Bimorph Beam 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.

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.

Design, tuning and in-field validation of energy harvesters for railway bridges

Energy harvesters are a promising technology for powering infrastructure condition monitoring systems without batteries. When deployed on railway bridges they are typically tuned to the bridge’s natural frequency, however due to the dominance of train-induced forced vibration of the structure, this results in sub-optimal energy harvesting. As a solution, this paper presents a novel tuning strategy for energy harvesters on railway bridges. The strategy is based on a statistical analysis of the mechanical energy generated in the bridge during train passage and involves four steps: (i) measurement of bridge response due to train traffic, (ii) calculation of mechanical energy during train passage, (iii) statistical characterisation of the energy distribution, and finally, (iv) calculation of the tuning frequency. A case study is presented to compare the potential of the proposed strategy against tuning based upon the bridge natural frequency. First, an in-service railway bridge is monitored to determine its natural frequency and response to train traffic. Combining the field data with the proposed tuning strategy, the design of energy harvesters for the bridge is optimised. The design of harvesters tuned to natural frequencies is also studied. The underlying harvester type is a cantilever bimorph beam with a mass at the tip and load resistance. Additive manufacturing is used for the substructure, which is formed from PAHT-CF15 (High Temperature Polyamide carbon fibre reinforcement). The harvesters are manufactured and deployed on the bridge subject to live railway traffic. Field results show the devices designed using the new tuning strategy harvest up to 300% more energy. The energy harvested in a time window of three hours (18 train passages) is 7.65mJ.

Finite element modeling of piezoelectric cantilever-beam energy harvester

Piezoelectric energy harvesting from mechanical vibrations has attracted considerable attention during the last decade. The homogeneous harvesters were studied experimentally or numerically by various models such as single degree of freedom (SDOF) modeling, finite element (FE) modeling as well as using analytical solutions. In this work, FE models for simulating a piezoelectric beam bimorph power harvester consisting of a laminated piezoelectric beam, a proof mass, and an electrical load (series or parallel connections) configurations are developed. The effects of the material and size of the substrate, the proof mass have been studied on the resonance frequencies and the output parameters of the piezoelectric generator (PEG). Numerical results obtained using the proposed procedure for piezoelectric bimorph power harvesters are in good agreement with the experimental data available in the literature. The proposed method can be used for modeling accurately this class of energy harvesting devices.

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.

3D printed energy harvesters for railway bridges-Design optimisation

This paper investigates the optimal design of 3D printed energy harvesters for railway bridges. The type of harvester studied is a cantilever bimorph beam with a mass at the tip and a load resistance. These parameters are adjusted to find the optimal design that tunes the harvester to the fundamental frequency of the bridge. An analytical model based on a variational formulation to represent the electromechanical behaviour of the device is presented. The optimisation problem is solved using a genetic algorithm with constraints of geometry and structural integrity. The proposed procedure is implemented in the design and manufacture of an energy harvesting device for a railway bridge on an in-service high-speed line. To do so, first the methodology is validated experimentally under laboratory conditions and shown to offer strong performance. Next the in-situ railway bridge is instrumented using accelerometers and the results used to evaluate energy harvesting performance. The results show the energy harvested in a time window of three and a half hours (20 train passages) is E=109.32mJ. The proposed methodology is particularly useful for bridges with fundamental mode shapes above 4.5Hz, however optimal design curves are also presented for the most common railway bridges found in practice. A novelty of this work is the use of additive manufacturing to 3D print energy harvesters, thus maximising design flexibility and energy performance.

On analysing vibration energy harvester with auxetic core and magneto-electro-elastic facings

