Piezoelectric stack energy harvesting with a force amplification frame: Modeling and experiment

With the continuous growth of global demand for renewable energy, the utilization of rainwater resources has gradually become a focal point of research. Piezoelectric energy harvesting has received significant attention due to its simple structure, high energy conversion efficiency, and self-powering capability. However, conventional piezoelectric energy harvesters are constrained by the narrow resonant frequency bandwidth and the insufficiency of waterproofing capabilities, limiting the energy conversion adaptability to variable environmental excitations. To address this issue, this study aims to design broadband piezoelectric cantilever energy harvesters for rainwater energy harvesting. Theoretical analysis, numerical simulations, and experimental validations are employed to investigate the influence mechanisms of droplet impact parameters, waterproof encapsulation techniques, and MFC cantilever structures on the electrical output performance. It reveals that the droplet's Weber number exhibits a direct proportionality with the impact force, which is distributed within the 0-80 Hz frequency range. Simulations and experimental results demonstrate that the U-shaped piezoelectric energy harvester significantly outperforms other designs in terms of broadening the resonant frequency range and extending oscillation duration, achieving an oscillation time of 23.7 s, a charge transfer of 2.82 μC, and an output power density of 37.76 W/m<sup>2</sup> under a single impact. It demonstrates its efficient energy harvesting capability over a wide resonance frequency range. Additionally, the U-shaped design also improves its waterproof performance, further enhancing its applicability in rainwater environments. This study provides a novel, universally applicable approach for rainwater energy collection, expands the application scenarios of piezoelectric energy harvesting technology, and offers theoretical references and practical guidance for the design and application of broadband energy harvesters.

Energy harvesting using piezoelectric materials is an alternative method for low power electronics, such as MEMS, wireless sensor network, portable devices, and nano structures, from extracting the ambient energy. Most piezoelectric energy harvesters are based on cantilever beams with laminated piezoelectric patches. To generate higher dynamic response of piezoelectric energy harvesters, tip mass is attached at the free end of the cantilever beams. Piezoelectric energy harvester array is another way to improve the power, i.e., installing a set of cantilever piezoelectric energy harvesters in close distance. In this research, a new design of piezoelectric energy harvester is proposed. The present design consists of an array of cantilever beams with permanent magnets at the free ends. The permanent magnets are introduced to transfer the excitation force to every cantilever beams. An experimental model is manufactured and experimental energy harvesting is carried out. Piezoelectric patches are laminated on clamped end of cantilever beams, and the permanent magnets are fixed at the free ends. All the magnets have opposite poles with each other to generate repelling force. Then these piezoelectric electric energy harvesters were connected to an AC/DC circuit and the power was measured. Also, the power of proposed piezoelectric energy harvester was compared with the piezoelectric harvesters without permanent magnets. The results show that, present design can generate higher power at the same excitation. Under the base excitation at the first natural frequency, the array of the cantilever beam show similar motion pattern, i.e., there is no phase difference between each other. At higher frequencies, the beams have a phase difference of π. Thus the crash between the cantilever beams can be effectively avoided. At lower excitation frequencies, the presented piezoelectric energy harvester vibration likes the first mode of a simple multi-degree-of-freedom system; and at higher excitation frequencies, the vibration of the presented piezoelectric vibrates like a second mode of a MDOF system.

A theoretical model of a micro piezoelectric energy harvester is proposed based on the nonlocal elasticity theory, which is operated in the flexural mode for scavenging ambient vibration energy. A nonlocal scale is defined as the product of internal characteristic length and a constant related to the material. The dependences of performance of the harvester upon the nonlocal scale and the scale ratio of the nonlocal scale to the external characteristic parameter are investigated in detail. Numerical results show that output power of the harvester decreases, and resonance frequency reduces gradually at first then increases rapidly when nonlocal scale increases. The results of nonlocal elasticity theory are compared with that of classic beam theory. All the results are helpful for material and structure design of the micro piezoelectric energy harvester.

All structures in nature have vibration energy which can be converted into Electrical energy. This electrical energy can be used as a source of energy to operate sensors thereby replacing limited storage capacity equipment's such as battery. Piezoelectric vibration energy harvesting scheme utilizes direct piezoelectric effect to convert mechanical energy into electrical energy. The output voltage from the piezoelectric vibration energy harvester depends on the relative motion between the base and proof mass. The resulted mechanical strain developed on the PZT patches is converted into electrical power because of direct coupling piezo electric effect. This article present a study of the effect of length of PZT patch on single modal linear vibration based piezo electric energy harvester (PEH). A coupled series piezo patch-electrical circuit finite element model is used to analyze the power output of a vibration based piezoelectric energy-harvesting device (EHD) when it is connected to a load resistor. Mathematical model of linear single modal Vibration -based Energy harvester is developed using Ansys APDL (Ansys parametric design Language). The modeling configuration is done with a series configuration of piezo electric layers. Accuracy of the developed FEM model is validated against the existing coupled FEM model. First modal analysis is performed to find the natural frequency of the piezoelectric energy harvester. Then harmonic analysis is carried out to estimate the voltage responses and power output which are measured through the PZT patches.

