Piezocomposite Plate Research Articles

Influence of flexoelectricity on coupled electromechanical response of 2D MXene/graphene-based hybrid piezocomposites.

This study investigates the influence of flexoelectricity on the coupled electromechanical behavior of MXene/graphene-based hybrid piezocomposite (MGHPC) plates. We developed an analytical model based on Navier's solution and Kirchhoff's plate theory, as well as an approximate model based on the Ritz method for validation purposes. A three-phase micromechanical modeling is developed for determining the effective properties of MGHPC composed of 2D MXene and graphene nano-reinforcements embedded in an epoxy matrix. These micromechanical models were implemented to predict the static and dynamic electromechanical response of MGHPC plates subject to various edge support and loading conditions. Both the analytical and approximate solutions provided unequivocal evidence of the profound impact of the flexoelectric effect on the bending and modal analysis of MGHPC nanoplates. The flexoelectric effect enhanced the stiffness of the nanoplate, irrespective of the support condition. This implies that MGHPC plates can be tailored for precise resonance frequencies and static deflection within nanoelectromechanical systems. This can be achieved by manipulating parameters such as boundary conditions and geometric attributes, including plate thickness/aspect ratio and graphene/MXene nano-reinforcements volume fractions.

Higher-order asymptotic homogenization for piezoelectric composites

In this work, we developed a higher-order asymptotic homogenization method (AHM) for efficient multiscale analysis of piezoelectric composite structures. Instead of solving the composite structural problems directly with all heterogeneities considered, AHM first solves the microscale problem at each order of expansion to obtain the corresponding microfluctuation functions and effective properties; the latter is then passed to the macroscale to solve coupling governing differential equations, with the macroscale physical quantities passed back to the microscale and combined with microfluctuation functions to recover the local response. Governing differential equations are formulated and solved in Cartesian coordinates, which is much beneficial for understanding the multiscale-multiphysics behavior of flat piezocomposite structures such as Micro Fiber Composite transducers. Two numerical examples are solved using AHM, i.e., a 1D piezocomposite rod and a 2D piezocomposite plate, and the results are compared with direct numerical solution (DNS) to validate the accuracy and efficiency of the proposed method. The developed multiscale analysis algorithm largely saves the computational cost compared with DNS when a large number of inclusions are included in piezocomposites, thus making it an efficient tool for solving multiphysics composite structural problems with piezoelectricity.

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.

Observer based sliding mode control for subsonic piezo-composite plate involving time varying measurement delay

In this study, an observer based sliding mode control (SMC) scheme is proposed for vibration suppression of subsonic piezo-composite plate in the presence of time varying measurement delay by using the piezoelectric patch (PZT) actuator. Firstly, the state space form of the subsonic piezo-composite plate model is derived by Hamilton’s principle with the assumed mode method. Then an state observer involving time varying delay is constructed and the sufficient condition of the asymptotic stability is derived by using the Lyapunov-Krasovskii function, descriptor method and linear matrix inequalities (LMIs) for the state estimation error dynamical system. Subsequently, a sliding manifold is constructed on the estimation space. Then an observer-based controller is synthesized by using the SMC theory. The proposed SMC strategy ensures the reachability of the sliding manifold in the state estimate space. Finally, the simulation results are presented to demonstrate that the proposed observer-based controller strategy is effective in active aeroelastic control of subsonic piezo-composite plate involving time varying measurement delay.

