Bimorph Piezoelectric Energy Harvester Research Articles

Modeling and analysis of a macro-fiber piezoelectric bimorph energy harvester operating in d33-Mode using Timoshenko theory

Piezoelectric bimorph cantilevered beams are frequently employed in energy harvesting applications. The use of macro-fiber composites, which combine piezoelectric fibers with rectangular cross-sections and interdigitated electrodes, has significantly enhanced their performance by enabling operation in the 33-mode of piezoelectricity, thereby increasing conversion efficiency. In this article, the Timoshenko beam theory is applied to overcome the limitations of the Euler-Bernoulli theory in modeling transverse vibrations of harvesters with low slenderness ratios (length to thickness ratios). The mixture rule formulation is applied to determine the equivalent properties of the macro-fiber composite (MFC) structure. The electromechanical properties of a representative volume element (RVE) bounded by two successive interdigitated electrodes are coupled to the overall electro-elastic dynamic model of the structure using the Timoshenko theory. Frequency response functions for the power and tip vibration displacement of the MFC bimorph beam are determined from the model. Experimental data from the literature are used to validate the improved results predicted by the model developed in this article. A comparative analysis between the electromechanical responses predicted using a model based on Timoshenko and a model based on Euler-Bernoulli theory is conducted showing agreement, for harvesters with large slenderness ratios and discrepancies of up to 30% for low slenderness ratios. It has also been shown that the model based on Euler-Bernoulli theory overestimates both the mechanical and the electrical responses for low slenderness ratios as the shear and rotary inertia effects are not negligible in this case.

Experimental investigation of damages in the bimorph piezoelectric energy harvester with multilayer composite substrate

Composite materials, regarding their lightweight, can be considered a suitable option for the next generation of piezoelectric energy harvesters, which are used for supporting low-power applications. Also, due to the broader selection range and different stacking sequences, one of the advantages of these materials is that they can provide better stiffness adjustment of the structure to achieve the desired frequency of energy harvesting from the ambient vibration. Despite all these advantages, one of the challenges in the widespread use of this type of material is the complex damage behavior and less information about their damage behavior compared to other traditional materials. The bimorph piezoelectric energy harvester studied in this work has a three-layer woven substrate in the form of [0/90]; its behavior and performance in the presence of some well-known damage mechanisms in the composite structures, such as the mid-layer transverse cracks are investigated. A crack density-based stress transfer method, from a micromechanical point of view, is employed to calculate stiffness reduction due to damages in the bimorph. The effect of the damping coefficient on analytical modeling is considered, and the parameter of the damping ratio is given by the experimental test. Effects of damages on the mechanical parameters like resonance frequency, as well as the electrical parameters like output voltage, are investigated. It is observed that the presence of fabricated transverse cracks in the mid-layer of the bimorph piezoelectric energy harvester increases the value of the damping ratio and also decreases its stiffness. Finally, the output voltage is investigated, which reduces by the mid-layer transverse cracks.

Exact solutions for doubly curved laminated cross-ply and antisymmetric angle-ply shell substrate based bimorph piezoelectric energy harvesters

Exact solutions for doubly curved laminated cross-ply and antisymmetric angle-ply shell substrate based bimorph piezoelectric energy harvesters

Nonlinear dynamic response of bimorph piezoelectric energy harvester with functionally graded porous core

This study deals with piezoelectric energy harvesters carrying the magnet at the free end while a magnifier connected them to the base. The harvester consists of a cantilever beam with Functionally Graded (FG) porous foam core and two piezoelectric faces while taking into account the von-Karman strains and the magnetic interaction of two magnets. The governing equation has been developed using Hamilton’s principle and reduced-order via the Galerkin method. Frequency response of vibrations and voltage derived using harmonic balance method and the adjusted model has been confirmed by parametric studies of the lumped parameter model. A parametric study is also performed to expose the effects of porosity coefficient and pattern, magnifier ratios, and excitation level on the responses. Results show that by correct selection of the magnifier parameters, the proposed harvester can provide a higher output over a wider frequency band. Also, the core porosity increases the flexibility of the beam and raised the voltage by a factor of 1.8.

