Piezoelectric Composite Plates Research Articles

Nonlinear vibrations, bifurcations and chaos of piezoelectric composite lattice sandwich plate with four simply supported edges

This paper is devoted to investigate the nonlinear dynamics, bifurcation and chaos of the piezoelectric composite lattice sandwich plate with 1:3 internal resonance. Galerkin method is used to discretize the nonlinear partial differential governing equations of motion into the ordinary differential equations. The multi-scale method is used to obtain the modulation equations of the piezoelectric composite lattice sandwich plate in the polar coordinates and Cartesian coordinates in the primary and parametric resonances, respectively. Using Newton-Raphson method, the bifurcation diagrams of the steady-state equilibrium solution are obtained for the modulation equation with the change of the system parameters. The stability of the steady-state equilibrium solution is analyzed for the modulation equation. The existence of the static bifurcations, such as the saddle-node bifurcation, pitchfork bifurcation and Hopf dynamic bifurcations are found. The complex nonlinear jump phenomena caused by the existence of the multiple nonlinear steady-state solution regions are analyzed in detail. Fourth-order Runge-Kutta method is used to continue tracing the nonlinear periodic solution of the modulation equation in Cartesian coordinates. The time-history diagram, phase portrait and Poincaré map are obtained for the piezoelectric composite lattice sandwich plate in the nonlinear resonance. The dynamic process of the nonlinear periodic solution is described for the modulation equation from the limit cycle oscillation to the chaotic attractor in detail.

Stability of composite plates integrated with graphene-reinforced piezoelectric layers

Graphene enhances piezoelectric matrix properties due to its exceptional conductivity and physical characteristics. However, existing models encounter significant challenges in analyzing buckling behavior of graphene-reinforced composite piezoelectric (GRCP) actuators. Inaccuracy in describing transverse shear deformations impact plate stability, particularly due to the disparities in material properties at the interfaces. A new plate model is proposed, featuring a refined interlaminar shear stress field for accurate modeling. Validity is confirmed via 3D elasticity solutions and alternative theories. Compared to existing models, the proposed theory shows superior precision. Additionally, a parametric study explores key factors influencing buckling behaviors of piezoelectric composite plates.

Transmission of Lamb wave in a micro-mechanically piezoelectric fiber-reinforced composite plate

The present work addresses the propagation characteristics of Lamb wave in a piezoelectric fiber-reinforced composite material plate. The considered plate is micro-mechanically modeled using the analytical techniques of the Strength of Materials and Rule of Mixtures. Secular equations are deduced for symmetric and antisymmetric modes of Lamb wave by employing suitable boundary conditions. The data of two distinct PFRC materials are taken into account, viz. PZT-5A-epoxy and CdSe-epoxy with different fiber volume fractions to investigate the latent characteristics of Lamb wave propagation. The amplitudes of dilatation and electrical potential of considered material are examined numerically and manifested graphically for both kinds of modes, i.e., symmetric and antisymmetric modes. The obtained graphical results are also compared for both kinds of modes. A comparative study has been carried out to exhibit the concealed characteristics of Lamb wave propagation for various distinct cases of considered structure for both symmetric and antisymmetric modes. The determined analytical results are in well agreement with the results present in the existing literature.

Innovative deep energy method for piezoelectricity problems

This work introduces a novel investigation into the use of the deep energy approach for addressing multi-physics issues often encountered in the field of piezoelectricity. The deep energy approach has become known as a robust numerical technique, demonstrating remarkable ability in handling complex nonlinearities and producing very precise results. This research aims to comprehensively investigate the roles and impacts of several network characteristics, including layers, neurons, and activation functions, on the accuracy of the approach. The reliability and novelty of our technique are shown by the successful resolution of three intricate 2D piezoelectric problems, exhibiting remarkable accuracy. This is particularly evident when using the tanh activation function, which outperforms other solutions. Furthermore, our technique is expanded to include the examination of piezoelectric composite plate actuators. This expansion yields results that closely align with well-established analytical solutions and empirical evidence, therefore showcasing the flexibility and effectiveness of our approach. This study not only unveils the deep energy method as a potential alternative to traditional numerical techniques for intricate multi-physics phenomena but also provides a comprehensive understanding of the role of activation functions. The tanh activation function has demonstrated superior precision across configurations, significantly enhancing model accuracy and flexibility for real-world engineering applications.

