., the ratio of the elastic layer's to the piezoelectric layer's thickness; the ratio of the elastic modulus of the elastic layer to the piezoelectric layer; and the piezoelectric materials' electromechanical coupling coefficient squared, k312. It is also found that the upper-limit relative corrections are only related to k312, i.e., the higher k312 is, the larger the upper-limit relative corrections will be. For a PZT-5 unimorph harvester, the relative corrections of bending stiffness and corresponding resonant frequency are up to 17.8% and 8.5%, respectively. An inverse problem to identify the material parameters based on experimentally obtained power output performance is also investigated. The results show that the accuracy of material parameters identification is improved when considering a non-uniform electric field.

Analysis and Modeling of Intermittent Fluctuation Mechanisms of Piezoelectric Impact-Induced Vibration Cantilever Energy Harvester

Analysis and Modeling of Intermittent Fluctuation Mechanisms of Piezoelectric Impact-Induced Vibration Cantilever Energy Harvester

Fractal-inspired multifrequency piezoelectric energy harvesters

In this Letter, we propose fractal-based piezoelectric energy harvesters (PEHs) for broadband energy scavenging. The introduction of fractal topology into transducers significantly alleviates the inherent limitation of a narrow working bandwidth in commonly used cantilever PEHs. We conduct a finite element analysis and experiments to exploit the performance of fractal cantilever PEHs with different iteration times. Our findings reveal that the higher-order fractal structures generate an increased number of eigenfrequencies as well as modal patterns within a certain range of working bandwidth (i.e., <50 Hz). Experimental results indicate that the efficient energy harvesting bandwidth of the fractal PEHs of iterative levels 1 and 2 is 2.05 and 2.15 times, respectively, larger than the conventional PEHs (i.e., level 0). In addition, the harvested voltage and power of fractal PEHs can be enhanced by attaching a proof mass to compensate for the energy loss in producing iterations. This method exhibits superiority over capturing energy in low-frequency vibration environments, such as wave energy and human movement energy.

Accurate finite element modeling of multilayered flexible piezoelectric energy harvesting devices with strong coupling of structure, piezoelectricity, and circuit

Multilayered flexible piezoelectric energy harvesting devices (FPEDs) are a new future harvesting technology which are highly flexible and lightweight than familiar cantilever piezoelectric energy harvesters. This mechanical vibration driven FPED is a strongly coupled multiphysics phenomena that involve complex natural three-way interaction among the composite piezoelectric structure, the electric charge accumulated in the piezoelectric material, and a controlling electrical circuit attached to it. Efficient and accurate computational solution approaches are essential for analyzing these mechanical vibration-driven FPEDs to capture the main physical aspect of the coupled phenomena and to accurately predict the output voltage. While there are some numerical models for simple familiar cantilever type piezoelectric energy harvester reported in the literature, a fully three-dimensional strongly coupled model for complex material distributed, complex geometry, and multilayered FPED involving strong coupling of structure, piezoelectricity, and circuit phenomena has not yet been developed. A partitioned iterative algorithm is developed using a hierarchical decomposition approach wherein the coupled three fields are solved separately and coupled through loop union integration techniques that provide an efficient and accurate simulation of FPEDs. The simulation results matched the experiment results very well. This study provides a basis for the natural extension of partitioned iterative finite element coupled algorithm to simulate the future piezoelectric energy harvesting technologies involving a strong coupling of structure, piezoelectricity, and circuit phenomenon.

Effect of Flow Disruptors on the Performances of a Cantilever Piezoelectric Energy Harvester

Effect of Flow Disruptors on the Performances of a Cantilever Piezoelectric Energy Harvester

Optimal design of piezoelectric energy harvesters for bridge infrastructure: Effects of location and traffic intensity on energy production

Piezoelectric energy harvesters (PEHs) can be used as an additional power supply for a Structural Health Monitoring (SHM) system. Its design can be optimised for the best performance, however, the optimal design depends on the input vibration and locations. In this work, we extend an optimisation framework from our previous studies to include the effect of the PEH’s location, which uses the cantilevered PEH Kirchhoff–Love plate model discretised by IsoGeometric Analysis (IGA) and coupled with Particle Swarm Optimisation (PSO) algorithm to find the designs with maximum energy outputs for a large number of input acceleration histories, extracted from the recorded dynamic response data of a real cable-stayed bridge in Australia. Then, clustering and evaluation under 24-h excitation are performed to find several best PEHs for the entire bridge. By comparing the best PEH at all locations with a typical benchmark device, the substantial performance improvement brought by the optimisation framework of this work is verified. The comparison results show a significant energy harvesting enhancement of 1.6 times at the best locations, 2.4 times at A2 and A3, and 3.6 times at the edge girders, respectively. The results also reveal the variability of the best design at different locations of the same structure to maximise the energy harvesting of the entire bridge, and demonstrate the design rule that the fundamental frequency of the device can be tuned within a certain frequency range to improve the robustness of PEHs design. Additional studies are performed to explore the effect of location and traffic intensity on energy harvesting by analysing the optimal PEH design and location throughout the bridge structure. The results indicate that the key factors of maximising energy harvesting efficiency are related to the input excitation and the mode of vibration being excited. The position of maximum displacement in the vibration mode corresponds to the best location for energy harvesting. Also, the best device has a fundamental frequency close to the frequency of the corresponding vibration mode. In addition, the change of traffic intensity affects the amount of convertible mechanical energy and also directs the tuning of the fundamental frequency of the PEH to achieve the highest energy conversion.