Integrated vibration isolation and energy harvesting via a bistable piezo-composite plate

In passive vibration isolation, a bistable composite plate can be used to generate high-static low-dynamic stiffness, and in vibratory energy harvesting, when used with piezoelectric film flexing, the bistable composite plate can enhance the performance via snap-through motion. In the present work, we designed a bistable piezo-composite plate for both vibration isolation and energy harvesting. The analytical model for performance prediction is derived from the virtual work principle and the composite elasticity. Displacement transmissibility and output voltage generation were analytically determined for different mechanical and electrical parameters. The results illustrate that the bistable piezo-composite plate improves the feasibility and effectiveness of the integration design. Hardening and softening nonlinear phenomena coexist in both the displacement transmissibility and the output voltage plot. Approximate analytical solutions and numerical simulations are in good agreement. Both analytical and numerical results demonstrate that, at a certain frequency bands, enhanced energy harvesting is accompanied by a vibration transmissibility reduction. Compared with a linear system with the bistable piezo-composite plate removed, it achieved a reduction in the displacement transmissibility of about 13 dB at 100 Hz, simultaneously, and produced a considerable output voltage of about 0.05 V.

Analysis of mechanical vibration (SH wave) in Piezo-composite plates

The present problem aims to study the propagation behaviour of Shear Horizontal (SH) surface waves in a composite structure comprising of functionally graded piezoelectric plate fused with a porous piezoelectric plate. The material properties of the functionally graded piezoelectric material (FGPM) are assumed to be vary in quadratic manner. Method of separation of variables is used to obtain the solutions for the displacement and stress components in both the media. Solutions are obtained in terms of modified Bessel functions of first and second kinds. Dispersion relations are obtained for both the electrically open and short cases. Effects of thickness of the plates, gradient parameter, dielectric coefficient and piezoelectric coefficient on dispersion curve have been marked distinctly and portrayed through graphs. The electromechanical coupling factor is also plotted against wave number. Findings of the present investigation may set guidelines for the designing of more efficient Surface acoustic wave (SAW) devices.

Integration and test of piezocomposite sensors for structure health monitoring in aerospace

The paper presents an innovative approach for Structure Health Monitoring utilizing piezocomposite plates as active sensors. The present work is motivated by the increasing interest in reduction of maintenance costs for aircrafts, which can be achieved by implementing self-sufficient sensor networks into the aircraft to predict risk states and prevent structural failures. These networks could supplement and possibly replace the expensive maintenance inspections. Piezoelectric materials have recently been under a rapid development, have been utilized in various fields of industry and due to their inexpensive and robust nature they can be used as sensors in non-intrusive Structure Health Monitoring networks. The presented approach uses piezocomposite sensors embedded into the structure of a small civil aircraft to directly measure structural vibrations. The functionality of the entire measurement chain was tested during an experimental flight, the acquired data will be used for further research of data-processing, impact detection and structure health prediction.

A solution method based on Lagrange multipliers and Legendre polynomial series for free vibration analysis of laminated plates sandwiched by two MFC layers

In this paper, a new solution approach based on Lagrange multipliers is developed to investigate the free vibrations of rectangular composite plates equipped with piezoelectric layers such as Macro Fiber Composites (MFCs). The piezo-composite plate has general stacking sequences and is subjected to the elastic edge restraints. Using the first-order shear deformation theory (FSDT) and Hamilton’s principle, the boundary conditions of the problem are deduced. To solve the problem, the generalized displacements and electric potentials are expanded using the Legendre polynomial series as the base functions. Afterward, the strain and kinetic energies of the problem are achieved. Then, all the boundary conditions have been added to the energy expression by means of Lagrange multipliers to form the functional. This functional is extremised to give the natural frequencies and mode shapes of the problem through the generalized eigenvalue problem. Capability and credibility of the proposed approach are confirmed by comparing the results with those achieved by the experimental, finite element method (FEM) and 3D elasticity. The method finally is used to investigate the effects of MFCs orientations on the vibrational behavior of the smart plates.

Buckling and Postbuckling of Concentrically Stiffened Piezo-Composite Plates on Elastic Foundations

This research presents the modeling and analysis for the buckling and postbuckling behavior of sandwich plates under thermal and mechanical loads. The lay-up configurations of plates are laminated composite with concentric stiffener and surface mounted piezoelectric actuators. The plates are in contact with a three-parameter elastic foundation including softening and/or hardening nonlinearity. Several types of grid shapes of stiffeners are studied such as ortho grid, angle grid, iso grid, and orthotropic grid. The equations of structures are formulated based on the classical lamination theory incorporating nonlinear von-Karman relationships. The stress function and Galerkin procedure are applied to derive explicit formulations of the equilibrium paths. New results are introduced to give the influences of voltage through the thickness of piezoelectric actuators, different stiffeners, and nonlinear elastic foundations.