Buckling analysis of composite plates surface bonded with graphene‐reinforced piezoelectric actuators

AbstractGraphene is a highly conductive and exceptional material that has shown potential for significantly improving the piezoelectric and mechanical properties of piezoelectric matrix. This paper examines the stability of composite plates surface bonded with graphene‐reinforced composite piezoelectric (GRCP) actuators. However, the significant differences in material characteristics at the interfaces will pose some challenges in analyzing the buckling behavior of piezoelectric composite plates by means of existing higher‐order shear deformation theories. To address this issue, a refined plate theory is developed for the buckling analysis of piezoelectric composite plates. The developed theory includes a new interlaminar shear stress field that precisely describes the distribution of interlaminar shear stresses, which differs from earlier higher‐order theories. It should be emphasized that the finite element formulation can be simplified by removing the second‐order derivatives of in‐plane displacement parameters from interlaminar shear stresses. In terms of the developed theory, a four‐node C0 quadrilateral plate element is introduced to examine the buckling behavior of piezoelectric composite plates. Furthermore, the modified interlaminar shear stress field is absorbed into the strain energy, significantly improving the ability to predict the critical loads of composite plates with GRCP actuators. The refined plate model is evaluated through the utilization of three‐dimensional (3D) elasticity solutions and results obtained from other associated theories. Numerical results demonstrate that the refined plate model is capable of producing favorable results, and a comprehensive examination is conducted to analyze the effects of significant parameters on the buckling behaviors of piezoelectric composite plates. This study sets a solid foundation for future research and development on the application of graphene‐reinforced composite piezoelectric actuators in composite structures.Highlights Buckling analysis of composite plates with GRCP actuators is conducted. A refined plate theory with modified interlaminar shear stresses is developed. The ability to predict critical loads can be significantly improved. The finite element formulation can be simplified based on the proposed model. Comprehensive parametric studies on buckling behavior are caried out.

Nonlinear Dynamic Bifurcation and Chaos Characteristics of Piezoelectric Composite Lattice Sandwich Plates

This paper investigates the nonlinear bifurcation and chaos characteristics of piezoelectric composite lattice sandwich plates at 1:3 internal resonance. The nonlinear vibration partial differential equation is first discretized to become an ordinary differential equation by applying the Galerkin method. The main resonance modulation equations and the parametric resonance for the external excitation frequency that is close to the system’s second-order modal frequency are then obtained by using the multiscale method. The Newton–Raphson method is subsequently applied to obtain the bifurcation diagram of the steady-state equilibrium of modulation equation with varying system parameters. The equilibrium stability is finally analyzed. We confirm the existence of static bifurcation such as saddle-node bifurcation, pitchfork bifurcation, and Hopf dynamic bifurcation. A detailed analysis is also conducted on the complex nonlinear jump phenomenon caused by the presence of multiple nonlinear steady-state solution regions. In the dynamic Hopf bifurcation interval, the fourth-order Runge–Kutta method is used to continue to track the dynamic periodic solution of the modulation equation in Cartesian coordinates. It is found that there are multiple boundary crises and attractor merging crises in the vibration system for piezoelectric composite lattice sandwich plates.

