Piezoelectric Bimorph Cantilever Research Articles

Investigation and hybrid deep belief neural network-based validation of piezoelectric bimorph cantilever composites assisted with tip mass

This work fabricated the piezoelectrical material using PMMA (polymethyl methacrylate) and Ce-doped ZnO nano-powders. The study was conducted to validate the piezoelectric performance of the proposed material and its suitability for the cantilever structure. The PMMA/Ce-ZnO makes the cantilever structure more flexible and performs better. The frequency response is applied to the beam using an electrical circuit to analyze the power and voltage output. The acceleration is given to the cantilever beams to analyze their resonant frequencies. The change in resonant frequencies results in a high voltage and power output. The resistive loads are used in the circuit to find the electrical load. The frequency response is analyzed in three different inner (18 mm, 20 mm, 22 mm) and outer (23 mm, 25mm, 27 mm) active layer lengths of beams. As a result, the maximum voltage of 21.94 V with 13.67 mW power and 2.9 mA current is obtained at a resonant frequency of 51.06 Hz and 1 g acceleration amplitude, which are approximately 42%, 45% and 15% higher voltage, power and current obtained from the lowest performer of proposed piezoelectric cantilevers. The experiment results are validated using the hybrid DBN-SSO (Deep Belief Network based Salp Swarm Optimization) machine learning technique. The proposed DBN-SSO achieved 0.9998 and 0.9966 regression coefficients for voltage and power outputs, thus proving the fitness of predicted results with the experiments. As per findings, a 27 mm inner and 18 mm outer active layer based energy harvesting system is suggested as a suitable energy source where ever 10-12 mW power, 2.5-2.9 mA current and 20-21.94 V voltage are applicable.

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.

Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

This paper demonstrates the importance of three-dimensional (3-D) piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator. It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects (i.e., piezoelectric coupling effect). In addition, there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end (i.e., 3-D effect). Hence, modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices, which contributes to the accurate prediction of their behavior.

Broadband Piezoelectric Energy Harvester Based on Coupling Resonance Frequency Tuning.

The bandwidth of piezoelectric energy harvesters (PEHs) can be broadened by resonance-based frequency tuning approaches, including mechanical tuning and electrical tuning. In this work, a new coupling tuning mechanism for regulating the near-open-circuit resonance frequency by changing the effective electrode coverage (EEC) is presented. A linear model of a bimorph piezoelectric cantilever with segmented electrodes is used to evaluate the power harvesting behavior near the open-circuit resonance frequency when EEC changes from 0 to 100%. According to the theoretical analysis, it is found that the variation of EEC brings about the change in coupling strength, which is positively associated with the near-open-circuit resonance frequency of PEH. Two cantilever PEHs with segmented electrodes based on PZT and PZT-PT are constructed for validation of the coupling tuning mechanism. The analytical and experimental results illustrate remarkable improvements in both bandwidth and average power through the coupling resonance frequency tuning method. In addition, adopting extraordinary piezoelectric single crystals and optimizing the proof mass and piezoelectric layer dimensions were theoretically shown to be effective methods for further improvement of bandwidth.

Needle selector failure detection based on piezoelectric sensor and driver co-location characteristics

Aiming at the problem of the malfunction of knitting machines caused by the unstable operation of the piezoelectric needle selector during the jacquard process, a state detection scheme for the piezoelectric needle selector that integrates the sensor and drive function co-located is proposed. The motion state of bimorph piezoelectric cantilever beam and its bi-directional piezoelectric effect in the jacquard process of piezoelectric needle selector are analyzed. Electrical and dynamic models were established for the electrical characteristics inside the bimorph piezoelectric cantilever beam and the dynamic characteristics of the cutter head and baffle of the needle selector. The signal detection circuit is designed to realize the real-time detection of the piezoelectric needle selector state by analyzing the time domain and frequency domain characteristics of the electrical signal. The results show that in the normal working state of the piezoelectric needle selector, the internal electric signal of the piezoelectric driver has two characteristic frequencies, which are between 155 and 180 and between 1630 and 1670 Hz, and the time for the piece to swing to the limit position is relatively long under abnormal working conditions.

A Cantilever-Based Piezoelectric MEMS for Arbitrary XY Path Generation.

