Thickness Of Piezoelectric Layer Research Articles

Performance Correction and Parameters Identification Considering Non-Uniform Electric Field in Cantilevered Piezoelectric Energy Harvesters.

In the current electromechanical model of cantilevered piezoelectric energy harvesters, the assumption of uniform electric field strength within the piezoelectric layer is commonly made. This uniform electric field assumption seems reasonable since the piezoelectric layer looks like a parallel-plate capacitor. However, for a piezoelectric bender, the strain distribution along the thickness direction is not uniform, which means the internal electric field generated by the spontaneous polarization cannot be uniform. In the present study, a non-uniform electric field in the piezoelectric layer is resolved using electrostatic equilibrium equations. Based on these, the traditional distributed parameter electromechanical model is corrected and simplified to a practical single mode one. Compared with a traditional model adopting a uniform electric field, the bending stiffness term involved in the electromechanical governing equations is explicitly corrected. Through comparisons of predicted power output with two-dimensional finite element analysis, the results show that the present model can better predict the power output performance compared with the traditional model. It is found that the relative corrections to traditional model have nothing to do with the absolute dimensions of the harvesters, but only relate to three dimensionless parameters, i.e., the ratio of the elastic layer's to the piezoelectric layer's thickness; the ratio of the elastic modulus of the elastic layer to the piezoelectric layer; and the piezoelectric materials' electromechanical coupling coefficient squared, k312. It is also found that the upper-limit relative corrections are only related to k312, i.e., the higher k312 is, the larger the upper-limit relative corrections will be. For a PZT-5 unimorph harvester, the relative corrections of bending stiffness and corresponding resonant frequency are up to 17.8% and 8.5%, respectively. An inverse problem to identify the material parameters based on experimentally obtained power output performance is also investigated. The results show that the accuracy of material parameters identification is improved when considering a non-uniform electric field.

Electro-mechanical vibration characteristics of imperfect sandwich FG piezoelectric honeycomb nanoplates resting on Kerr foundation

This study presents an innovative analytical approach to examine the electro-mechanical vibration characteristics of sandwich nanoplates featuring a honeycomb core and two surface layers composed of imperfect piezoelectric functionally graded (FG) material, incorporating porosities, atop a Kerr elastic foundation. Utilizing nonlocal elasticity theory and four-variable refined plate theory (HSDT-4), we account for nanoscale effects and model the electric potential variation across the piezoelectric layer thickness as a combination of cosine and linear variations satisfying Maxwell's equation. The proposed method's novelty lies in its comprehensive analysis of the interplay between porosity, elastic foundation parameters, material properties, geometrical dimensions, external voltage, and nonlocal parameters on the free vibration frequency of these nanostructures. Numerical simulations validate the model's reliability and assess the significant impacts of these factors. Our findings contribute to the optimization of nanostructural designs for advanced engineering applications, highlighting the method's added value in predicting the behavior of imperfect piezoelectric FG honeycomb nanoplates.

Performance study of novel metal corrosion probes based on the adjust method of series and parallel connections

Rod-type metal corrosion probes based on electromechanical impedance (EMI) technique can quantitatively assess the amount of corrosion, which have a promising application in pipeline corrosion monitoring and have received much more attention. In the field of structural health monitoring, the EMI technique based on series and parallel connections has been widely studied and is very promising, but it is yet to be used in the probe design. In this work, a kind of novel metal corrosion probe with two piezoelectric elements in series and parallel connections was proposed, and its performance was investigated comprehensively by combining theoretical analysis with experiment research. Theoretical models of the proposed probe in the longitudinal vibration mode for both series and parallel connections were established, and verified by the experimental results. Influences of the thicknesses of piezoelectric layer and ceramic layer on the probe performance were analyzed. Artificial quantitative corrosion tests and accelerated corrosion tests were designed to evaluate the quantitative corrosion monitoring capacity. Temperature sensitivity tests were conducted to study the temperature dependence. The wireless impedance measurement was performed to confirm the online monitoring ability. Comparisons for the probe performance between the series and parallel connections were also presented. This work provided a comprehensive understanding for this kind of novel probe, which is beneficial to develop low-cost, high-precision, high-stability pipeline corrosion real-time monitoring technology.