FIV and energy harvesting using bluff body piezoelectric water energy harvester with different cross-sections

Research utilizing piezoelectric fiber composites to power network nodes or micro-sensors by capturing energy from the surrounding environment is becoming a hot spot, and the structural design to efficiently improve the performance of energy harvesting is very important. The performance of a vertical cantilever piezoelectric water energy harvester (PWEH) with three different cross-sections including circular, square and equilateral triangle, each with a mass ratio of 4.8, was investigated at Reynolds number within 770–8800. Emphasis is placed on the effects of the bluff body cross-section, load resistance, and flow velocity on the flow-induced vibration (FIV) and energy response of the vertical cantilever beam of the PWEH. Except for the decreasing amplitude in the lower branch of the circular cylinder water energy harvester (CWEH), there is no distinction in the vibration response branches compared to the classical elastically supported circular cylinder. The resistance has little effect on the vibration response, while it has a significant effect on the voltage and power response. The maximum amplitude and pendulum angle of the square cylinder water energy harvester (SWEH) are slightly larger than those of the CWEH. The maximum voltage and power are smaller for the SWEH than for the CWEH. The equilateral triangular cylinder water energy harvester (TWEH) demonstrates excellent performance. It has a maximum amplitude of 3.8 D, 3.4 times that of the CWEH. The peak pendulum angle of TWCH is 13.9°, 3.2 times that of CWEH. It has a voltage of 0.057 V at a resistance of ∞, which is 3.4 times that of CEWH. In addition, the TWCH has an output power of 0.38 nW at a resistance of 106Ω, which is 9.5 times that of the CWEH. This study suggests that the best energy efficiency of TWEH is achieved by coupling vortex-induced vibration (VIV) and galloping excitation.

Modeling and Dynamic Design of a Piezoelectric Cantilever Energy Harvester with Surface Constraints

Modeling and Dynamic Design of a Piezoelectric Cantilever Energy Harvester with Surface Constraints

Global Dynamic Analysis of a Typical Bistable Piezoelectric Cantilever Energy Harvesting System

This paper focuses on global dynamic behaviors of a bistable piezoelectric cantilever energy harvester with a tip magnet and a single external permanent magnet at the near side. The initial distance between the magnetic tip mass and the external magnet is altered as a key parameter for the enhancement of the energy harvesting performance. To begin with, the dynamical model is established, and the equilibria as well as potential wells of its non-dimensional system are discussed. Three different values of the initial distance are selected to configure double potential wells. Next, the saddle-node bifurcation of periodic solutions in the neighborhood of the nontrivial equilibria is investigated via the method of multiple scales. To verify the validity of the prediction, coexisting attractors and their fractal basins of attraction are presented by employing the cell mapping approach. The best initial distance for vibration energy harvesting is determined. Then, the Melnikov method is utilized to discuss the threshold of the excitation amplitude for homoclinic bifurcation. And the triggered dynamic behaviors are depicted via numerical simulations. The results show that the increase of the excitation amplitude may lead to intra-well period-2 and period-3 attractors, inter-well periodic response, and chaos, which are advantageous for energy harvesting. This study possesses potential value in the optimization of the structural design of piezoelectric energy harvesters.

Design and Analysis of an Extended Simply Supported Beam Piezoelectric Energy Harvester

The harvesting efficiency of a cantilevered piezoelectric energy harvester is limited by its uneven strain distribution. Moreover, a cantilevered harvester requires a large workspace due to the large displacement of its free end. To address these issues, a novel piezoelectric energy harvester based on an extended simply supported beam is proposed. The proposed design features a simply supported piezoelectric main beam with an extended beam attached to its roller end and a tip mass to reduce the resonant frequency. The theoretical model of the proposed piezoelectric energy harvester is developed based on the Euler–Bernoulli beam theory. The model has been experimentally validated through the fabrication of a prototype. The extended beam and tip mass are adjusted to see their influence on the performance of the harvester. The resonant frequency can be maintained by shortening the extended beam and increasing the tip mass simultaneously. A shorter extend beam leads to a more even strain distribution in the piezoelectric layer, resulting in an enhanced output voltage. Moreover, the simulation results show that a torsional spring is installed on the roller joint which greatly influences the voltage output. The strain distribution becomes more even when proper compressive preload is applied on the main beam. Experiments have shown that the proposed design enhances the output power by 86% and reduces tip displacement by 63.2% compared to a traditional cantilevered harvester.