Postbuckling and deflection response of imperfect piezo-composite plates resting on elastic foundations under in-plane and lateral compression and electro-thermal loading

ABSTRACTThis article presents closed-form solution for the buckling, postbuckling, and nonlinear deflection of laminated composite plate with two piezoelectric actuators on elastic foundation and under transverse pressure, in-plane compression, thermal, and electrical loads for the first time in the literature. Material properties are assumed to be temperature-dependent. Two cases of boundary conditions and initial imperfection of the plate are considered. The formulations are based on the classical laminated plate theory (CLPT). The Galerkin method is employed to obtain load–deflection relations. The effects of elastic foundation, lateral pressure, in-plane compression, temperature dependency of material properties, electrical and thermal loading, imperfection, and aspect ratio are studied.

Annular 1-3 piezocomposite high intensity focused ultrasound transducer of a concave geometry

For medical therapeutic applications, we have developed a concave annular high intensity focused ultrasound (HIFU) transducer that is made of a 1-3 piezocomposite plate and operates at 3 MHz. The transducer has 16 annular channels, and the annuli have been designed to focus at the geometrical center of the sphere. The focal point can be controlled to scan a three dimensional volume by electronic and mechanical means. The focal point is moved along the normal axis of the transducer by electronically steering the sixteen annular channels. The focal point is also rotated back and forth by mechanically wobbling the piezocomposite plate with a kinematic linkage. The kinematic linkage is driven by an electric motor installed inside the transducer. The optimal combination of the number of channels, the width of the kerf between channels, and the width of each channel were determined by means of the OpQuest-Nonlinear programming algorithm and the finite element method. The objective of the optimization was to minimize the side lobe levels while focusing the ultrasound beam to a prescribed position. Based on the design, an experimental prototype of the transducer was fabricated and its performance was measured, which showed excellent agreement with the design.

New explicit solution for static shape control of smart laminated cantilever piezo-composite-hybrid plates/beams under thermo-electro-mechanical loads using piezoelectric actuators

In this paper, a new explicit exact analytical solution is proposed for obtaining static deformation and optimal shape control of smart laminated cantilever piezo composite hybrid plates and beams under thermo-electro-mechanical loads using piezoelectric actuators. The linear piezoelectricity and plates theories were adapted for the analysis. A novel double integral multivariable Fourier transformation method combined with discretised higher order partial differential unit step function equations were employed. The effect of various parameters including arbitrary loads such as non-uniform thermal stresses, electrical and mechanical loads, layup thickness, piezoelectric actuators size and placement, stacking sequence, and geometrical dimension were considered. The results were then compared with some published benchmark results and good agreement was observed. Unlike the earlier studies, the proposed method does not require the characteristic and trial deflection function to be predetermined. Both, the embedded and bounded actuators are considered. Until now, the shape control task of reducing mid-plane deformation at free end in smart laminated cantilever plates and beams was unsolvable and approximations were typically employed in numerical analysis Yu et al. (2009). This problem becomes more complicated for wider and longer plates but the method proposed herein successfully resolves this issue.

