Piezoelectric Bimorph Beam Research Articles

Finite element analysis of the electro-mechanical coupling effects in piezoelectric laminated structures

This study utilized the COMSOL Multiphysics software to conduct finite element analysis on the piezoelectric coupling effect of the composite layer structure. The article begins by introducing the basic principles and history of the piezoelectric effect, emphasizing the importance and widespread application of piezoelectric materials in the field of smart materials. Subsequently, it defines in detail the models of bimorph piezoelectric beams and multilayer composite piezoelectric plates, and conducts potential verification. The bimorph piezoelectric beam model uses PVDF material, and the potential distribution is monitored by boundary probes, confirming the influence of the quantity and distribution of sensor electrodes on voltage distribution. The multilayer composite piezoelectric plate model combines a Si non-piezoelectric semiconductor layer with a PZT-4 piezoelectric material layer, demonstrating the in-plane distribution of potential under lateral mechanical loads. This study not only verifies the reliability of COMSOL software in piezoelectric coupling analysis but also provides an in-depth understanding of the behavior and performance of piezoelectric materials in complex environments.

3D meshless modeling of piezoelectric structure based on the radial point interpolation method

Piezoelectric materials find widespread applications in high-precision actuators and sensors. However, the traditional finite element method falls short in meeting the simulation needs of piezoelectric structures due to complexities in mesh generation and precision requirements for accurate simulations. This paper focuses on adapting and generalizing the meshless modeling technique based on the radial point interpolation method to address three-dimensional simulations of piezoelectric structures and accurately model positive and inverse piezoelectric behaviors. The piezoelectric body is discretized into point cloud data, and displacement and potential are approximated by interpolating values through the radial point interpolation method. Subsequently, a 3D meshless model for general piezoelectric structures is formulated based on the principle of minimum potential energy. The influences of key factors on interpolation accuracy and computational cost were discussed. Numerical examples, featuring a 3D piezoelectric bimorph beam as actuators and sensors, validate the efficacy of this extended approach. Results affirm that the three-dimensional meshless method, rooted in the radial point interpolation technique, achieves superior accuracy in predicting piezoelectric behavior compared to the traditional finite element method. This adaptation not only enhances the applicability of meshless modeling but also represents a significant advancement in accurately simulating complex three-dimensional piezoelectric structures.

Integrated mechatronic design of an industrial piezoelectric vibration energy harvester

Increased consumption of non-renewable energy sources, such as batteries, have led to increased environmental pollution and critical energy crises. Harvesting energy from vibration sources, using piezoelectric cantilevers, may be one of the main solutions to extending the life of the battery of some autonomous devices and either reducing or eliminating the need to replace them in service. This would make sensors self-powered, for instance. To minimize the volume of the Energy Harvester, a configuration with a circular frame supporting a radial set of bimorph piezoelectric beams with a proof mass at the tip is proposed. An analytic model is first developed to investigate the behavior of the electromechanical coupling, preliminarily sizing the design parameters, and to estimate the maximum power converted. A numerical model is then developed, in the COMSOL® Multiphysics software, to analyze all of the system details. Some FEM analyses allow for verifying the accuracy of the analytic model and predicting the dynamic system behavior under different load conditions. A critical issue in properly predicting the performance of such device is the electric circuit which is coupled to extract the charge produced. Therefore, the design of this read-out circuit is herein addressed. The LTspice XVII® software is then used to model the charge readout circuit. The electronic components interconnected within the circuit are first determined, and their electrical dynamic behavior is studied when coupled with the mechanical system. The efficiency of charge production and energy storage is evaluated by integrating the whole electromechanical system, including the readout circuit with the numerical model. The performance looks compatible with the required values proposed for some practical industrial applications, being also described.