Reliable formulas for accurately determining the resonance and antiresonance frequencies of thin film bulk acoustic resonators

Expanding upon Lakin’s theory by considering the phase shift of the acoustic waves in the metallic layers, we have developed an impedance formula for a piezoelectric layer covered by a finite thickness of metal layers, enabling the precise determination of its resonant and anti-resonant frequencies. Compared to experimental data and 3D finite element simulations, our formula can accurately and quickly predict resonant, anti-resonant frequencies, and bandwidth across a wide range of piezoelectric and metallic layer thickness combinations.

On Flexural Wave Dispersion of a Higher-Order Metamaterial Sandwich Composite Plate Based on a Visco-Pasternak Foundation

This paper elaborates on the wave propagation characteristics of a smart sandwich plate consisting of smart piezo composite layers on a plate’s upper and lower borders via an auxetic core. This study’s equation of motion was derived using a refined version of the Shear-deformation theory at a higher order, or HSDT. Additionally, detecting the properties of the auxetic core and piezoelectric composite layers employs a micromechanical model. The fundamental equations of the smart sandwich plates were formulated utilizing the Hamiltonian principle and Maxwell’s law. Then, the governing equations of a sandwich plate are solved using an exponential form and an analytical method. Furthermore, the phase velocity of the intelligent sandwich plate is provided based on the layer thicknesses of the auxetic core and thicknesses of intelligent piezoelectric composite layers. In addition, each figure calculates and presents the weight of the Winkler–Pasternak coefficient, the viscoelastic substances factor, the source of the outside electricity, and the volume percent of reinforcement in the matrix on the phase velocity.

Electro-mechanical coupling model and interlaminar stress analysis of laminated plates containing GSR actuator

Due to its remarkable physical features, graphene nanosheets (GPN) are one of the most appealing reinforcing materials for composites. For polyvinylidene fluoride (PVDF), GPN reinforced composites can dramatically increase its piezoelectric and mechanical characteristics. If the interlaminar shear deformation of laminated plates containing uniform graphene sheets reinforced (GSR) smart piezoelectric layer, which material properties vary widely from layer to layer and subjected to electromechanical loading cannot be accurately predicted, the interlaminar stresses may be very high, eventually leading to interlaminar failure. In light of this, an effective mechanoelectrical coupling model for the accurate prediction of interlaminar stress for composite plates contains GSR actuators is developed in present study. Meanwhile, the finite element formulation (FEF) can be substantially simplified due to the expression of transverse shear stress components becoming more succinct. Therefore, by using the suggested electro-mechanical coupling theory, a three-node FEF is easily constructed. The refinement of transverse shear stress prediction in the context of electromechanical coupling can be accomplished through the application of the Reissner mixed variation theory (RMVT). The performance of the recommended plate model will be evaluated using the results derived from three-dimensional (3D) elastic theory and the selected model. By employing the RMVT method, we improve predictions of transverse shear stresses while considering the electromechanical coupling effect. The results from our model are compared with alternative models and 3D elasticity theory, demonstrating its superiority in satisfying the continuity requirements of transverse shear stresses and exhibiting excellent agreement with exact solutions. This validates the accuracy and applicability of our proposed model. Further to that, the prediction of mechanical characteristics for laminated plates with GSR actuators were systematically studied from the thoroughly perspectives of electromechanical load, piezoelectric layer thickness, graphene volume fraction, and some other parameters.