This work pertains to the design of a cantilever-based piezoelectric MEMS device that is capable of generating arbitrary paths of its tip. The conceived device consists of a pair of rigidly coupled piezoelectric bimorph cantilevers, and a theoretical model is developed for the analytical evaluation of the proper voltage distribution to be supplied to the inner and outer electrodes of each piezoelectric actuator, in order to drive the tip along any desired trajectory. Such a device could be appealing in some microsurgical operations, i.e., the unclogging of arteries, endoluminal treatment of obstructive lesions, but also as a 2D micropositioning stage, etc. Theoretical predictions of voltage versus time that allow several pathways such as circles, ellipses, spirals, etc., to be accomplished have been verified with multiphysics FEM simulations and the numerical outcomes seem to corroborate the proposed model.

Duffing-type digitally programmable nonlinear synthetic inductance for piezoelectric structures

Piezoelectric shunt damping techniques using linear circuits (e.g. resistive-inductive) and switching circuits (e.g. synchronized switch on inductor) have been extremely well studied for suppressing resonant vibrations in flexible structures. Both analog circuits and synthetic impedance circuits with digital control have been explored for linear concepts. In a parallel body of work, from the domain of mechanical methods of vibration attenuation, it is also known that leveraging nonlinearities (e.g. stiffness nonlinearity) can enhance the frequency bandwidth and offer amplitude-dependent suppression over a range of frequencies. However, the existing piezoelectric shunt damping techniques have been mostly limited to linear or switching nonlinear circuits, with the exception of a few nonlinear capacitance efforts. This work aims to introduce cubic inductance to emulate Duffing-type hardening nonlinearity in the shunt circuit with precise digital programming and tuning capability. Experiments are performed on a piezoelectric bimorph cantilever under base excitation for concept demonstration and model validation. First, linear frequency response functions of the cantilever are obtained for the short- and open-circuit conditions, and for linear resistive-inductive synthetic shunt damping, to confirm the standard linear behavior and electromechanical model parameters. Then, cubic inductance is introduced to the circuit and nonlinear experiments (up- and down-frequency sweep) are conducted. Cantilever tip to base motion transmissibility frequency response is measured along with piezoelectric voltage to base motion counterpart for a range of base excitation amplitudes. The distortion of the frequency response curves with increased base acceleration levels is observed. The nonlinear cubic coefficient is then varied to alter the manifestation of nonlinear frequency response at a given base excitation level, demonstrating the ease of tuning and triggering the nonlinear behavior on demand by means of the digitally-controlled synthetic impedance shunt. Nonlinear electromechanical model simulations are also validated against the experiments, yielding a very good agreement.

Piezoelectric Energy Harvesting from Low-Frequency Vibrations Based on Magnetic Plucking and Indirect Impacts

This work proposes a mono-axial piezoelectric energy harvester based on the innovative combination of magnetic plucking and indirect impacts, e.g., impacts happening on the package of the harvester. The harvester exploits a permanent magnet placed on a non-magnetic mass, free to move within a predefined bounded region located in front of a piezoelectric bimorph cantilever equipped with a magnet as the tip mass. When the harvester is subjected to a low-frequency external acceleration, the moving mass induces an abrupt deflection and release of the cantilever by means of magnetic coupling, followed by impacts of the same mass against the harvester package. The combined effect of magnetic plucking and indirect impacts induces a frequency up-conversion. A prototype has been designed, fabricated, fastened to the wrist of a person by means of a wristband, and experimentally tested for different motion levels. By setting the magnets in a repulsive configuration, after 50 s of consecutive impacts induced by shaking, an energy of 253.41 μJ has been stored: this value is seven times higher compared to the case of harvester subjected to indirect impacts only, i.e., without magnetic coupling. This confirms that the combination of magnetic plucking and indirect impacts triggers the effective scavenging of electrical energy even from low-frequency non-periodical mechanical movements, such as human motion, while preserving the reliability of piezoelectric components.

Piezoelectric unimorph and bimorph cantilever configurations: Design guidelines and strain assessment

Multi-stable configurations of piezoelectric harvester are quite successful in achieving the two important goals, the broadband frequency response and large orbit oscillations exhibiting periodic, multi-periodic, and chaotic solutions. However, in the quest of achieving large amplitude broadband frequency response, assessment of induced strain levels considering the limits on the strain in piezoelectric material has received minimal attention. In this context, the investigation presents analytical formulation for the assessment of induced strain and voltage(s) in piezoelectric unimorph and bimorph cantilevers. The formulation quantifies not only the induced voltages in individual piezoelectric layers of a bimorph, but also the equivalent voltages in parallel and series connection modes, respectively. Also, while computing the induced voltage in the first piezoelectric layer, the contribution from the induced voltage of second piezoelectric layer to the acting bending moment is captured in the formulation. The formulations are validated through the experiments and results from the literature. Further, we have applied two practically useful normalization schemes, the - and -normalizations to the analytical expressions. Using the two normalization schemes, influences of variation of substrate and adhesive layer thicknesses, elastic moduli of layers, and substrate-to-composite length fraction are visualized and discussed. Based on the results, summarized guidelines for design and selection of geometric and material parameters are presented, which may also be applicable for other sensing and actuation applications. At last, practically suitable ranges and optimum values for the normalized design variables are proposed.