In order to reduce the natural frequency of the piezoelectric vibration energy harvester, improve performance of the piezoelectric vibration energy harvester, and meet the requirements of energy acquisition in the low-frequency vibration environment, a variable-section circular piezoelectric vibration energy harvester is presented. The dynamic model and electromechanical coupling model of variable-section circular piezoelectric vibration energy harvester are established. The main factors affecting the output performance of piezoelectric vibration energy harvester are analyzed. The structure parameters of piezoelectric vibration energy harvester are optimized by orthogonal experiment. An experimental platform is built to test output voltage and output power of piezoelectric vibration energy harvester. The experimental results show that when the number of energy harvester is 4 and the external load is 180KΩ, the parallel output power can reach 0.213mW, which can meet the requirements of micro-power device power supply.

In this work, a magnetic coupling 2-degree-of-freedom bistable piezoelectric energy harvester was designed and developed. The device consisted of a primary beam with a magnet attached to the tip and a parasitic beam. The magnets between the primary beam and the pedestal generated nonlinear repulsive force. By controlling the distance between two magnets, the system could oscillate between two stable equilibrium points which allowed the device to exhibit broadband characteristics. Theoretical and experimental investigations of this energy harvester were presented over a range of excitation frequencies. Lumped-parameter nonlinear equations of the bistable Duffing oscillator with magnetic coupling were introduced to describe the broadband voltage response. Compared with the theoretical results, at an excitation acceleration of 3 m/s2, it is experimentally verified that the proposed device achieved the operation frequency bandwidth adding up to 8 Hz at around the first and second resonance regions which was about 2.7 times higher than conventional 2-degree-of-freedom linear harvester one. In addition, energy harvesting efficiency could be improved by increasing the frequency bandwidth. The results of this work can be applied to optimize the design of piezoelectric energy harvester and harvest low-frequency vibration energy in the environment to supply power for sensor network nodes.

This study presents the analytical solution and experimental investigation of the galloping energy harvesting from oscillating elastic cantilever beam with a rigid mass. A piezoelectric wafer was attached to galloping cantilever beam to harvest vibrational energy in electric charge form. Based on Euler-Bernoulli beam assumption and piezoelectric constitutive equation, kinetic energy and potential energy of system were obtained for the proposed structure. Virtual work by generated charge and galloping force applied onto the rigid mass was obtained based on Kirchhoff's law and quasistatic assumption. Nonlinear governing electro-mechanical equations were then obtained using Hamilton's principle. As the system vibrates by self-exciting force, the fundamental mode is the only one excited by galloping. Hence, multi-degreeof-freedom equation of motion is simplified to one-degree-of-freedom model. In this study, closed-form solutions for electro-mechanical equations were obtained by using multi-scale method. Using these solutions, we can predict galloping amplitude, voltage amplitude and harvested power level. Numerical and experimental results are presented and discrepancies between experimental and numerical results are fully discussed.

Piezoelectric energy harvesting has received great attention over the last years. The main goal of this work is to discuss the potential advantages of introducing nonlinearities in the dynamics of a beam type piezoelectric vibration energy harvester. The device is essentially a cantilever beam partially covered by piezoelectric material with a magnet tip mass. Also, we consider the nonlinear constitutive piezoelectric equations. The electromechanically coupled equations are solved numerically, through the initial value problems for ordinary differential equations. The frequency response of the system is approximated using the method of multiple scales. The electrical power output is calculated by varying the amplitude of the base acceleration, the distance between the magnets and the load resistor. The stability of the system is also investigated. Stochastic variations are introduced in some key parameters and the propagation of these uncertainties is investigated through Monte Carlos simulations. From the numerical results it is found that the influence of the parameters investigated in the frequency range of operation of the device and the nonlinear effects present on the device energy harvester extend the useful frequency range of these. Moreover uncertainty parameters affect the natural frequency and the power output harvester. Through experimental tests it has been confirmed the benefits of introducing nonlinearities in piezoelectric energy harvesters.

Vibrational energy harvesters, also referred to as MEMS (Micro-Electro-Mechanical Systems) piezoelectric energy harvesters, have garnered significant attention for their potential to power wireless sensor networks and low-power electronics without external power sources. Piezoelectric materials, due to their high energy conversion efficiency and seamless integration into microsystems, are widely utilized in such designs. In this study, we simulate MEMS piezoelectric energy harvesters using PZT (lead zirconate titanate) material, each constructed with a silicon core layer and PZT piezoelectric layers. The simulations, conducted using COMSOL Multiphysics, analyze the performance of cantilever-shaped harvesters under identical boundary conditions, including solid mechanics, electrostatics, and an electric circuit with a 10 kΩ resistive load. The results show that natural frequencies range from 100 Hz to 500 Hz depending on the cantilever shape, with the generated voltage varying between 1.2 V and 3.5 V and corresponding power outputs ranging from 0.2 μW to 1.5 μW. These variations highlight the influence of cantilever geometry on energy harvesting efficiency. The study also identifies specific advantages, such as higher power density and tunable frequency ranges, making these harvesters suitable for powering remote sensing devices and microscale electronics. By quantifying performance metrics and demonstrating shape-dependent benefits, this research provides valuable insights into the design and optimization of MEMS piezoelectric harvesters for diverse applications.Keywords: Piezoelectric vibration energy harvesters, COMSOL simulation, MEMS vibrational energy harvesters, bimorph design.