Improving energy harvesting from low-frequency excitations by a hybrid tri-stable piezoelectric energy harvester

This paper presents the design of a novel hybrid tri-stable piezoelectric energy harvester (HTPEH) that improves the energy harvesting efficiency of piezoelectric energy harvesters operating at low frequencies. The proposed HTPEH is an extension of a conventional tri-stable cantilever piezoelectric energy harvester with an elastic base (TPEH + EB), and it incorporates vertical and rotational elastic amplifiers that are installed between the mass block at the left end of a cantilever beam and the left side of a U-shaped frame to enhance the system's nonlinear characteristics. By utilizing Hamilton's principle, a HTPEH's nonlinear electromechanical equation is formulated, and the harmonic balance method is used to obtain analytical solutions for the displacement amplitude, voltage amplitude, and power amplitude. The study investigates the effects of various parameters, including the elastic amplifier-to-base stiffness ratio and elastic amplifier-to-piezoelectric cantilever beam mass ratio on the energy harvesting performance of the HTPEH. The results indicate that the displacement and voltage amplitude of the HTPEH exhibit two peaks as the external excitation frequency increases, and adjusting the relative mass and stiffness between the elastic amplifier and the piezoelectric cantilever beam can alter the frequency band interval where the two response peaks of the system are located. This allows the HTPEH to enter inter-well motion at low-level external excitation, resulting in high output power. The HTPEH outperforms the TPEH + EB in terms of energy harvesting efficiency under low-frequency environmental excitation.

Development and performance evaluation of a wheel-type cantilevered piezoelectric rotational energy harvester via an unfixed exciting magnet

A wheel-type cantilevered piezoelectric rotational energy harvester (wheel-type PREH) via an unfixed exciting magnet was presented to harvest energy from rotational motion without or far away from a fixed support. To verify the structural feasibility and figure out the effect of rolling exciting magnet and excited magnet on the dynamic characteristics and power generation performance of the wheel-type PREH, the theoretical analysis, simulation, fabrication and experimental testing were performed. The results showed that the performance of the wheel-type PREH depended on the rotary speeds, proof mass and piezo-cantilever mass, number of exciting magnets, cylindrical sleeve materials and so on. When other parameters were constant, there were multiple optimal rotary speeds for the maximal amplitude-ratio, output voltage, electrical energy and output power to achieve peak. Besides, the total number of voltage crests per second did not change with rotary speed. There was a constant optimal resistance load for the wheel-type PREH at different rotary speeds to achieve maximal power. The PREH prototype could yield a maximum output power of 0.74 mW at 767 r/min with optimal load resistance of 215 kΩ and 40 different color LEDs in parallel and a low power light strip could be lighted by wheel-type PREH.

Parametric excitation analysis for system performance of piezoelectric energy harvesters

Capitalizing on the advantages of parametric excitation and real-life low frequency vibration, the steady-state response of piezoelectric energy harvesting system composing of a cantilever beam with a tip mass and horizontal excitation at the fixed end is investigated. By applying Hamilton's principle, the nonlinear partial differential equation of a cantilever bimorph piezoelectric energy harvesting system with an additional tip mass is derived and analyzed. The cantilever is modeled as an axially non-elongated Euler Bernoulli beam with geometric and damping nonlinearities. By using the Galerkin method, the nonlinear partial differential equation is reduced to an electromechanical coupling system that governs a cantilever piezoelectric energy harvesting system with a tip mass under parametric excitation. The first-order resonance response of this harvesting system is studied by using the method of multiple scales. The analytical response expressions and first-order amplitude functions for vertical displacement, output voltage and output power are derived and analyzed. The influence of different impedance and tip mass on the piezoelectric energy harvesting system performance is summarized and concluded. For the parametric excitation system, the load resistance shows significant influence on the initial threshold of the piezoelectric energy harvesters under parametric excitation. For a short circuit, the initial threshold increases with increasing load resistance. For an open circuit, the initial threshold decreases with increasing load resistance. For an open circuit resistance or a short circuit resistance under parametric excitation, an increase in the end block mass effectively reduces the resonance frequency of the piezoelectric energy harvesters. Consequently, the energy harvesting bandwidth is increased, and the harvesting effect of the piezoelectric energy harvesters is enhanced. In this paper, a more accurate and practical theoretical model is established to predict the electromechanical coupling behavior of cantilever piezoelectric energy harvester under parametric excitation. Using this approach, it is possible to complement parametric and direct excitation such that the advantages of parametric excitation can be achieved. It is also significant to improve the energy conversion efficiency of energy harvesting system.