Comparative Study of Tapered Shape Bimorph Piezoelectric Energy Harvester via Finite Element Analysis

We report the power efficiency comparison of two tapered shape bimorph piezoelectric energy harvesters. Typically, the rectangular-shaped cantilever bimorph piezoelectric energy harvester is widely used in piezoelectric energy harvesting. Using the finite element analysis toolbox, we have compared the power efficiency of the triangular and trapezoidal shape bimorph piezoelectric energy harvester. The resonance frequency of these tapered shape harvesters has been extracted using modal analysis, at which maximum power efficiency of the harvester can be achieved. Our study shows that triangular shape bimorph piezoelectric energy harvesters generate more power than trapezoidal harvesters. In addition, lower resistance is required for the triangular bimorph harvester to generate maximum power at resonance, ensuring greater efficiency with minimal loss in sensing applications than the trapezoidal bimorph harvester.

Lightweight Piezoelectric Bending Beam-Based Energy Harvester for Capturing Energy From Human Knee Motion

Harvesting energy from the human body has attracted substantial attention from industries and academics as it is a promising solution to address the battery life issue. In this article, we developed a bimorph piezoelectric bending beam-based energy harvester to scavenge energy from the human knee motion for powering body-worn electronics such as smartwatches and health monitors. During walking, the human knee will flex and extend to periodically deform piezoelectric macro fiber composites (MFC) bounded to the bending beam, thus generating electricity. The mathematical models of the whole system including the model of the large deflection of the bending beam, movement analysis of the end of the bending beam (slider-crank mechanism), the model of piezoelectric transducers, and measurement of the human knee angle are developed to comprehensively study the harvester. To validate the presented mathematical models, experimental testing on a human body when the subject walks on a treadmill at three different walking speeds is conducted here. The experimental results show good agreement with the simulation results, which indicates that the developed models can characterize the harvester. In addition, the performance of the harvester walking in different contexts is also evaluated. The average power can reach 12.79 mW for level-ground walking, 9.91 mW for stair descending, and 7.70 mW for stair ascending, when walking at a self-selected speed.

Investigation of a nonlinear piezoelectric energy harvester with advanced electric circuits with the finite element method

In this contribution, a system simulation method based on the finite element method (FEM) is applied to simulate a strongly coupled bimorph piezoelectric vibration-based energy harvester (PVEH) with various nonlinear, non-ideal and active circuits: The standard circuit, the synchronized switch harvesting on inductor circuit and the synchronized electric charge extraction circuit are considered. Furthermore, nonlinear elastic behavior of the piezoelectric material is taken into account and harmonic base excitations of different magnitudes at a fixed frequency are applied. The holistic FEM-based system simulation approach solves the complete set of piezoelectric equations together with the equation of the electric circuit such that all electromechanical coupling phenomena are taken into account. This fully coupled numerical analysis enables the detailed evaluation of the influences of the electric circuits on the vibrational behavior and the harvested energy of the PVEH with respect to the magnitude of base excitation. Results from literature on the efficiency of electric circuits are confirmed and interactions between mechanical and electrical nonlinearities of PVEHs are revealed.Article highlightsSystem simulations of a mechanically and electrically nonlinear piezoelectric energy harvester are performed using only one software tool.The infuence of electric circuits on the vibration behavior and the effciency of an energy harvester are investigated in detail.Interactions between mechanical and electrical nonlinearities of an energy harvester are revealed.

Nonlinear analysis of unimorph and bimorph piezoelectric energy harvesters with flexoelectricity

This work investigates the nonlinear behaviors of nanoscale unimorph and bimorph piezoelectric energy harvesters under harmonic base excitations. In the modeling, the energy harvesters are based on cantilevered beams with tip mass, and the effects of geometric nonlinearity, inertial nonlinearity and flexoelectricity are considered. Based on the Hamilton’s principle and the theory of flexoelectricity, the nonlinear coupled governing equations of the system are derived. Galerkin’s method is employed to discrete the nonlinear equations, which are then numerically solved. Results indicate that geometric nonlinearity leads to a typical hardening nonlinear behavior of the frequency response curve while inertial nonlinearity leads to a softening behavior in contrast. In addition, influences of the tip mass and amplitude of the base acceleration on the harvesters’ electrical outputs are examined. By comparing lead zirconate titanate (e.g. PZT-5H) and polyvinylidene difluoride (i.e. PVDF) as the material for piezoelectric layers, it is found that the performance enhancement of PVDF energy harvester due to flexoelectricity is more prominent. It is also interesting to observe the flexoelectricity-induced size-dependent voltages. This work compares the performance of energy harvesters with various structures and materials, which will provide guidance for the design and optimization of piezoelectric energy harvesters utilizing flexoelectricity.