Design and testing of ultraminiature microelectromechanical systems middle ear accelerometers

Moderate to severe hearing loss is a debilitating condition that affects over 5% of the world’s population. Hearing aids and cochlear implants positively impact the lives of those who suffer from sensorineural hearing loss. However, both display numerous limitations that affect their adoption and use rates, notably including those associated with the external elements of these devices (e.g., microphone and signal processor). These external components impact device safety, appearance, acoustic performance, and ease-of-use. A totally implantable auditory prosthesis would help to address these issues by eliminating external components. A major barrier to progress toward this goal is the lack of a completely implantable acoustic sensor capable of matching or exceeding the performance of commercial external microphones. Our previous studies have indicated that piezoelectric microelectromechanical systems (MEMS) accelerometers have the potential to function as implantable sensors within the middle ear meeting a 20-phon noise floor over a 100–8 kHz range. In this paper, we describe a process to design and fabricate dual and tri-resonance devices that are comprised of piezoelectric cantilever bimorph beams tip-loaded by a proof mass, can meet or exceed the 20-phon noise floor, and can produce a measurable voltage output when deflected by sound-induced ossicular vibrations.

A novel method to fully suppress single and bi-modal excitations due to the support vibration by means of piezoelectric actuators

Vibration attenuation and control is a typical topic in mechanical, civil and aeronautical engineering. In recent years, there has been extensive research on smart materials and among all of them, the piezoelectrics seem to be the most attractive for passive and active vibration damping applications. Furthermore if multiple modes are concurrently excited, as in case of turbomachinery blades, active damping systems may remarkably increase their life-cycle and outweigh the shortcomings of implementing such systems. However the damping efficiency of the piezoelectric actuators is strictly bound to their driving voltage, size and location on the structure.In this work, a cantilever piezoelectric bimorph beam under base motion is considered and the analytical expression of the electric potential that nullifies the elastic tip displacement of the beam is derived in case of single and bi-modal excitations.The model allows to identify for every bi-modal excitations a set of solutions, each of them represented by three parameters: voltage amplitude, left and right corner positions of the piezoelectric actuators pair. As a result, designers can choose the best solution for their specific application demands. For example, if the supply voltage must to be kept as low as possible, then wider actuators should be used and vice versa. It was also found out that the control parameters do not depend on the spectral distribution between the two excited modes. Hence, even if the spectral distribution between the two coupled modes changes over time, it is not necessary to adjust either the voltage or the position of the actuator pair.The analytical predictions were compared with the results of FEM multi-physics simulations for several base motion excitations and a fair agreement was observed.

Piezoelectric vibration energy harvesting device based on water sloshing-inspired extensions

Inspired by shallow-water sloshing in a moving tank, a novel type of vibration-based piezoelectric energy harvesting device composed of a piezoelectric bimorph beam and an extension tank is proposed in this paper. The structure and working principle of the proposed device are provided. Then, the effects of different heights of water filling in the tank on the performances of the harvester are studied and analyzed. Experiments are set up to investigate the actual device performance by changing the base excitation frequency and load resistance for different water heights. The results show that by modulating the water height, the resonant frequency and bandwidth can be adjusted, which can enhance the energy harvesting performance of the device at different ambient vibration frequencies. This study provides some clues to improve the performance of the vibration-based energy harvesting devices.

A study on the integral resonant vibration control of a piezoelectric bimorph beam with a negative direct feedthrough

A study on the integral resonant vibration control of a piezoelectric bimorph beam with a negative direct feedthrough

Design and simulation of MEMS piezoelectric vibration energy harvesters with centre mass block

MEMS-based piezoelectric vibration energy harvesters (MEMS-PVEHs) with center mass block are designed with the overall size 10 × 10 × 2 mm3, two prototypes including piezoelectric unimorph and bimorph beams are used respectively. This paper studies the characteristics of MEMS-PVEHs by modeling and simulation in COMSOL. Their eigenfrequencies are analyzed firstly, their optimal piezoelectric outputs are explored by changing excitation frequency and load resistance secondly, then the piezoelectric unimorph and bimorph beams are compared finally. The simulation results show that the optimal excitation frequency is slightly higher than the eigenfrequency, and the maximum piezoelectric power of the PVEH can be obtained only when the appropriate excitation frequency and load resistance are selected, and the power generation efficiency is 0.5. It has little difference between unimorph and bimorph to improve the MEMS-PVEH piezoelectric output. Finally, the piezoelectric unimorph with double opposite electrodes is designed based on the MEMS fabrication process.

A Frequency Up-Converted Hybrid Energy Harvester Using Transverse Impact-Driven Piezoelectric Bimorph for Human-Limb Motion.