Role of nonlinear viscous dissipation on the magnetic domain wall motion in multiferroic heterostructures

This work theoretically investigates the strain-mediated magnetic domain wall propagation in a magnetostrictive layer, which is perfectly attached to a thick piezoelectric layer under the combined mechanism of nonlinear viscous and dry friction dissipation. The mathematical model of this study is formulated within the framework of the one-dimensional Extended Landau-Lifshitz-Gilbert equation, considering the simultaneous action of the applied magnetic and electric fields, nonlinear dissipations and piezo-induced strains. We use the traveling wave ansatz to derive analytical expressions of the key features like threshold, breakdown, and domain wall velocity in steady and precessional regimes. More precisely, our prime focus is to examine how nonlinear viscous dissipation affects the dynamics of domain walls in both isotropic and anisotropic magnetostrictive materials. The velocity profile of the magnetic domain wall becomes nonlinear due to the inclusion of the nonlinear viscous dissipation, which also significantly affects the Walker breakdown limit, thus leading to the expansion of the steady-state regime. Finally, we present a numerical illustration of the obtained analytical results, which agree well with recent observations.

Design of an Energy Harvester Based on a Rubber Bearing Floating Slab Track

It is known that a large amount of vibration mechanical energy will be generated during train operation. If the mechanical energy can be obtained from the track structure, it can greatly optimize the energy configuration of the metro. Currently, most sensors are limited to disk or cymbal structures and are not used in the track bed; different from existing structures, this paper designs a spherical energy harvester based on a rubber bearing floating slab track, wherein the size range of the spherical energy harvesting structure was approximately determined based on the geometric spatial relationships of the actual track bed internal structure. Compared to the traditional disk and cymbal energy harvesters, the mechanical and electrical properties of the spherical energy harvesting structure was studied by a numerical simulation method, and the optimal size of the spherical energy was determined by calculation. The main conclusions are as follows: (1) Compared with the traditional disk harvester and cymbal harvester, the spherical harvester had better mechanical and electrical properties. (2) By calculating the output power of energy harvesters under load matching, we found that the output power of the spherical harvester was two orders of magnitude higher than that of the disk harvester and 53% higher than that of the cymbal harvester. (3) The optimum size of the spherical harvester was when the thickness of piezoelectric layer was 2 mm, the radius was 16 mm, the axial ratio of the spherical shell was 0.4, and the thickness of the spherical shell was 4 mm.

Electro-Mechanical Buckling of Shallow Segments of Functionally Graded Porous Toroidal Shell Covered by Piezoelectric Actuators

The current work deals with the mechanical buckling behavior of saturated porous toroidal shell segments sandwiched by piezoelectric actuator layers. Material properties of the porous shells with nonuniform distributed porosities are assumed to vary as a specific function of the thickness and porosity parameters. The nonlinear equations of the sandwich toroidal shell having either positive or negative Gaussian curvature are obtained on the basis of Biot’s poroelasticity theory. The energy method as the minimum potential energy principle is applied to derive the governing equations of the sandwich shells. The buckling equations of the piezo-porous sandwich shells under various types of mechanical loading are established by employing the adjacent equilibrium criterion. The governing equations as a set of the coupled partial differential equations are solved using an analytical method including the Airy stress function. Closed-form solutions are derived for shallow segments of the sandwich toroidal shell with positive/negative Gaussian curvature under lateral pressure, axial compression, and hydrostatic pressure loadings. Novel numerical results are presented in this work to show the effects of important factors such as the piezoelectric layer thickness, applied voltage, shell geometrical ratio, and variation of the porosity coefficient on the buckling behavior of these structures.

Effects of piezoelectric synthetic jet actuator parameters on synthetic jet formation process and actuator performance