Introducing an extremely high output power and high temperature piezoelectric bimorph energy harvester technology based on the ferroelectric system Bi(Me)O3-PbTiO3

Here, we outline the material selection and design of a novel bimorph piezoelectric energy harvester with an extremely high energy harvesting output power density of over 8 mW/g2 cm3 up to 250 °C. With optimized mass loading, the performance can achieve five times higher output power density from 5.64 to 29.77 mW/g2 cm3, with reduced frequencies of 580–69 Hz in loading tip masses of 0.8 and 30 g, respectively. The novel harvesters were fabricated utilizing (1 − x)BiScO3-xPbTiO3 piezoceramic composition and designed to achieve the maximum figure of merit (d33 × g33), which was 15.5 × 10−12 m2/N when x = 64%. The harvester remains operational even at temperatures above 250 °C but demonstrates a systematic falloff of the high performance values with power densities of 8.7, 5.4, and 1.4 mW/g2 cm3 at 250, 300, and 350 °C, respectively. It should be noted that these performance numbers are still high compared to previous reports in the literature. The focus was then to improve the bonding/interface and dimensions that minimize clamping and depoling conditions in order to optimize the overall harvester design. We systematically outline the design considerations for room temperature and high temperature performance. Hence, we introduce a guideline for a novel bimorph harvester to provide significantly increased output power levels (mW) for higher temperature applications.

A Lead-Free Spiral Bimorph Piezoelectric MEMS Energy Harvester for Enhanced Power Density

Tiny sensor nodes are the demand of smart and intelligent systems. These sensor nodes require on-board self-powered generating systems. Also, such generators should have lesser size. MEMS energy harvesters are profoundly used as the on-board self-powered generators. However, the size constrain imposes an important design trade-off on such devices. This trade-off is in-between areal dimension and the resonant frequency. In this paper, we have proposed an efficient bimorph energy harvester design which produces higher power density at very low resonance frequency. We have considered the poisonous behavior of lead-based devices as well and proposed lead-free designs in our work. The proposed design consists of a bimorph square plate of 2.25 mm2 with two Zinc Oxide (ZnO) layers of 0.5 µm each sandwiched a copper electrode layer of 1 µm. A spiral cut of 5 µm thickness is made over the plate in order to form a fixed free beam structure. Furthermore, without the inclusion of tip mass, the resonant frequency of the beam is controlled by varying the number of spiral turns. Our proposed design outperformed the previous designs by producing maximum output power of 15 nW at 110 Hz with seven spiral turns with very lower active volume. Also, it has a normalized volumetric power density of 3 × 10−2 µW/mm3 g2 Hz.

Multi-piezoelectric materials based doubly clamped energy harvester

The challenge of continuously powering the wireless sensor network located at remote areas has been resolved by the emergence of piezoelectric energy harvester. This paper evolved a new idea of using different piezoelectric materials together within segmented doubly clamped bimorph piezoelectric energy harvester (DCBPEH). The finite element modeling of the device has been presented here using COMSOL multiphysics software. This paper starts with concept of strain nodes and further better performance of segmented electrodes-based beam over the continuous electrode-based beam has been achieved. Next, a performance analysis study with continuous electrode-based beam has been carried out for different variants of two piezoelectric materials, namely, PMN-xPT and PZT. From this study, PMN-35%PT and PZT-5H piezoelectric materials are found to be best variants. Finally, the performance of segmented DCBPEH has been observed for different positioning formats of PMN-35%PT (M1) and PZT-5H (M2) piezoelectric materials on different segments of the beam. From this analysis, M1–M1–M2 and M2–M1–M1 are noted to be two favorable positioning formats which provide similar and maximum performance (7.78 mW) as compared to other formats.

Nonlinear broadband performance of energy harvesters

Broadband nonlinear energy harvesting capabilities of a parametrically excited bimorph piezoelectric energy harvester is investigated for the first time. The performance of the energy harvester is significantly enhanced via use of stoppers and an added tip mass in conjunction with parametric excitation. A fully nonlinear electromechanical model of the energy harvester was developed using beam theory of Euler-Bernoulli and the coupled constitutive equations for piezoelectric materials, with the motion constraints modelled as nonlinear springs. A multi-modal discretisation was conducted utilising the Galerkin scheme; the resultant set of equations was examined numerically through use of continuation technique. It is shown that a resonance bandwidth of 46% (normalised with respect to parametric resonance frequency) is achieved which is almost 10 times the resonance bandwidth of the system without any constraints.