Fast-moving piezoelectric micro-robotic fish with double caudal fins

Micro-robotic fish (length ≤10 cm) driven by smart materials have remarkable advantages over conventional motors and piston-based robotic fish. In particular, they are highly efficient and compact. One of the key challenges is attaining high mobility with high energy density, low driving voltage and power loss. In this work, a double caudal fin micro-robotic fish actuated by two piezoelectric bimorph cantilevers is proposed and fabricated from rigid carbon fiber/resin composites and flexible polyimide hinges. Its weight is about 1.93 g and the maximum uniform swimming velocity is as high as about 0.75 BL/s (4.5 cm/s), which is much faster than previously reported micro-robotic fish actuated by ionic polymer–metal composites, shape memory alloys and dielectric elastomers. A theoretical model is validated by the experimental results and can be used to design and analyze a variety of piezoelectric robotic fish propelled by caudal fins.

Measurement of quasi-static and dynamic mechanical properties of soft materials based on instrumented indentation using a piezoelectric cantilever

Instrumented indentation is a powerful in-situ mechanical characterization method and has been intensively investigated in recent years. In this work, we proposed an instrumented indentation method for soft materials based on a piezoelectric bimorph cantilever where the indentation force (F) is measured by a strain gauge and the indentation depth (h) is monitored by a piezoelectric motor driven displacement platform. The quasi-static mechanical properties of the soft samples are obtained by using the F-h curve and the dynamic properties are extracted from the contact resonance curve of the piezoelectric cantilever which is measured by using electromechanical impedance (EMI). Firstly, the working principle of this indentation method for quasi-static and dynamic mechanical property measurement is presented. Then, both the quasi-static and dynamic indentation testing were conducted on a silica gel sample, and the testing results fit well with that obtained using tensile testing. Later, the viscoelastic properties of a Polydimethylsiloxane (PDMS) sample was tested which is strongly dependent on the indentation force. Finally, modulus imaging was conducted on a silica gel sample containing a stiffer elastomer sphere using the local contact stiffness (LCS) as the indicator, and the elastomer can be clearly revealed. The proposed piezoelectric cantilever based instrumented indentation method is very convenient for mechanical characterization of soft materials and may be widely used in near future.

Graded multifunctional piezoelectric metastructures for wideband vibration attenuation and energy harvesting

Unlike well-studied locally resonant (LR) metamaterials with a periodic array of identical resonators, ‘graded’ LR metamaterials consist of an array of resonators with a spatially varying parameter, yielding wideband wave attenuation and mode trapping/localization, among other features. In this work, we explore a graded LR piezoelectric metamaterial-based structure (i.e. metastructure) in which the grading parameter, namely the inductive shunt resonant frequency of the unit cells, follows a predefined variation pattern in space (e.g. first-order, quadratic, or fractional). We investigate the effect of such patterns on (i) the vibration attenuation bandwidth, (ii) the localization of vibration modes, and (iii) the harvested power. To this end, we consider a piezoelectric bimorph cantilever hosting an array of piezoelectric unit cells with spatially varying inductive shunts. Fully coupled electromechanical equations describing the metastructure’s linear transverse displacement and unit cell voltages are given with a modal analysis framework and solved using the matrix inversion method. The results show that (i) the first-order grading pattern yields the widest bandgap with 65% increase in the bandwidth compared to the standard uniform LR pattern, (ii) the localization of vibration modes follows in shape the corresponding frequency grading pattern, and (iii) the largest power is harvested for the fractional grading pattern. Furthermore, all of the graded resonator configurations result in wider bandwidth in energy harvesting as compared to the uniform resonators case. Overall, the results unveil the fundamental characteristics of this class of graded piezoelectric metastructures and support the design of such multifunctional piezoelectric metastructures for concurrent vibration attenuation and energy harvesting.