TO ASSESS THE RATIO OF ECHO SIGNAL LEVELS AND STRUCTURAL NOISE DURING ULTRASONIC TESTING OF CERTAIN TYPES OF STEEL USED IN THE MANUFACTURE OF NUCLEAR POWER PLANT EQUIPMENT

Based on computer modeling, the signal-to-noise ratio estimates are made for models of reflectors in the form of a side drilled hole and a round flat bottom hole small size during ultrasonic method by an angle probe of products made of a number of types of steel used in the manufacture of equipment for nuclear power plants. It is shown that for steels of types 20, 12X1MF and 10GN2MFA, the ratio of the levels of the echo signal and structural noise (signal/noise) for both models with a large margin satisfy the criterion of Prof. I. N. Ermolov reliable detection of a useful echo signal. For steel of type 15X2MFA-A, due to a sufficiently large value of the average grain size and, accordingly, an increased level of structural noise, the signal-to-noise ratio may not meet the criterion of Prof. I. N. Ermolov, which necessitates an increase in this ratio, for example, by increasing the damping of the piezoelectric plate of the angle probe. To increase the signal-to-noise ratio and increase the amplitude of the echo signal, it may be advisable to use a angle probe with a composite piezoelectric plate.

Multilevel Fully Integrated Electromechanical Property Modulation of Functionally Graded Graphene‐Reinforced Piezoelectric Actuators: Coupled Effect of Poling Orientation

AbstractThis article explores the coupled static and dynamic electromechanical responses of single and multilayered functionally graded (FG) graphene platelet (GPL)‐reinforced piezoelectric composite (GRPC) plates by developing a 3D finite‐element model. The bending and eigenfrequency of piezoelectric FG composite plates are investigated, wherein an active behavior is proposed to be exploited in terms of the functional design of poling angle for a more elementary level property modulation. The numerical results reveal that the mechanical behavior concerning deflection and resonance frequency of FG‐GRPC plates can be significantly enhanced and modulated due to the influence of piezoelectricity and a small fraction of GPLs along with the consideration of poling angle in a multiscale fully integrated computational framework. The notions of on‐demand property modulation, actuation, and active control are established here by undertaking a comprehensive numerical analysis considering the coupled influences of poling orientations, different distributions, patterns, and weight fractions of GPLs along with different electromechanical loadings. Against the backdrop of the recent advances in microscale manufacturing, the current computational work will provide necessary physical insights in modeling piezoelectric multifunctional FG composites for active control of mechanical properties and harvesting electromechanical energy in a range of devices and systems.

A fully-coupled vibro-acoustic model of an electronic stethoscope

A piezoelectric based stethoscope picks pressure fluctuations originating from the patient and the physician sides. This may include unwanted acoustic signals from the patient and the doctor sides of the stethoscope, which needs to be filtered either electronically or mechanically by appropriately designing the vibro-acoustic elements of the electronic stethoscope. This work intends to establish a mathematical model of the piezoelectric stethoscope. Initially, a multi-degrees of freedom vibration model of the electronic stethoscope is developed. The model is used to compute the response of the piezoelectric plate due to the pressure excitations on the input side and that due to the displacements of the connected mechanical elements in the stethoscope. Further, a two-port lumped parameter model of the piezoelectric composite plate is developed to compute the output voltage created by the displacement of the piezoceramic disc. Here, an axisymmetric plate vibration model (Kirchhoff's plate theory) is used to find the displacement of the piezoelectric composite plate. Subsequently, the vibration and the lumped parameter piezoelectric models are combined to represent the vibro-acoustic characteristics of the piezoelectric stethoscope. Further, using the developed fully-coupled vibroacoustic model, the output voltage of the device is studied for different patient and physician side excitations.

Hybrid acoustic, vibration, and wind energy harvester using piezoelectric transduction for self-powered wireless sensor node applications