Energy harvesting from human-body-induced motion is mostly challenging due to the low-frequency, high-amplitude nature of the motion, which makes the use of conventional cantilevered spring-mass oscillators unrealizable. Frequency up-conversion by mechanical impact is an effective way to overcome the challenge. However, direct impact on the transducer element (especially, piezoelectric) increases the risk of damaging it and raises questions on the reliability of the energy harvester. In order to overcome this shortcoming, we proposed a transverse mechanical impact driven frequency up-converted hybrid energy harvester for human-limb motion. It utilizes the integration of both piezoelectric and electromagnetic transducers in a given size that allows more energy to be harvested from a single mechanical motion, which, in turn, further improves the power density. While excited by human-limb motion, a freely-movable non-magnetic sphere exerts transverse impact by periodically sliding over a seismic mass attached to a double-clamped piezoelectric bimorph beam. This allows the beam to vibrate at its resonant frequency and generates power by means of the piezoelectric effect. A magnet attached to the beam also takes part in generating power by inducing voltage in a coil adjacent to it. A mathematical model has been developed and experimentally corroborated. At a periodic limb-motion of 5.2 Hz, maximum 93 µW and 61 µW average powers (overall 8 µW·cm−3 average power density) were generated by the piezoelectric and the electromagnetic transducers, respectively. Moreover, the prototype successfully demonstrated the application of low-power electronics via suitable AC-DC converters.

A study on a U-shaped piezoelectric coupled beam and its corresponding ingenious harvester

In order to harvest ambient renewable or recovery energy, a novel piezoelectric energy harvester which mainly includes vibrators, a rotor and a cylindrical outer casing is presented in this paper. The vibrator is made of a U-shaped bimorph piezoelectric beam with a magnet slab mounted on its free end, and the rotor is a disc with magnet slabs embedded in the grooves along its periphery. The theoretical analysis model of the harvester is established and the mechanical and electrical responses are obtained. The results indicate that the harvester can achieve a maximum response by adjusting the rotor speed to make it work near resonance. As the beam section width or the substrate thickness decreases, or the piezoelectric patch thickness increases, the effective power of the harvester generally increases. On the whole, the substrate thickness has the greatest influence on the responses of the harvester, the piezoelectric patch thickness follows, and the influence of the beam section width is the smallest. In particular, the electric power generated from the harvester can reach 8.19 KW by adjusting the values of the related design parameters, which is comparable to a traditional small windmill generator, and therefore the proposed harvester has an appealing application prospect.

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.

A generalized approach on bending and stress analysis of beams with piezoelectric material bonded

The modeling and analysis of piezoelectric cantilevers are critically important in the design of micro intelligent systems, where piezoelectric beams serve as major components in micro sensors, actuators or energy harvesters. In this paper, we propose an analogy modeling method for the unimorph and bimorph piezoelectric beams, which helps to improve the accuracy of the neutral plane location of piezoelectric beams with different thickness ratios and total thicknesses. In particular, the strains of each layer are obtained by employing the analogy modeling method with the consideration of the transverse strain effect, where the force balance and moment balance equations of the final state of piezoelectric beams are derived under electric fields to reveal the relationship between the external deflection and the internal stress distribution of piezoelectric beams. To verify the effectiveness of the proposed approach, the bending characteristics of unimorph and bimorph piezoelectric beams (PZT-5A) are comprehensively tested under various electric fields, where theoretical values agree well with experiments and simulations. Compared with existing results, the proposed method provides a more general and accurate approach to characterize the properties of deflection and internal stress distribution for piezoelectric beams, which can be better used to study the stress of the adhesive layers, the geometric dimension optimization and the dynamics of piezoelectric beams in micro sensor or actuator applications.

Piezoelectric wind energy harvesting device based on the inverted cantilever beam with leaf-inspired extensions

Inspired by the fluttering of leaves in wind, we propose a novel type of wind energy harvesting device composed of a piezoelectric bimorph beam and flexible extensions. Working principle and advantages of the proposed design are discussed with numerical simulations conducted to investigate the influence of extension shape upon the device performance. Fabricated prototypes are tested in a simple experiment setup to give a description of the actual device performance. Results show that the leaf-inspired sector-shaped flexible extension corresponds to a better device performance. The test for the dual attachment case of the flexible extensions shows unexpected results, showing that the interaction and collision between the two flexible extensions are to be further explored and optimized.