Aiming at the problem that the non-linearity between the piezoelectric vibrator deflection and the excitation amplitude of the piezoelectric synthetic jet actuator (SJA) causes it difficult to obtain the variation laws of the synthetic jet (SJ) velocity accurately, a theoretical model of the whole flow field of the piezoelectric SJA is established and four important parameters (half period jet mean velocity, Reynolds number, effective jet length and energy) for evaluating the performance of the SJ are proposed. Then a two-dimensional axisymmetric numerical simulation is carried out with k-ω turbulence model to study the SJ formation process and the velocity characteristics of the SJ at the orifice. The results show that the fluid pressure in the cavity is the main reason causing the non-linearity between the piezoelectric vibrator deflection and the excitation amplitude, the influence of which decreases with the increase of the orifice diameter. The SJ velocity increases first and then decreases slowly with the increase of excitation frequency. The extreme point occurs at the first resonant frequency of the piezoelectric vibrator and the position of the maximum velocity occurs at 0.5 mm outside the orifice. Other conditions being constant, both the piezoelectric vibrator deflection and jet velocity have a maximum value when the radius ratio of the piezoelectric layer to the elastic layer is 0.75. Smaller piezoelectric layer thickness leads to larger lateral displacement of the piezoelectric vibrator, and the optimum thickness ratio is 0.25. The results of this study have important guiding significance for accurately obtaining the variation laws of the SJ velocity as well as rationally designing the piezoelectric SJA.

Free vibration and nonlinear dynamic response of sandwich plates with auxetic honeycomb core and piezoelectric face sheets

This article analyses the nonlinear dynamic behavior and the free vibration of a piezoelectric auxetic honeycomb sandwich plate resting on a Pasternak elastic substrate. The plate includes two face sheets of piezoelectric material and an auxetic honeycomb core with a negative Poisson ratio. The first-order shear deformation plate theory, together with the von Kármán type nonlinear strain-displacement relationship, is used to establish the nonlinear equations of motion. Linear electric potential change with piezoelectric layer thickness is assumed. Two types of boundary conditions, namely immovable and movable simply supported, are considered. The displacement-time and acceleration-displacement curves under dynamic loads are determined by using the Galerkin and Runge-Kutta fourth-order methods. Verification examples have been performed and confirmed the accuracy of the model. Finally, several novel investigations have been conducted to evaluate the effect of material, geometrical parameters, and elastic substrate coefficients on the frequency and nonlinear dynamic characteristics of piezoelectric auxetic honeycomb sandwich plates for both open-circuit and closed-circuit operation.

Design and Modeling of a PVDF-TrFe Flexible Wind Energy Harvester

This study presents the simulation, experimentation, and design considerations of a Poly(vinylidene fluoride co-trifluoroethylene)/ Polyethylene Terephthalate (PVDF-TrFe / PET), laser-cut, flexible piezoelectric energy harvester. It is possible to obtain energy from the environment around autonomous sensor systems, which can then be used to power various equipment. This article investigates the actuation means of ambient vibration, which is a good candidate for using piezoelectric energy harvester (PEH) devices. The output voltage characteristics were analyzed in a wind test apparatus. Finite element modeling (FEM) was done for von Mises stress and modal analysis. Resonance frequency sweeps, quality factors, and damping ratios of the circular plate were given numerically. For a PVDF-TrFe piezoelectric layer thickness of 18 µm and 1.5 mm radius, a damping ratio of 0.117 and a quality factor of 4.284 was calculated. Vmax was calculated as 984 mV from the wind setup experiments and compared with the FEM outputs.

Comparative Study of Three SAW Configurations for Temperature Sensing

This paper demonstrates three SAW configurations' electrical and mechanical behaviors: a one-port resonator, a two-port resonator, and a delay line that works as temperature sensors of around 440 MHz characteristic frequencies. We investigate the sensitivity of the sensors for temperatures up to 200 °C. A linear behavior of the frequency shift versus temperature is observed; the resulting sensitivity of the sensors is evaluated at 22.74 ppm/°C for the one-port resonator, 23.17 for the two-port resonator, and 3.83 ns/°C for the delay line structure. The electromechanical coupling coefficient (k2) is 0.492 % for the delay line, 0.489 % for the one-port resonator, and 0.55% for the two-port resonator. The quality factor QFactor calculated from Y11 electrical input admittance is 2858 for the one-port resonator, 2977 for the delay line, and 2903 for the two-port resonator. The optimized piezoelectric layer thickness value, for the one port resonator, is hAlN=1.5µm.