Optimization of the structure of 1–3 piezocomposite materials to maximize the performance of an underwater acoustic transducer using equivalent circuit models and finite element method

The structure of 1–3 piezocomposites has been optimized with such design variables as volume fraction of piezoceramics inside the composite and the thickness and aspect ratio of the piezoceramic pillars to enhance the performance of an underwater acoustic transducer operating in the thickness mode of the piezocomposites. Influence of the design variables on the transducer performance was analyzed with equivalent circuits and finite element method. In operation of the transducer, inter-pillar modes of vibration were likely to occur between piezoceramic pillars due to the lattice-structure of the piezocomposite, which could deteriorate the performance of the transducer. The structure of the 1–3 piezocomposite plate has been optimized to maximize transmitting, receiving and transmitting–receiving performance of the underwater acoustic transducer while preventing the coupling of the thickness mode with inter-pillar modes within the frequency range of interest. As results, volume fraction (VF) of 40.5% and aspect ratio (AR) of 0.4 showed the highest transmitting performance while VF of 30.0% and AR of 0.5 showed the highest receiving performance. For the transmitting–receiving performance, VF of 43.7% and AR of 0.5 were the optimal. Genetic algorithm was used in the optimal design.

Thermal Effects on Vibration and Control of Piezocomposite Kirchhoff Plate Modeled by Finite Elements Method

Theoretical and numerical results of the modeling of a smart plate are presented for optimal active vibration control. The smart plate consists of a rectangular aluminum piezocomposite plate modeled in cantilever configuration with surface bonded thermopiezoelectric patches. The patches are symmetrically bonded on top and bottom surfaces. A generic thermopiezoelastic theory for piezocomposite plate is derived, using linear thermopiezoelastic theory and Kirchhoff assumptions. Finite element equations for the thermopiezoelastic medium are obtained by using the linear constitutive equations in Hamilton’s principle together with the finite element approximations. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQG-Kalman filter is applied. By using this model, the study first gives the influences of the actuator/sensor pair placement and size on the response of the smart plate. Second, the effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. It is shown that the effectiveness of the control is not affected by the applied thermal gradient and can be applied with or without this gradient at any time of plate vibrations.

An Active Functionally Graded Piezocomposite Plate Subjected to a Stochastic Pressure

Abstract In the paper the analysis of random vibration of an actively damped laminated plate with functionally graded piezoelectric actuator layers is presented. The simply supported plate is subjected to stochastic loading represented by a uniformly distributed pressure. The random input is assumed as a Gaussian sta- tionary and ergodic process. The actuators are regarded as a multi-layer structure arranged of piezofiber composite sub-layers. The sub-layers differ each other with amount of PZT (lead-zirconate-titanate) fibers and are stacked to achieve a desired change of the PZT volume fraction through the actuator thickness. The gradation scheme of constituents and material properties are estimated by parabolic and power functions. Numerical simulations are performed to recognize the influence of the applied random excita- tions and the actuator properties gradations on the characteristics of the stochastic field of active plate deflection i.e. power spectral density, autocorrelation function and variance

Estimation of Certain Material Properties of a 1-3 Piezoelectric Composite as Functions of Temperature, Uni-Axial Stress and Electric Field

A method to estimate certain material properties of a 1-3 piezoelectric composite from the electrical impedance spectra, measured as functions of temperature, uni-axial stress and applied electric field, is proposed. A theoretical model is formulated to determine the impedance of lossy piezocomposite plates vibrating in the thickness-mode using complex material parameters. The impedance data are least-squares fitted to the model, and the relevant dielectric, mechanical and piezoelectric parameters are first determined by regression analysis and then refined by iteration. Good agreement between the theoretical impedance spectra with the measured spectra validates the method. The complex material parameters and the device parameters are found to vary non-linearly with variations in temperature, stress and electric field. This type of characterisation is important to understand and predict the behaviour of transducers that are subjected to varied environmental conditions and are driven at high electric fields during operation.