A constrained broadband nonlinear energy harvester

This paper investigates the nonlinear electromechanical behaviour of a constrained bimorph piezoelectric energy harvester utilising a coupled multi-modal fully nonlinear model, for the first time. The electromechanical system is modelled via using the nonlinear beam theory of Euler-Bernoulli, while assuming an inextensible centreline, and the piezoelectric constitutive equations. The motion constraints are modelled as nonlinear springs, consisting of linear and cubic terms. The coupled electromechanical model, including the electrical circuit equation, is obtained for both parallel and series connections of the piezoelectric layers. The Galerkin scheme is used to discretise the partial differential-type model while retaining a large number of modes to guarantee converged results. Next, the electromechanical model consisting of geometric, inertial, impact, and piezoelectric-type nonlinearities is solved using a well-optimised continuation code. The proposed model and numerical method are verified through comparison to experimental data in the literature. It is shown that adding a tip mass of 50% of the bimorph cantilever mass increase the power output by 263%. Additionally, it is shown that for a power output threshold of 15 mW, the addition of motion constraints results in a 66.8% resonance bandwidth (normalised with respect to first natural frequency) which is almost 10 times the bandwidth of the unconstrained system.

Global sensitivity analysis of piezoelectric energy harvesters

Vibration energy harvesting using the direct effect of piezoelectricity has attracted increasing attention during the last two decades. Different modeling techniques have been applied to describe the electromechanical coupling effect of a piezoelectric harvester and to predict its electrical output. This study aims to identify the most important properties of both harvester substrate material and piezoelectric material that cause uncertainty in the predicted performances of the harvester. Global sensitivity analysis, applied in this paper, is a promising method used to identify systems parameters which have significant impact on the system output. In this paper, the Elementary Effects method (EEs), a particular implementation of the global sensitivity method, is used to identify the impact of substrate and piezoelectric material properties on the voltage frequency response function of a typical bimorph piezoelectric energy harvester with fixed geometry. With a small number of model evaluations at selected ranges of material properties, it has been found that the elastic modulus and density of the piezoelectric layer are the parameters which lead to the largest output variability. Furthermore, it has been found that the order of importance of the parameters can change from short-circuit to open-circuit conditions.

Design, Fabrication, and Characterization of Bimorph Micromachined Harvester With Asymmetrical PZT Films

This paper presents a high-performance bimorph MEMS cantilever harvester with partially covered asymmetrical functional piezoelectric layers on both sides of a beryllium bronze foil. The optimal PZT coverage length is employed to improve the output power density. The two piezoelectric layers with the controlled different thicknesses for the top and bottom PZT layers can provide three different output powers. Furthermore, a proof mass tungsten bonded at the free end of the cantilever can reduce the resonant frequency. The experimental results showed that the serial-connected bimorph piezoelectric energy harvester can obtain the maximum power density of 26.90 mW/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> at the matched loading resistance of 660 kQ under 1.5-g acceleration at the resonant frequency of 38.89 Hz. The normalized power density of the harvester can reach 307.4 μW·g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> · cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Meanwhile, the harvester provides good stability under 1.5-g acceleration amplitude.

Topology optimization of bimorph piezoelectric energy harvesters considering variable electrode location

With the advances on additive manufacturing techniques for piezoelectric materials, it is becoming steadily more viable to produce piezoelectric structures with complex geometries. Since such devices can have more sophisticated shapes, the application of topology optimization techniques can be used to explore optimized topologies for piezoelectric energy harvesters with varying thickness. In this context, challenges arise in the application of the electrode equipotential constraints during the optimization process. In this work, an algebraic formulation was proposed to tackle this issue when optimizing a harvester’s topology. A bimorph piezoelectric energy harvester with series connection of the piezoceramic layers was modeled under plane strain hypothesis in the thickness profile, first not applying and then considering periodicity constraints in the optimization process, while concurrently improving the electrodes. This paper shows how the open-circuit harvesting device was modeled and its finite element formulation. Lastly, an adaptation of the bidirectional evolutionary structural optimization method is proposed, in order to approach this problem.