MEMS piezoelectric bionic directional sound sensor based on ZnO thin film

In view of the low sensitivity of MEMS directional sound sensor, a bionic sensitive structure has been studied using finite element method (FEM). The MEMS piezoelectric bionic directional sound sensor, based on ZnO material was prepared and evaluated. In comparison to general structural optimization, which was only capable of determining the maximum theoretical sensitivity, the work carried out in this study introduced the additional parameter of electrical energy to the MEMS system, in order to incorporate and hence investigate the effect of stray capacitance, on the actual sensitivity of the device. Through a comprehensive analysis of the theoretical sensitivity, as well as the electrical energy (the product of theoretical sensitivity and the electrical energy was taken as parameter that was optimized), the thickness of the ZnO piezoelectric layer was optimized, to achieve the maximum actual sensitivity for the sound sensor. Through optimization of the fabrication process, the MEMS bionic piezoelectric directional sound sensor was developed on a 4 mm × 4 mm × 0.5 mm chip, with a relatively low residual stress exerted on the vibration film. The test results showed that the single channel sensitivity of the MEMS piezoelectric bionic directional sound sensor reached up to a high value of 0.8 mV/Pa (without amplification, 51 dB). The sensitivity with four channels in series was about 3.2 mV/Pa, and the device exhibited good directivity, as well.

Sparse 2-D PZT-on-PCB Arrays With Density Tapering.

Two-dimensional (2-D) arrays offer volumetric imaging capabilities without the need for probe translation or rotation. A sparse array with elements seeded in a tapering spiral pattern enables one-to-one connection to an ultrasound machine, thus allowing flexible transmission and reception strategies. To test the concept of sparse spiral array imaging, we have designed, realized, and characterized two prototype probes designed at 2.5-MHz low-frequency (LF) and 5-MHz high-frequency (HF) center frequencies. Both probes share the same electronic design, based on piezoelectric ceramics and rapid prototyping with printed circuit board substrates to wire the elements to external connectors. Different center frequencies were achieved by adjusting the piezoelectric layer thickness. The LF and HF prototype probes had 88% and 95% of working elements, producing peak pressures of 21 and 96 kPa/V when focused at 5 and 3 cm, respectively. The one-way -3-dB bandwidths were 26% and 32%. These results, together with experimental tests on tissue-mimicking phantoms, show that the probes are viable for volumetric imaging.

PZT-Film-Based Piezoelectric Micromachined Ultrasonic Transducer with I-Shaped Composite Diaphragm.

We proposed a PZT-film-based piezoelectric micromachined ultrasonic transducer (pMUT) with an I-shaped composite diaphragm to improve the sensitivity and resonant frequency of pMUTs with the same diaphragm area. The finite element method (FEM) simulation results indicated that the pMUT with an I-shaped composite diaphragm had relatively high sensitivity and resonant frequency. The pMUT with an I-shaped diaphragm had a 36.07% higher resonant frequency than a pMUT with a circular diaphragm. The pMUT with an I-shaped diaphragm had a 3.65 dB higher loop gain (loss) than a pMUT with a rectangular diaphragm. The piezoelectric layer thickness of the pMUT with an I-shaped composite diaphragm was then optimized. Maximum loop gain (loss) was reached when the piezoelectric layer thickness was 8 μm. The pMUT with an I-shaped composite diaphragm was fabricated using the MEMS method, and its performance was evaluated.

Environmental vibration energy collection technology based on piezoelectric and electromagnetic model

In this paper, the vibration model of the piezoelectric cantilever, the piezoelectric and electromagnetic output model are established. The simulation analysis of the cantilever vibration is performed using Comsol Multiphysics software. The effects of structural parameters, including cantilever length, cantilever thickness, piezoelectric layer length, piezoelectric layer thickness, coil size and position, on the resonance frequency and output voltage were analyzed. A cantilever vibration energy collection device is designed. The feasibility and accuracy of theoretical analysis were verified through the experiment, and the resonance frequency and the output voltage of the experiment basically agree with the theoretical calculation value.