A Reliable Plain Solution for Rectangular Plates with Piezoceramic Patches

The present study investigates the behavior of a laminated composite plate with embedded or bonded piezoelectric materials. An exact mathematical model based on Reissner—Mindlin theory for plates (FSDT) has been developed for laminated composite plates with continuous piezoelectric layers. The flexural behavior has been solved based on Levy's method for plates. Therefore, the study has been limited to obtain exact solutions only for the cases of plates with at least two opposite simply supported edges, and only continuous piezoelectric layers. For a plate with piezoelectric patches, an approximate energy solution is presented, using Reissner—Mindlin theory, where the lateral displacement and the two bending rotations are expressed as infinite series. The point of merit for this model is its simplicity and reliability (depending on the number of terms) to solve a plate with any required boundary conditions and lay-ups. Furthermore, this model can be easily adapted to solve piezo-composite plates with an unlimited number of piezoelectric patches in arbitrary locations over the plate. A comprehensive parametric investigation has been performed to study the behavior of a plate actuated by extension or shear piezoelectric mechanisms. This investigation has been performed to yield results for plates with various boundary conditions and arbitrary patch locations.

Experimental and theoretical determination of 1–3 piezocomposite electroacoustic tensor

We report the development of two methods for determining the effective electroacoustic tensor of 1–3 piezocomposite material, one experimental and one theoretical based on homogenization techniques. The main aim was to compare and validate the results provided by these approaches. The slowness surfaces of bulk wave were computed in the large wavelength domain and were fitted to obtain the effective properties of the composite. Model predictions are discussed and compared with the Smith’s model. The experimental method is an inversion technique comparing measurement of transmission coefficient through the piezocomposite plate with the simulated coefficient. The accuracy and stability of the minimization procedure is discussed. Experimental results obtained from two piezocomposite test plates are presented and compared with theory.

Design of an underwater Tonpilz transducer with 2-2 mode piezocomposite materials

The performance of a transducer is determined by the properties of constituent materials and the effects of many structural parameters. In this study, the use of 2-2 piezocomposite materials in an underwater Tonpilz transducer was investigated. Through finite element analyses, the relationship between the piezocomposite material properties and the performance of the transducer was investigated, i.e., operation frequency, bandwidth, and sound pressure. Based on the analysis result, the geometry of the Tonpilz transducer that could provide the highest sound pressure for a given electric field amplitude while satisfying requirements such as bandwidth and operation frequency was optimized. The optimization result was compared with that of a traditional piezoceramic transducer to confirm the superiority of the piezocomposite transducer; a Tonpilz transducer made of 2-2 mode piezocomposite plates could provide a higher effective coupling factor and thus a wider bandwidth at a desired operation frequency with a smaller size than a traditional piezoceramic transducer.

2D ultrasonic arrays with low-voltage operation for high density electronics

The use of ultrasonic array transducers for NDT is growing rapidly, as commercial array controllers become more widely available. However, conventional 1D array designs limit the flexibility of such systems, for example, making it impossible to skew the beam on curved surfaces. As 2D arrays allow 3D beam steering, they are thus of major interest. However, the use of conventional excitation voltages, typically 200 V, with the many elements in 2D arrays may be inconvenient, making investigation of low-voltage operation worthwhile. The work reported here relates to array design for low-voltage operation for NDT. A 1D array was first produced, operating at approximately 1.5 MHz. This was based on a piezocomposite plate made with PZT 5A ceramic and epoxy resin. The plate was bonded to a PCB whose copper tracks defined the array elements, 10 mm long, 0.28 mm wide, and with edge-to-edge separation of 0.4 mm. The device was excited with a standard logic voltage of 3.3 V on a 75 mm-thick aluminium block. The pulse-echo insertion loss, using a signal reflected from the back wall of the aluminium, was found to be 59 dB. A 2D ultrasonic array has also been produced, with 16 elements in a 4 x 4 matrix, using the same piezocomposite material. In this case, the element size is 1.2 mm x 1.2 mm, and the edge-to-edge separation is 0.4 mm. In tests with 3.3 V peak-to-peak excitation voltage, the insertion loss was found to be 73 dB. The results suggest that arrays made with monolithic piezocomposite material have better performance for NDT than previous arrays made with monolithic ceramic and that low-voltage excitation will be viable in practice, with low noise amplification and appropriate signal processing.