Energy harvesters are considered to be a promising solution for long lasting operation of wireless sensor nodes, moreover, make these power-sustainable in hazardous, implantable, remote, harsh, embedded, and abandoned environments where frequent battery replacement is a challenge. Existing energy harvesters utilize only one or two ambient energy sources, however, in this paper, we developed a novel piezoelectric-based energy harvester that converts three ambient energies (acoustic, vibration, and wind) simultaneously into electrical energy. The developed harvester comprises a Helmholtz resonator, a unimorph piezoelectric composite plate, and a cambered aerofoil connected with a piezoelectric plate using a base support. Acoustic, vibration, and wind induced deformation in the harvester’s piezoelectric plate and intrun electrical energy is produced based on piezoelectric phenomena. The harvester showed two peaks (at 802 and 1417 Hz frequencies) when subjected to a forward frequency sweep (FFS) which corresponds to its resonant frequencies. Under resonance, in the acoustic and vibrations environment, the harvester produced a maximum power of 210.6 µW, and 1.38 mW on excitation at 130 dB sound pressure level (SPL) and 0.8 g base acceleration, respectively. Furthermore, the harvester produced maximum power of about 285 µW when exposed to 8 m/s wind speed. The developed harvester can be a potential power source for self-powered wireless sensors used for the structural health monitoring of bridges, tall buildings, and railway tracks.

Active vibration control of a piezoelectric composite laminate

An active vibration control method of the piezoelectric composite laminated plate under the external disturbance is studied. Firstly, the dynamic model of the piezoelectric composite laminated plate is derived based on the classical laminated plate theory and the Hamilton's principle. And subsequently, a sliding mode observer is developed for the external disturbance, and the stability of the observer is verified by the Lyapunov equation, and also the LQR controller is designed based on the observed state. The particle swarm algorithm is adapted to optimize the weighting matrix. In the end, the impacts of the geometric parameters and the stacking sequences on the dynamic behavior of the piezoelectric composite material plate is analyzed. Results indicate that the sliding mode observer can accurately track the original state, and the vibration of the piezoelectric composite material plate can be suppressed effectively by the LQR control based on the particle swarm

Expression of Concern: “Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory” [JCOMB, Volume 95, 15 June 2016, Pages 209–224

Expression of Concern: “Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory” [JCOMB, Volume 95, 15 June 2016, Pages 209–224

Optimize multilayer matching layer design for tone-burst underwater acoustic transducers.

In this study, a theoretical model has been constructed to address the optimization of matching layers for tone burst excitation underwater acoustic transducers and to investigate the functional mechanism change of matching layers. Single, double, and triple matching layers are attached to piezoelectric composite plates, and tone burst signals with a different number of burst-cycles are applied. Acoustic pressure function (Sp) and acoustic pressure transient response (PTR) are compared among these transducers. The results demonstrated that when the cycle number M ≤ 2, more matching layers lead to shorter ringdown with similar PTR amplitude. Since the objective is for better axial resolution, three matching layers have noticeable advantage, whereas for the case of M > 5, far detection distance is the main objective, and more matching layers caused the decrease in PTR amplitude. Besides, matching layers become part of the resonance structure; they do not serve as a transmission medium anymore. Therefore, the transducer with single matching is optimal for the long tone burst excitation. For the case of 2-5 cycle excitation, one may use double matching layers, which has a balance between the transmitting voltage response amplitude and bandwidth. With the increase in M, the role of matching layers changes from a bridging transmission medium to amplifying vibration velocity and introducing additional vibration modes to broaden the bandwidth.

Isogeometric Analysis of Graphene-Reinforced Functionally Gradient Piezoelectric Plates Resting on Winkler Elastic Foundations.

In this paper, the refined plate theory (RPT), Hamilton’s principle, and isogeometric analysis (IGA) are applied to investigate the static bending, free vibration and buckling behaviors of functionally graded graphene-platelet-reinforced piezoelectric (FG-GRP) plates resting on a Winkler elastic foundation. The graphene platelets (GPLs) are distributed in polyvinylidene fluoride (PVDF) as a power function along the plate thickness direction to generate functionally gradient materials (FGMs). The modified Halpin–Tsai parallel model predicts the effective Young’s modulus of each graphene-reinforced piezoelectric composite plate layer, and the rule of the mixture can be used to calculate the effective Poisson’s ratio, mass density, and piezoelectric properties. Under different graphene distribution patterns and boundary conditions, the effects of a plate’s geometric dimensions, GPLs’ physical properties, GPLs’ geometric properties and the elastic coefficient of the Winkler elastic foundation on deflections, frequencies and bucking loads of the FG-GRP plates are investigated in depth. The convergence and computational efficiency of the present IGA are confirmed versus other studies. Furthermore, the results illustrate that a small amount of GPL reinforcements can improve the FG-GRP plates’ mechanical properties, i.e., GPLs can improve the system’s vibration and stability characteristics. The more GPL reinforcements spread into the surface layers, the more effective it is at enhancing the system’s stiffness.