Design and Simulation of MEMS Piezoelectric Vibration Energy Harvesters with Center Mass Block

MEMS-based piezoelectric vibration energy harvesters (MEMS-PVEHs) with center mass block are designed with the overall size 10 × 10 × 2 mm3, two prototypes including piezoelectric unimorph and bimorph beams are used respectively. This paper studies the characteristics of MEMS-PVEHs by modeling and simulation in COMSOL. Their eigenfrequencies are analyzed firstly, their optimal piezoelectric outputs are explored by changing excitation frequency and load resistance secondly, then the piezoelectric unimorph and bimorph beams are compared finally. The simulation results show that the optimal excitation frequency is slightly higher than the eigenfrequency, and the maximum piezoelectric power of the PVEH can be obtained only when the appropriate excitation frequency and load resistance are selected, and the power generation efficiency is 0.5. It has little difference between unimorph and bimorph to improve the MEMS-PVEH piezoelectric output. Finally, the piezoelectric unimorph with double opposite electrodes is designed based on the MEMS fabrication process.

Deflection of coupled elasticity–electrostatic bimorph PVDF material: theoretical, FEM and experimental verification

Piezoelectric materials have wide applications in the field of mechanical, aerospace and civil engineering because of its voltage dependent actuation. Piezoelectric material goes through voltage generation whenever deflection is induced in it and vice versa. Piezoelectric bimorph beam has been widely used for sensing and actuating. In the actuation mode, an electric field is applied across the beam thickness, one layer contracts while the other expands. This results in the bending of the entire structure and tip deflection. In the sensing mode, the bimorph is used to measure an external load by monitoring the piezoelectric induced electrode voltages. In this research work, a 2D bimorph piezoelectric actuator model having two layers made of polyvinylidene fluoride (PVDF) material was developed to examine the inverse piezoelectric effect. Finite element analysis (FEA) was carried out on specially designed actuator model by using MATLAB Partial Differential Equation (PDE) Toolbox™. Theoretical analysis has been carried out to measure the tip deflection under applied electric field. The laboratory test was performed to investigate the deformation behavior of piezoelectric actuator. It is observed that, more the electric field applied, more the material would be deformed in a particular direction. The experimental results are in good agreement with numerical results.

Electrode Coverage Optimization for Piezoelectric Energy Harvesting from Tip Excitation

Piezoelectric energy harvesting using cantilever-type structures has been extensively investigated due to its potential application in providing power supplies for wireless sensor networks, but the low output power has been a bottleneck for its further commercialization. To improve the power conversion capability, a piezoelectric beam with different electrode coverage ratios is studied theoretically and experimentally in this paper. A distributed-parameter theoretical model is established for a bimorph piezoelectric beam with the consideration of the electrode coverage area. The impact of the electrode coverage on the capacitance, the output power and the optimal load resistance are analyzed, showing that the piezoelectric beam has the best performance with an electrode coverage of 66.1%. An experimental study was then carried out to validate the theoretical results using a piezoelectric beam fabricated with segmented electrodes. The experimental results fit well with the theoretical model. A 12% improvement on the Root-Mean-Square (RMS) output power was achieved with the optimized electrode converge ratio (66.1%). This work provides a simple approach to utilizing piezoelectric beams in a more efficient way.

Modeling and Experiment of a V‐Shaped Piezoelectric Energy Harvester

Vibration‐based energy harvesting technology is the most promising method to solve the problems of self‐powered wireless sensor nodes, but most of the vibration‐based energy harvesters have a rather narrow operation bandwidth and the operation frequency band is not convenient to adjust when the ambient frequency changes. Since the ambient vibration may be broadband and changeable, a novel V‐shaped vibration energy harvester based on the conventional piezoelectric bimorph cantilevered structure is proposed, which successfully improves the energy harvesting efficiency and provides a way to adjust the operation frequency band of the energy harvester conveniently. The electromechanical coupling equations are established by using Euler‐Bernoulli equation and piezoelectric equation, and then the coupled circuit equation is derived based on the series connected piezoelectric cantilevers and Kirchhoff′s laws. With the above equations, the output performances of V‐shaped structure under different structural parameters and load resistances are simulated and discussed. Finally, by changing the angle θ between two piezoelectric bimorph beams and the load resistance, various comprehensive experiments are carried out to test the performance of this V‐shaped energy harvester under the same excitation. The experimental results show that the V‐shaped energy harvester can not only improve the frequency response characteristic and the output performance of the electrical energy, but also conveniently tune the operation bandwidth; thus it has great application potential in actual structure health monitoring under variable working condition.