Current research on wind energy piezoelectric energy harvesters (PEHs) mainly focuses on tandem smooth cylinder energy harvesters; however, the traditional tandem smooth cylinder energy harvester has low voltage output and narrow energy harvest bandwidth. In this study, a D-type bionic fin is designed and installed on a smooth cylindrical surface to improve its performance. The influence of the spacing ratio on the amplitude and voltage of PEHs with D-type bionic fins added under elastic interference was investigated through wind tunnel tests. Three installation positions were designed: only installed upstream, only installed downstream, and not installed upstream and downstream (BARE). It was found that the maximum displacement of the upstream PEH (UPEH) was not apparently affected by the D-type bionic fin. Contrastingly, the fin changed the maximum amplitude from a small to a large spacing ratio for the downstream PEH (DPEH). D-type bionic fin can enhance energy harvest performance by coupling “coupled vortex-induced vibration” and wake induced galloping, increasing the surface velocity of PEHs and expanding the bandwidth of the voltage harvested by the PEHs. Analysis of the power under the experimental wind speed showed that installing D-type fins in the PEHs can increase the output power of the upstream and downstream PEHs by 392.28% and 13%, respectively, compared with that of the BARE-PEH. Additionally, computational fluid dynamics was used to analyze the flow pattern, wake structure, and lift coefficient of the PEHs, and to explain why the upstream D-type bionic fin installation has an impact on the harvest performance of the upstream and downstream PEHs at a spacing ratio of 1.5. This study provides an efficient and simple scheme for designing wind PEHs.

The suspension system is an important component of a truck. It provides stability to the vehicle, maneuverability, and comfort. A lot of energy is dissipated through this system. In order to scavenge this dissipated energy, piezoelectric stacks can be installed in the system. One of the factors which significantly impacts the harvested power voltage is the location and connection type of the piezoelectric stack in the suspension system. The series connection between the suspension spring and the piezoelectric material has been preferred in this study for it will not affect the mechanical properties and performances of the system. The equivalent system stiffness is increased and the ride comfort is negatively affected in case of a parallel connection between the suspension spring and the piezoelectric stack. The equations of motion of the truck were derived. Harmonic excitation simulations have been run in the MATLAB Simulink software in order to assess the potential of the energy harvesting from truck suspension systems through piezoelectric stacks.

Piezoelectric energy harvesting has been extensively investigated to provide a sustainable power supply for small-scale devices. Though significant progress has been made in the past two decades, accurate modeling of piezoelectric energy harvesters (PEHs) still remains difficult or usually involves parametric identification from experimental results. This paper explores and leverages deep learning techniques for modeling behaviors of nonlinear PEHs. To this end, we present a deep learning-based surrogate model for nonlinear response analysis of PEHs with high complexity and strong nonlinearity. The key concept is to establish a long short-term memory (LSTM) neural network to capture the dynamic properties of the piezoelectric energy harvesters from limited training data and infer the voltage and power given unseen excitations in a data-driven fashion without the need of conventional time-consuming numerical simulation or parametric identification. In addition, the input and output sequences are preprocessed into stacked structures to reduce the complexity and enhance the feature learning. The performance of the proposed approach was successfully demonstrated through numerical data of a monostable PEH of Duffing stiffness nonlinearity and piezoelectric material nonlinearity. The results indicate that the proposed framework is a promising, reliable and computationally efficient approach for nonlinear response modeling of complex piezoelectric energy harvesters.

Energy harvesting is defined as a process of acquiring energy surrounding a system and converting it into electrical energy for usage. Piezoelectric energy harvesting is a very important concept in energy harvesting in microelectronics. In this report, an analysis of the cantilever type piezoelectric energy harvester is conducted using the finite element method (FEM) based software COMSOL Multiphysics. A unimorph type cantilever beam of the silicon substrate, structural steel as proof mass and support, and PZT-5A material as piezoelectric constitute the physical system.

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.

Context: Energy harvesting has positioned itself an emerging area of research due to recent developments in low-power electronics, the Internet of Things, and artificial intelligence. Various diode-based circuits and alternatives have been proposed in the literature, but the application of CMOS cross-coupled circuits, specifically in piezoelectric energy-harvesting systems, has not been properly explored. Method: An experimental study was conducted in order to assess the performance of a two-stage cross-couple MOS-based voltage multiplier in piezoelectric and solar energy harvesting. A piezoelectric disc was used to evaluate the output. The piezoelectric output was obtained by applying a small pressure to the input, and a 6 V panel was employed in the solar energy setup. Results: The proposed circuit provides a 1.91-fold voltage gain in the piezoelectric energy harvester. Conclusions: The two-stage MOS-based cross-coupled voltage multiplier circuit performs better than the diode-based alternative in the piezoelectric energy harvester. These experimental results show encouraging prospects for green energy, low-power electronics, and Internet of Things applications, among others.