Powering systems without heavy maintenance-intensive batteries is a challenge for various engineering applications. Often, energy in the form of heat, vibration, sound etc., is squandered while operating many machines/structures. A judicious utilisation of these potent energies using energy harvesters (EH) will reduce the degree of dependency on depletable energy sources. Sometimes, EH acts as a parasitic mass and consumes additional space. To address this issue, the current work proposes a lightweight vibration-based bimorph beam (VBBB) EH constituted of multifunctional magneto-electro-elastic (MEE) facesheets and auxetic metamaterial core (AMC). The frequency response functions, which consider series and parallel configurations of the active ME layers, are derived using distributed parameter single-mode formulation to quantify the system’s output response. The overall effect of the negative Poison’s Ratio of the auxetic materials, combined with the material, geometric and parameters such as the number of turns and resistances, is investigated. The advantage of using an auxetic core to enhance the energy harvester’s performance is realised through an improved power output as the thickness of the auxetic core layer rises. The maximum values of the output parameters are witnessed for larger auxetic angles and lower rib–length ratios. Meanwhile, greater values of the geometrical parameters like length-to-thickness ratio and length-to-width ratio result in enhanced power harvested. A comparative study justifies that under similar working conditions, the power output of the auxetic-based energy harvester is almost 1.5 times more than the conventional metal-based energy harvesters. Further, auxetic-based EH reported a 22% weight reduction for the same power output obtained from the conventional metal-based EH. This enables the lightweight construction of low-powered smart systems with enhanced efficiency. It is believed that the results of this article will lead to further studies on utilising multifunctional composites and metamaterials for complex engineering applications.

Hybrid magnetorheological elastomers enable versatile soft actuators

Recent advances in magnetorheological elastomers (MREs) have posed the question on whether the combination of both soft- and hard-magnetic particles may open new routes to design versatile multifunctional actuators. Here, we conceptualise ultra-soft hybrid MREs (≈1–10 kPa stiffness) combining experimental and computational approaches. First, a comprehensive experimental characterisation is performed. The results unravel that the magneto-mechanical performance of hybrid MREs can be optimised by selecting an adequate mixing ratio between particles. Then, a multi-physics computational framework provides insights into the synergistic magneto-mechanical interactions at the microscale. Soft particles amplify the magnetisation and hard particles contribute to torsional actuation. Our numerical results suggest that the effective response of hybrid MREs emerges from these intricate interactions. Overall, we uncover exciting possibilities to push the frontiers of MRE solutions. These are demonstrated by simulating a bimorph beam that provides actuation flexibility either enhancing mechanical bending or material stiffening, depending on the magnetic stimulation.

Static and dynamic analyses of FGPM cylindrical shells with quadratic thermal gradient distribution

Functionally graded material (FGM) has great potential in the application of thin-walled structures, since delamination failure can be suppressed. Functionally graded piezoelectric material (FGPM) is a special kind of FGM, which couples with elastic and electric fields. The modeling of FGPM coupled smart structures under nonlinear thermal load is still a challenge task. This paper develops an electro-thermo-elastic finite element (FE) model of FGPM integrated smart structures based on the first-order shear deformation hypothesis. The FE model proposes two different nonlinear configurations of thermal gradient distribution through the thickness, which are compared with linear thermal gradient distribution. An eight-node quadrilateral shell element is developed for finite element analysis. The present FE model is firstly validated by a PVDF bimorph beam under nonlinear thermal loads. Later, the model is applied to the static and dynamic simulation of FGPM cylindrical shells. The results show that thermal distribution configurations have great impact on structural response, which should be carefully chosen in the simulation of thermal coupled problems.

Design and Experimental Assessment of Low-Noise Piezoelectric Microelectromechanical Systems Vibration Sensors.

The ubiquity of vibration sensors and accelerometers, as well as advances in microfabrication technologies, have led to the development of implantable devices for biomedical applications. This work describes a piezoelectric microelectromechanical systems accelerometer designed for potential use in auditory prostheses. The design includes an aluminum nitride bimorph beam with a silicon proof mass. Analytic models of the device sensitivity and noise are presented. These lead to a minimum detectable acceleration cost function for the sensor that can be used to optimize sensor designs more effectively than typical sensitivity maximizing or electrical noise minimizing approaches. A fabricated device with a 1 μm thick, 100 μm long, and 700 μm wide beam and a 400 μm thick, 63 μm long, and 740 μm wide proof mass is tested experimentally. Results indicate accurate modeling of the system sensitivity up to the first resonant frequency (1420 Hz). The low-frequency sensitivity of the device is 1.3 mV/g, and the input referred noise is 36.3 at 100 Hz and 11.8 at 1 kHz. The resulting minimum detectable acceleration at 100 Hz and 1 kHz is 28 and 9.1 , respectively. A brief explanation of the use of the validated cost function for sensor design is provided, as well as an example comparing the piezoelectric sensor design to another from the literature. It is concluded that a traditional single-resonance design cannot compete with the performance of acoustic sensors; therefore, novel device designs must be considered for implantable auditory prosthesis applications.