Deflection and stress analysis of piezoelectric laminated composite plate under variable polynomial transverse loading

Among many smart materials, piezoelectric materials have emerged as the most studied ones for practical applications. They owe their success to several factors, including low price, high bandwidth, availability in various formats, and ease of handling and implementation. The present study focused on the performance of piezoelectric laminated composite plate under various electromechanical loading conditions by utilizing the first-order shear deformation theory with the Newton–Raphson residual and iteration with Gauss integration point in Ansys. For the first time, the effects of electrical loading, circuit arrangement, voltage variation, and polynomial variable transverse loading are studied over piezoelectric composite plate (PCP). The effects of plate aspect ratio, thickness ratio, boundary conditions, ply orientations, nature of loading conditions, and voltage variation are presented. The study also utilized open and close circuit arrangements as sensors and actuators to gauge the performance of PCP in the form of static bending analysis. The maximum OC (open circuit) output voltage is generated with the N4 type of loading compared with Ni (i = 1–4); on the other hand, the OC output voltage is minimum with N5. The combined effect of external load and voltage presented in the study will be useful for analyzing the deflection variation, and it can further be implemented in reducing deflection or vibration. It is noted that, with a higher piezoelectric to laminate thickness (t/h) ratio, the maximum OC output voltage is observed. In addition, the rate of voltage generation observed is the highest under the N4 loading condition and the lowest under the N5 type of load.

Shape Control of Composite Structure with Suitably Placed Piezoelectric Sensors Under Electro-Thermo-Mechanical Condition with Non-linear Analysis

In this paper, the application of piezoelectric actuators to the composite control card is studied statically. The electro-thermo-mechanically coupled mathematical model is used for the analysis. The main section of this paper is static control. Shape control is stated here as determining the shape control parameters, including the actuation voltage and the adjustment of the actuator orientation, so that the structure which is activated using these parameters also adapts as closely as possible to the required shape. In this paper, we have presented FE model for the control analysis of the shape of piezoelectric laminated (PZT) composite plates using Ansys. The piezoelectric layer and composite plate are modeled in the form of additional layers to be attached to the upper or lower surface or to be integrated into the laminated composite plate. Ansys finite element software is used for modeling and has been successfully validated with experimental and numerical results which are readily available in the literature. The present analysis shows that with the application of an appropriate voltage to the piezoelectric actuator, the desired shape of the composite plate can be obtained. Keywords: Composite plate, FEM, Intelligent structure, Non- linear, piezoelectric, sensor, voltage

Electromechanical characterization and kinetic energy harvesting of piezoelectric nanocomposites reinforced with glass fibers

Piezoelectric composites are a significant research field because of their excellent mechanical flexibility and sufficient stress-induced voltage. Furthermore, due to the widespread use of the Internet of Things (IoT) in recent years, small-sized piezoelectric composites have attracted a lot of attention. Also, there is an urgent need to develop evaluation methods for these composites. This paper evaluates the piezoelectric and mechanical properties of potassium sodium niobate (KNN)-epoxy and KNN-glass fiber-reinforced polymer (GFRP) composites using a modified small punch (MSP) and nanoindentation tests in addition to d33 measurements. An analytical solution for the piezoelectric composite thin plate under bending was obtained for the determination of the bending properties. Due to the glass fiber inclusion, the bending strength increased by about four times, and Young's modulus in the length direction increased by approximately two times (more than that of the KNN-epoxy); however, in the thickness direction, Young's modulus decreased by less than half. An impact energy harvesting test was then performed on the KNN-epoxy and KNN-GFRP composites. As a result, the output voltage of KNN-GFRP was larger than that of KNN-epoxy. Also, the output voltage was about 2.4 V with a compressive stress of 0.2 MPa, although the presence of the glass fibers decreased the piezoelectric constants. Finally, damped flexural vibration energy harvesting test was carried out on the KNN-epoxy and KNN-GFRP composites. The KNN-epoxy was broken during the test, however KNN-GFRP composite with a load resistance of 10 MΩ generated 35 nJ of energy. Overall, through this work, we succeeded in developing piezoelectric energy harvesting composite materials that can withstand impact and bending vibration using glass fibers and also established a method for evaluating the electromechanical properties with small test specimen.