Effect of geometric non-linearity and tip mass on the frequency bandwidth of a cantilever piezoelectric energy harvester under tip excitation

The research community is investigating a variety of approaches to convert mechanical energies to useful electrical energy in order to fulfil the ever-increasing demand for energy and fulfil the requirements of the various sectors. In this regard, numerous contributions toward increasing the capacity and efficiency of the various energy harvesting techniques have been proposed in recent times; one such promising technology is piezoelectric-based vibration energy harvesting. In the present work, the effect of geometric nonlinearity and tip mass is investigated on the operational frequency range of a cantilever nonlinear piezoelectric energy harvester. The proposed mathematical model is based on an energy-based variational approach. The methodology is formulated for the piezoelectric patched cantilever beam and, eventually solved using an efficient numerical technique . An amplitude incremental iterative algorithm is used to solve the non-linear governing equations of motion for the proposed non-linear broadband harvester along with the experimental validation. Firstly, a parametric study is performed to determine the optimum piezoelectric patch dimensions. Subsequently, the attempt is made to increase the frequency bandwidth for optimum energy harvesting by taking advantage of geometrically non-linear behaviour. Additionally, a tip mass, appropriate for the excitation level, can be added to the harvester design to make it effective for lower excitation frequency. Increased frequency bandwidth for improved energy harvesting capacity with the hardening type nonlinearity and tip mass is meaningfully shown with the help of frequency-amplitude response. Furthermore, to interpret the efficacy of nonlinear harvesters in terms of frequency band-width, power spectral density plots with improved harvesting capability are presented and compared with the conventional linear vibration energy harvester.

Structure optimization and performance of piezoelectric energy harvester for improving road power generation effect

This paper presents a cantilever piezoelectric energy harvester with excellent electrical output and mechanical characteristics for roads, which solves the problems of low electrical output level and low matching with road traffic of cantilever piezoelectric energy harvesters at present. Based on the finite element model, the structural characteristics of the energy harvester under different constraint forms are analyzed. The energy harvester structure is optimized according to the electrical output and stress distribution characteristics, and the size with high electrical output and good stress distribution is clarified. Finally, the good electrical effect of the proposed energy harvester structure and size is determined. The results indicate that the rigidly constrained energy harvester has higher potential and stress of the piezoelectric layer than the cantilever constrained, but the charge cancellation at both ends of the piezoelectric layer is obvious. Then the fixed end position and the displacement application position are considered to alleviate this phenomenon, and the former has obvious benefits in improving the electrical output effect and reducing the stress value. From the perspective of mechanics and electricity, the output voltage and output power of the energy harvester under the optimal size up to 24 V and 4.381 mW respectively, which are higher than other cantilever energy harvesters. The optimized energy harvester improves its electrical effect and mechanical characteristics under actual road traffic conditions, which lays a foundation for the cantilever piezoelectric energy harvester to collect road vibration energy.

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.

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.

A comprehensive analysis of piezoelectric energy harvesting from bridge vibrations

Piezoelectric energy harvesting from bridge vibrations has the potential to power wireless sensors used for bridge health monitoring. Often, it is necessary to store the harvested energy before it could be used to power the sensor intermittently. However, the behavior of the piezoelectric energy harvester (PEH) with nonlinear interface circuits for energy extraction and storage subject to realistic bridge vibrations has not been fully understood. This work performs a comprehensive analysis on the performance of the PEH subject to the measured railway bridge vibrations and compares the energy stored on a capacitor using four different interface circuits. Firstly, the dynamic characteristics of the railway bridge is analyzed. A cantilevered PEH is then designed and fabricated based on the dynamic characteristics of the bridge. Subsequently, four realistic energy extraction and storage interface circuits, namely, the standard energy harvesting (SEH), synchronized charge extraction (SCE), parallel synchronized switch harvesting on inductor (P-SSHI) and series SSHI (S-SSHI) circuits, are evaluated and compared when the PEH subject to the measured bridge vibrations. The influence of the storage capacitance and the 1st short-circuit natural frequency of the PEH on the stored energy with these four circuits is then discussed. An optimal storage capacitance exists in the systems based on SEH, P-SSHI and S-SSHI circuits. The system based on P-SSHI circuit has the highest efficiency on energy storage. This work provides a technical framework to develop the realistic energy harvesting and storage system for realization of self-powered bridge condition monitoring.

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.