Analysis of bimorph piezoelectric beam energy harvesters using superconvergent element

Cantilever-based piezoelectric energy harvesters have been utilized as structures to extract mechanical energy from the ambient mechanical vibrations and transfer it into the electrical output. In this article, the performance of bimorph piezoelectric beam energy harvesters is investigated. The cantilever beam is modeled by using both Timoshenko and Euler–Bernoulli beam theories. The equations are discretized using the conventional finite element method and superconvergent element. Besides the high rate of convergence, easy switching between the above beam theories is enabled by such type of element. The current model is presented for a Timoshenko beam model, but it could as well be used for a Euler–Bernoulli beam model. In addition, voltage, current, and power frequency response functions for different ranges of load resistance varying from the short-circuit to open-circuit conditions are determined to reach the maximum values. Effects of the slenderness ratio and the required beam model based on the geometric properties of the piezoelectric energy harvesters are discussed in the final part of this study. The results show that only for smaller values of the slenderness ratio (below 5), it is necessary to model the beam using the Timoshenko assumptions; otherwise both beam theories provide approximately the same responses.

Analytical modelling of a nanoscale series-connected bimorph piezoelectric energy harvester incorporating the flexoelectric effect

This paper concerns the derivation of analytical solutions for a nanoscale series-connected bimorph piezoelectric energy harvester incorporating the flexoelectric and the non-local effects. The complexity involved in a parallel-connected bimorph piezoelectric energy harvester case is also briefly discussed here. Considering electric Gibbs free energy density and Euler Bernoulli beam theory, the governing equations and associated boundary condition are derived using the extended Hamilton principle. The convergent series of eigenfunctions and generalised modal coordinates related to mechanical deformation is utilised to obtain the closed-form analytical solutions for non-periodic and harmonic base excitations. The modelled harvester is validated separately from piezoelectric as well as flexoelectric point of views. Results for harmonic base excitations show that, at each excitation frequency, the consideration of flexoelectric effect in series connected bimorph piezoelectric energy harvester abruptly increases the voltage, current and power density outputs whereas it decreases the tip velocity. Here, the addition of flexoelectricity enhances the power density by ten times. The benchmark presented here may be useful for the verification of future experiments and the present study suggests that the flexoelectric effect is a significant aspect for the effective exploitation of bimorph piezoelectric energy harvester in advanced applications such as smart nanosensors.

Bimorph piezoelectric vibration energy harvester with flexible 3D meshed-core structure for low frequency vibration

ABSTRACTThis paper proposes a bimorph piezoelectric vibration energy harvester (PVEH) with a flexible 3D meshed-core elastic layer for improving the output power while lowering the resonance frequency. Owing to the high void ratio of the 3D meshed-core structure, the bending stiffness of the cantilever can be lowered. Thus, the deflection of the harvester and the strain in the piezoelectric layer increase. According to vibration tests, the resonance frequency is 15.8% lower and the output power is 68% higher than in the conventional solid-core PVEH. Compared to the solid-core PVEH, the proposed meshed-core PVEH (10 mm × 20 mm × 280 μm) has 1.3 times larger tip deflection and the maximum output power is 24.6 μW under resonance condition at 18.7 Hz and 0.2G acceleration. Hence it can be used as a power supply for low-power-consumption sensor nodes in wireless sensor networks.

A new nonlinearly tapered FGM piezoelectric energy harvester

This work presents an analytical model for the development of a piezoelectric energy harvester with general nonlinear geometry and functionally graded material (FGM) properties based on Adomian decomposition method. The model is applied to geometrically and materially non-uniform beams with structural strain rate damping and surface bonded piezoelectric layers to derive the dynamic response of the smart structure to base motion excitations and efficiently harvesting the subsequent vibrational energy. Firstly, the steady state vibration response of the smart non-uniform FGM beam subjected to a harmonic base motion is obtained and then electromechanical outputs of the piezoelectric patches are analytically derived. Furthermore, a comprehensive parametric study for bimorph piezoelectric energy harvesters with different nonlinearly tapered geometry and FGM properties in a wide frequency range has been done. Considering the same volume of the harvester, it is demonstrated that the novel non-uniform FGM design can significantly increase the electrical output of the harvester by more than 19.76 times compared to the traditional uniform homogenous design. With the presented methodology, optimum structural design for piezoelectric energy harvesters with respect to the operation frequency domain can be effectively achieved.