Semi-analytical model of an acoustic black hole piezoelectric bimorph cantilever for energy harvesting

An acoustic black hole (ABH) beam termination can be achieved by decreasing its thickness according to a power-law profile. Waves entering the ABH slow down and vibrational energy strongly concentrates at the tip of the beam. This can be exploited for energy harvesting, as suggested in some recent works. The finite element method (FEM) is commonly used to carry out the simulations, which hampers long parametric analyzes. In this paper, we develop a semi-analytical approach to characterize the performance of a piezolectric bimorph cantilever with an ABH termination. The method can be easily extended to further configurations and allows one to determine ABH harvesting capabilities when varying system parameters, in a fast and efficient way. The Lagrangian of the ABH beam plus piezoelectric layers is constructed and the coupled equations for the flexural vibrations and voltage are derived from it. The flexural displacement field is expanded in terms of Gaussian basis functions. Vibration shapes and harvested power are computed with the proposed method and validated against FEM simulations. The ABH piezolectric bimorph cantilever is shown to substantially enhance the harvesting capabilities of a cantilever with uniform cross-section. The semi-analytical approach is then used to examine the influence of several ABH and piezoelectric layer parameters on energy harvesting efficiency. As regards the former, the effects of the tip truncation thickness and ABH order are explored. In what concerns the piezoelectric layer, we investigate the effects of its location, thickness, splitting it into several patches and varying the load resistors to enhance its performance in a broad frequency range. The proposed method constitutes a valuable tool for the design of ABH energy harvesting devices.

Characterization and Optimization of Piezoelectric Bimorph Cantilever Structure for Ambient Vibration-Based Energy Harvesting Application

Piezoelectric energy harvesting (PEH) provides an essential mode for the transformation of mechanical vibration to electrical form for providing continuous power to wireless sensor nodes in today’s connected world. This work describes an analytical model based on the Euler-Bernoulli model. The proposed model is in agreement with the FEM simulation model, with results differing by 6%. Variation in geometric parameter, the effect of resonant frequency, output power and stability of the design provides a constraint domain for structure optimization have been described along with the effect of damping. The designed harvester generates a power of 1.31 mW at 90 Hz resonant frequency.

An internal miniature diversion channel-integrated piezoelectric airflow sensor

In this note, we propose and develop a piezoelectric airflow sensor with a novel configuration composed of a piezoelectric bimorph cantilever (PBC) and an internal miniature diversion channel (IMDC) structure. With the existence of the IMDC, the airflow velocity in the tapered region of the IMDC can be magnified compared to the inlet airflow velocity, and the vibration amplitude of the PBC can also be enlarged compared to that directly exposed to airflow with the same velocity. A fluid-solid interaction (FSI) model computed by the finite element method (FEM) is presented to clarify the physical mechanism contained in the proposed sensor system. The experimental results show that the developed piezoelectric airflow sensor simultaneously holds desirable dynamic and stable response characteristics to stable external airflows. Also, the fast response and recovery characteristics of the piezoelectric airflow sensor to abrupt external airflows have been demonstrated by the experiments.

Hierarchically decomposed finite element method for a triply coupled piezoelectric, structure, and fluid fields of a thin piezoelectric bimorph in fluid

This paper proposes a numerical method for analyzing a thin piezoelectric bimorph in fluid. A hierarchically decomposed finite element method (FEM) is proposed for modeling the triply coupled piezoelectric-structure–fluid interaction. The electromechanical coupling (piezoelectric-structure interaction) behavior in a thin piezoelectric bimorph is described by the classical constitutive equation, the incompressible fluid flows by the Navier–Stokes equation and the structure by the Cauchy equation of motion. The piezoelectric-structure–fluid interaction system is decomposed into subsystems of fluid–structure interaction (FSI) and piezoelectric field, then the piezoelectric field and the FSI are coupled using the block Gauss–Seidel method, the fluid–structure interaction is split into the fluid–structure velocity field and the pressure field using an algebraic splitting and the fluid–structure velocity field is partitioned into fluid velocity field and structure velocity field. Using the proposed method, the resonance characteristics of a piezoelectric bimorph cantilever made of PVDF and PZT-5H material in fluid are investigated for actuation and sensor configurations.