Bending moment tracking and the reduction of the axial stress in vibrating beams by piezoelectric actuation

This contribution focuses on bending moment tracking in slender beam-type structures that are equipped with piezoelectric actuators. Bending moments are associated with the axial stress, which is the dominant stress component of laterally excited beam structures. If the maximum value exceeds a certain tensile stress limit, the structures will crack or be irreparably damaged. In the present contribution, a piezoelectric bimorph beam is considered and it is investigated in which manner the piezoelectric actuation devices have to be distributed along the beam length, such that a certain bending moment distribution is obtained. This is called bending moment tracking. First, the basic equations of a piezoelectric bimorph beam are recalled and the differential equations for the bending moment are derived. Then a positive semi-definite integral depending on the error of the bending moment is defined, which is the difference between the actual and the desired bending moment. The results of the derivations are conditions for the eigencurvature due to the piezoelectric actuation, such that a certain bending moment distribution is achieved. Approximate solutions for the eigencurvature are also presented for the lower- and for the high-frequency domain. The theory is verified by a support-excited piezoelectric bimorph. First, the frequency response curves for the deflection, the bending moment and the axial stresses are calculated. Then the responses due to a sinusoidal excitation are computed, showing that the suggested control algorithm enables the reduction of the bending moment and also of the axial stress in a satisfactory manner.

Analysis of the Dynamic Characteristics of a Micro-Piezoelectric Bimorph Beam Based on an Admittance Test.

A piezoelectric bimorph beam, as an upgraded cantilever beam structure, can be used to detect gas content and build a micro-actuator, among other functions. Thus, this beam is widely applied to microelectromechanical systems (MEMS), transformers, and precision machinery. For example, when photoacoustic spectroscopy is performed to detect oil-soluble gas in transformers, a micro-cantilever beam can be used to detect gas content. The dynamic characteristics of piezoelectric bimorph beams, such as resonant frequency, are important indexes in the applications of these beams. The equivalent circuit model for a piezoelectric bimorph beam is examined in this study and an admittance test is performed on the beam to accurately, quickly, and economically measure and analyze its dynamic characteristics. Then, the least squares method is applied to obtain the characteristic curves of the admittance circle, amplitude frequency, and phase frequency; identify the dynamic characteristics of the piezoelectric bimorph beam (e.g., resonant frequency); and determine the parameters of the equivalent circuit. The resonant frequency of the piezoelectric bimorph beam is 207.67 Hz based on the result of the admittance circle test, which is basically consistent with the results of microscope image method (i.e., 207.85 Hz) and the theoretical calculation (i.e., 222.03 Hz). This finding proves the validity of the proposed test method. This method cannot only improve the detection speed of piezoelectric bimorph beams, but can also provide a fast detection strategy for testing the characteristics of such beams during photoacoustic spectroscopy.

Analysis of functionally graded piezoelectric Timoshenko smart beams using a multiquadric radial basis function method

In the present work, a global interpolation scheme is proposed to describe the electro-mechanical static response of piezoelectric smart beams considering applied mechanical loads and electric potential. First, bimorph and three-layered Timoshenko smart beams are investigated and the model is validated for both actuator and sensor capabilities. Lastly, a functionally graded piezoelectric (FGP) bimorph beam is studied in its actuator configuration. The governing equations of motion are derived by the application of Hamilton’s principle considering an equivalent-single-layer first-order-shear-deformation theory (ESL-FSDT) with layerwise electric potential. The equations are subsequently solved using a grid free method based on Kansa’s asymmetric collocation using multiquadric radial basis functions (RBFs). The method relies on the Euclidean distance between nodes and on a shape parameter which must be warily selected to avoid matrix ill-conditioning. Accurate results are obtained while maintaining a very low computational cost.