On the solution technique for the interior electric displacement in a piezoelectric crack with the semi-permeable electric condition

In the study of crack problems in piezoelectric materials, the choice of electric conditions on the crack surface is crucial. The semi-permeable condition is believed to be more consistent with the real physical situation than the impermeable and permeable. In the semi-permeable crack condition, one task is to solve the crack interior electric displacement. However, there is no discussion in literature on the possible general method for its solution. A feasible method is proposed in this paper, addressed by taking as an example a penny-shaped crack in a piezoelectric layer with strip-like electrical saturation and mechanical yielding zones. The mixed boundary value problem is transformed into a set of coupling Fredholm integral equations of the second kind by Hankel transform and Copson method. With appropriate numerical discretization, the bisection method is adopted to solve the crack interior electric displacement. The algorithmic flow of the problem is given and some degenerated examples are presented to illustrate the effectiveness of the proposed technique. Finally, numerical results are presented for the relation of external load as well as the crack face electric displacement versus zone-lengths. Comparison and discussion are presented for the results of semi-permeable and impermeable crack condition. Results show that the crack interior electric displacement increases with electrical load but decreases with mechanical load. The electrical saturation zone-length is affected by the mechanical load as well as electrical load, regardless of the thickness of piezoelectric layer as well as the size relation of the mechanical and electrical zone-length. The present solution technique has a direct reference value for solving the problem of semi-permeable crack with distinct strip-like yielding zones in the finite piezoelectric material.

Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads

This paper presents an investigation on thermo-electro-mechanical nonlinear low-velocity impact behaviors of the geometrically imperfect functionally graded (FG) graphene-reinforced composite (GRC) beam with surface-bonded piezoelectric layers. Both uniformly distributed and FG patterns of graphene nanoplatelets (GPLs) are considered along the thickness of the GRC host beam. The effective Young’s modulus is calculated by the Halpin–Tsai model. The Poisson ratio and mass density are calculated by the rule of mixture. The modified nonlinear Hertz contact law is employed to predict the impact force between the spherical impactor and the geometrically imperfect GRC piezoelectric beam during impacting. By considering the first-order shear deformation theory and von Kármán nonlinear displacement–strain relationship, the nonlinear governing equations are obtained by Hamilton principle and dispersed by differential quadrature (DQ) method. The Newmark-β method associated with Newton–Raphson iterative process is adopted to parametrically identify the impact force and the dynamic response of the system. The effects of geometric imperfection, weight fraction and distribution pattern of GPLs, temperature variation, thickness of piezoelectric layer and impactor’s initial velocity on nonlinear low-velocity impact behaviors of geometrically imperfect GRC beams are discussed in detail. Our results illustrate that the coupling effect of geometric imperfection and thermo-electro-mechanical load has a significant effect on the nonlinear low-velocity impact behavior of GRC beam, and GPLs distributing into the piezoelectric layers is better for reducing the impact response of geometrically imperfect GRC piezoelectric beam.

Experiment and analysis of a piezoelectric energy harvester based on combined FEM modeling and spice simulation

This paper presents modeling and simulation of a cantilever-type piezoelectric energy harvester based on a combined FEM (Finite Element Method) and spice circuit. The PEH having dimension of 61 mm × 37 mm × 0.4 mm provides the maximum output power of 8 mW at resonant frequency of 127 Hz. The fabricated cantilever-type PEH (Piezoelectric Energy Harvester) has been characterized with variable resistor, which reveals that maximum power transfer is achieved at 10 kΩ. The modeling and simulation have beenperformed to study the effect of piezoelectric layer thickness on PEH output power in case of load resistance. FEM modeling and simulations have been carried out to extract electrical elements such as Rm, Lm, Cm, Cp and Γ. Those electrical elements have been included into a spice model to find optimal load resistance for maximum power transfer as well as. frequency response as function of piezoelectric layer thickness. Experiment and simulation show a good agreement on optimal load resistance.