برداشت انرژی با استفاده از تیر بایمورف متخلخل با لایه پیزوالکتریک تحت ارتعاشات القایی ناشی از جریان سیال خارجی

In this study, energy harvesting by porous beams exposed to external fluid flow is studied analytically. The nonlinear electromechanical non-linear differential equations governing the transverse vibration of porous beams under external fluid flow have been extracted using Euler-Bernoulli beam theory and Hamilton's principle. A cantilever bimorph beam with a concentrated mass at its end, which is equipped with piezoelectric layer, is considered as an energy harvesting system. After solving the nonlinear equations of motion, the effect of different parameters on the amount of harvested energy is examined. The results show that in the areas of the lock-in phenomenon, the amount of harvested energy by the beam has its maximum value. Also, the porosity distribution has significant effect on the maximum amplitude of oscillations, as well as the energy harvested by the porous beam. The lock-in phenomenon for the porous beam with distribution of symmetrical porosity (wall stiffness), asymmetric porosity distribution and uniform porosity distribution is taken around u=0.15. In addition, for electrical resistance R = 100kΩ, the maximum voltage generated for the bimorph porous beam by the distribution of symmetrical porosity in the wall stiffness, asymmetric porosity distribution and uniform porosity distribution is 0.39V, 0.44V and 0.57V, respectively.

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

System-level finite element analysis of piezoelectric energy harvesters with rectified interface circuits and experimental validation

The finite element method (FEM) has been widely used for numerical studies of piezoelectric energy harvesting (PEH) systems, through commercial finite element (FE) packages or specially developed FE formulations. As a convenient computational tool, FEM can deal with systems of high complexity and has evolved into a multiphasic solution to coupled problems in engineering. However, most of FE packages and formulations are limited to coupled-field simulations of PEH systems connected with a linear circuit. On the other hand, rectified circuits are a critical component in practical applications because electronic devices such as wireless sensor nodes and wearable electronics require a DC power supply. Based on the equivalent impedance analysis, this paper proposes a method to enable a coupled-field study of piezoelectric energy harvesters with the standard AC-DC interface circuit through an equivalent linear circuit. The proposed method enables FE packages and formulations to analyze, design, and optimize PEH harvesters at the system level, by either adding the capability of simulating rectified circuits, or reducing a nonlinear circuit interface simulation into a faster and more stable linear simulation that can be solved more conveniently. This equivalent linear circuit method was applied to a rectangular shaped bimorph beam harvester in ANSYS and validated experimentally. The results also match well with those obtained from a system-level analytical approach. As an application example, a comparison study was performed between the rectangular and triangular energy harvesters using FE packages and the proposed equivalent circuit, given the same natural frequency and material volume. In addition, the implementation of this method with FE formulations is briefly outlined and discussed.

Passive vibration suppression in a coupled linear–bistable continuous module excited near resonance

Vibration suppression for marine structures has been an important concern for a long time. In this paper, a specifically designed continuous module that consists of an Euler beam, a preloaded bimorph beam and a coupled spring unit produces self-increasing damping and strongly suppresses the steady-state response near resonance. Based on Hamilton’s principle, we derive a two-degree-of-freedom coupled linear–bistable (CLB) model of this module. Utilizing the harmonic balance method and a numerical simulation, we analyze the proposed CLB model under a harmonic excitation. When the preloaded beam moves toward the critical amplitude of the saddle point of the system potential, the unstable equilibrium greatly increases the velocity phase difference between the Euler and preloaded beams and spontaneously enhances the dissipation power of the system. The self-increasing damping decreases the amplitude of the steady-state vibration of the coupled module excited near resonance by an order of magnitude. Numerical results demonstrate the essential roles of the damping ratio and the shape of the potential function in determining how this module can better suppress vibrations. This investigation provides opportunities to suppress dynamical responses using a continuous CLB module.