Parity–time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time (PT) symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain. Here, we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits. By judiciously adjusting the resistances and inductances in the external circuits, we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility. Moreover, the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits, which represents the active control that makes the acoustic manipulation more convenient. Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.

Transverse vibration responses of the in-plane-wise functionally graded piezoelectric composite plates

Aided by the scaled boundary finite element method (SBFEM), analytical precise integration solutions to the transverse free vibration responses of functionally graded piezoelectric composite plates are provided for the first time. Distributions of the functionally graded piezoelectric materials follow arbitrary mathematical formulae as concerns the in-plane unidirectional or bidirectional coordinates. The vibration behaviors of piezoelectric composite plates with various geometrical shapes, multifarious boundary constraints and any number of laminae can be explored by the introduced technique. Additionally, the shear correction factors and assumptions on the changing patterns of mechanical and electrical variables are not needed to be offered in the employed methodology. The proposed approach regards only four quantities containing three elastic displacement components and the electric potential as the primary unknowns, which can be denoted as an analytical matrix exponent in terms of the thickness coordinate. Only two-dimensional high-order spectral elements are adopted to discretize the in-plane surface of the plate with less nodes and degree of freedoms, which promotes to lowering the calculative expense and advancing the computational efficiency. The introduced scaled boundary coordinate system and the dual vector technology are helpful to simplify the basic partial differential equations of piezoelectric materials into the first order ordinary differential SBFEM governing equation, from which the highly accurate global stiffness matrix are constructed by dine of the precise integration technique (PIT). With the aid of the kinetic energy scheme and compatibility conditions between neighboring layers, the whole mass matrix for the laminated piezoelectric plates can be built. According to solving the eigenvalue equation, the precise integration solutions to free vibration frequencies can be acquired. Finally, numerical experiments are afforded to elucidate the high precision and fast convergence of the present method. Moreover, the effect of different boundary constraints, gradation parameters and aspect ratios on the transverse vibration responses of in-plane-wise functionally graded piezoelectric composite plates is revealed.

A coupled nonlinear plate finite element for thermal buckling and postbuckling of piezoelectric composite plates including thermo-electro-mechanical effects

This paper investigates the thermo-electro-mechanical effects in the nonlinear response of piezoelectric laminated plates exposed to thermal and/or mechanical fields. The mechanics incorporate a) the direct piezoelectric effect through the coupling between electric-mechanical fields, b) the pyroelectric effect through the coupling between electric-thermal fields, and c) the geometric nonlinear effects due to large rotations and initial stresses. Building upon the nonlinear multifield mechanics an eight-node plate finite element is developed to discretize the generalized coupled nonlinear equations, which are subsequently linearized and iteratively solved, using the Newton-Raphson technique. Numerical evaluations demonstrate the capability of the present model to capture both of direct piezoelectric and pyroelectric effects in the nonlinear electromechanical response of piezoelectric composite plates, exposed to thermal and/or mechanical fields. The influence of direct piezoelectric and pyroelectric effects on thermal buckling and postbuckling response of various piezocomposite plates, is investigated. The possibility of pyroelectric effect to promote thermal buckling of piezocomposite plates with attached sensor patches is also quantified. The influence of thermo-electro-mechanical effects on the nonlinear response of smart composite plates, subject to either uniform or gradient temperature variations is finally illustrated.