Wind energy harvesting from a magnetically coupled piezoelectric bimorph cantilever array based on a dynamic magneto-piezo-elastic structure

This paper presents a novel wind energy harvester based on a magneto-piezo-elastic structure using a magnetically coupled piezoelectric bimorph cantilever. The harvester consists of a power-generating stator for the piezoelectrics and a wind-powered rotor and Savonius blades. A permanent magnet on the free-end-tip mass of the vertically aligned piezoelectric bimorph cantilever interacts with a rotating counterpart permanent magnet affixed onto the top disk plate of the Savonius rotor. Its operating principle provides a better understanding of the magneto-piezo-elastic energy conversion. A good arrangement of permanent magnets was demonstrated to be effective for a reduction of the resistance torque to approximately 94.6 mN∙m. The dynamic behavior of the magnetically coupled piezoelectric bimorph cantilever was also investigated according to the output voltage signal pattern in relation to the deflection dependent on the wind speed. As the wind speed was increased from 2.5 m/s to 6.5 m/s, the deflection and output power of the single piezoelectric bimorph cantilever tended to increase linearly. The highest output power of 24.95 mW, which corresponds to 2.10 mW/cm3, was obtained at a wind speed of 6.5 m/s for the parallel-connected piezoelectric bimorph cantilever array, implying better performance compared to those reported previously.

Energy harvesting characteristics of preloaded piezoelectric beams

A broad bandwidth is considered to be one of the most important characteristics of vibrational energy harvesters (VEHs) in order to enhance energy efficiency. To this end, an axially compressive load is applied to the VEHs of a conventional bimorph piezoelectric cantilever beam by pre-tensile cables. The theoretical framework is based on Euler–Bernoulli beam theory and the von Kárman nonlinear kinetic relation, and the electromechanical coupling governing equations are derived by using the Hamilton variational principle of the total potential energy. Treatments by Galerkin discretization and the perturbation method of multi-scales give the asymptotically analytic solutions of the displacement amplitude, the voltage amplitude and the average output power, which are validated by the experimental datum in the literature. With the aid of COMSOL Multiphysics, the parametric studies are addressed to explore the mechanisms of the axial preload, the harmonic excitation, the resistance, etc, acting behind the energy harvesting characteristics. The results show that the preload does improve the bandwidth characteristic significantly, specifically, a 64% reduction in the first natural frequency and 196.6% increase of the bandwidth. The present work provides fundamental theoretical support and guides the design of potential preloaded VEHs.

An optimized self-sensing piezoelectric cantilever for micro-robotic applications

Quasi-static piezoelectric actuators are used in micro-robotics due to the small displacements they can achieve, and they have been proven to be suitable for Self-Sensing Actuation (SSA) applications. The morphology and material of an actuator, and therefore its characteristics (i.e. stiffness, capacitance), all have an impact on the performance of the SSA implementation. This article presents a methodology that can be used to optimize the design parameters for a piezoelectric quasi-static bimorph cantilever for micro-robotic applications with sub-mN manipulation forces and sub-μ m positioning resolutions in mind. A model is established for this type of actuator, from which an objective function aiming to maximize β, the charge accumulation coefficient, is defined. Boundary conditions are set on the optimization study by imposing constraints on the design. An analytical optimization approach is then adopted to study the evolution of the objective function across the design space. The study evidences the existence of a subset of solutions satisfying the constraints and maximizing the objective function, and the partial derivatives of this subset are studied, leading to conclusions for an optimized design strategy. Experimental results show that inaccuracies in the prediction of the β parameter lie within the self-sensing actuator model due to the omission of the thin electrode layers inserted between each piezoelectric layer. Nonetheless, the presented optimization methodology has proven to be suitable to maximize the potential SSA performance of a design, with the fabricated optimized actuator having a higher β coefficient than a commercial actuator of similar external dimensions by a factor of approximately 7.

Experiments on a wireless power transfer system for wearable device with sol-gel thin-film PZT

This paper presents experiments on a low-frequency wireless power transfer system (WPTS) using a piezoelectric transducer with a magnet tip mass as a receiver. The thin-film piezoelectric bimorph cantilever is fabricated by sol-gel processing with the aim to miniaturize the system for wearable applications. The device couples an applied electromagnetic field to the mechanical transverse vibration of the beam, which then induces a voltage across a load resistance connected to the electrical ports. This coupled mechanism is therefore referred to as the magneto-mechano-electric (MME) effect. A power of 3.4 μW is generated in a resistance of 200 kΩ at a magnetic flux density of 100.3 μT. The potential of utilizing the same piezoelectric resonator for both energy harvesting and wireless power transmission modes is shown.