An advanced folded piezoelectric vibration energy harvester with low resonant frequency and high power density

This paper reports an advanced folded piezoelectric vibration energy harvester (PVEH) that has excellent power generation performance at the former two-order resonant frequencies. Its volume is ∼1 cm3 and its mass is less than 5 g. Extending piezoelectric transducer sheets can effectively avoid stress concentration and greatly improve the power generation performance of the device. Besides, by adjusting the height–length ratio of the folded structure under 0.35, the device can generate power effectively in the former two vibration modes. Finite element simulation analysis by COMSOL Multiphasic was performed to fabricate and test a series of PVEHs. Their resonant frequencies and peak output powers were analyzed. The advanced folded PVEH can harvest energy effectively at the former two resonant frequencies: 58 Hz and 136 Hz. A multi-line classical energy harvesting circuit is designed to harvest the energy generated by all bimorph beams. Under 0.4 g excitation acceleration, the two peak output voltages of the energy harvesting circuit are 19.4 V and 6.32 V and the two peak output powers of the energy harvesting circuit are 336.04 µW and 77.07 µW. In the former two-order vibration modes, the power densities are 2.1 mW/cm3/g2 and 0.48 mW/cm3/g2, respectively.

Analysis of the nonlinear hysteresis of the bimorph beam piezoelectric bending actuator for the deformable mirror systems

We propose an analytical nonlinear hysteresis model of the bimorph beam bending piezoelectric actuator for a deformable mirror system. An explicit solution is derived from the analytic method based on the nonlinear elasticity. As an application example, the nonlinear hysteresis behaviors of a bimorph beam bending piezoelectric actuator, which is sandwich compounds consisting of a lower and an upper piezoelectric ceramic (PZT8-50) layer and a middle layer made of the aluminum alloy, are examined with the model. The numerical calculations based on the analytical solution are presented. The numerical simulations have shown that the nonlinear hysteresis behaviors of the bending actuator are depended on the start values of the exciting electric field and the geometric parameters of the metallic layer. In addition, the numerical results have also shown that the thickness of metallic layer has little influence on the relative hysteresis, and the relationships between relative hysteresis Δd / ΔD and the driving electric field | Estart | are linear.

High structural damping based on the internal snap-buckling mechanism of a continuous metal module

A structural module that can bear load and dissipate dynamic energy effectively is desirable. In this paper, a continuous laminated metal module of a preloaded beam bimorph and elastic layer is developed to achieve versatility of damping properties based on internal snap-buckling mechanism. According to nonlinear Euler-Bernoulli beam theory, the dynamic model of this structure can be obtained. Multiple scales method is utilized to derive intra- and inter-well vibratory responses analytically. Based on numerical simulations, this continuous module would have a negative stiffness due to internal snap-buckling behavior in the inter-well oscillation, while the macroscopic displacement remains fixed, which brings about orders of magnitude of energy dissipation within a certain bandwidth. Numerical results demonstrate the essential role that the shape of the function of potential energy plays, in conjunction with the excitation, to determine whether this module can achieve high dissipation. Analytical functions that can be utilized to determine the loci of critical bifurcations are derived to approximate the effective bandwidth for high dissipation oscillation. For the structures with shallow and closely separated potential wells, the snap-buckling dynamics can occur easily within a considerable bandwidth, even if the system is excited with small amplitudes.

Investigation of output voltage, vibrations and dynamic characteristic of 2DOF nonlinear functionally graded piezoelectric energy harvester

With the aim of providing the larger frequency band and progress the energy harvesting proficiency of the bistable piezoelectric energy harvester (BPEH), a 2-DOF nonlinear distributed parameter model of BPEH with an elastic magnifier is considered in this paper. This study deals with bimorph beam with functionally graded piezoelectric (FGP) layers carrying concentrated mass at tip while taking into account the geometrical nonlinear terms and the nonlinear magnetic force to enhance energy harvesting performance. By presenting the magnifier, oscillations of the tip are inspired into high-energy orbits. Mathematical model of BPEH with a dynamic magnifier has been developed, then the nonlinear coupled equation of motion derived using Hamilton principle. Initially, frequency response of harvester derived according to harmonic balance method and the adjusted model has been confirmed by parametric studies of earlier lumped parameter model. Analytical results show that the harvesting voltage can be improved with correct selection of design parameters of the magnifier. The proposed 2-DOF harvester system can provide higher output over a wider frequency band and may cause a considerable change in harvester performance. A parametric study is consummated to expose the effects of power law index of FGP on the output voltage and dynamic characteristic.