Piezoelectric Fiber Reinforced Composite Research Articles

Bandgap adjustment of a sandwich-like acoustic metamaterial plate with a frequency-displacement feedback control method

Several types of acoustic metamaterials composed of resonant units have been developed to achieve low-frequency bandgaps. In most of these structures, bandgaps are determined by their geometric configurations and material properties. This paper presents a frequency-displacement feedback control method for vibration suppression in a sandwich-like acoustic metamaterial plate. The band structure is theoretically derived using the Hamilton principle and validated by comparing the theoretical calculation results with the finite element simulation results. In this method, the feedback voltage is related to the displacement of a resonator and the excitation frequency. By applying a feedback voltage on the piezoelectric fiber-reinforced composite (PFRC) layers attached to a cantilever-mass resonator, the natural frequency of the resonator can be adjusted. It ensures that the bandgap moves in a frequency-dependent manner to keep the excitation frequency within the bandgap. Based on this frequency-displacement feedback control strategy, the bandgap of the metamaterial plate can be effectively adjusted, and the vibration of the metamaterial plate can be significantly suppressed.

Impact of surface/interface elasticity on the propagation of torsional vibration in piezoelectric fiber-reinforced composite and anisotropic medium

This work has explored surface/interface theory-based torsional wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer on top of a functionally graded elastic substrate. PFRC is assumed to be composed of piezoelectric fiber and epoxy matrix. Micro-mechanical investigations have been performed to determine the coefficients of PFRC using strength of materials (SM) and rule of mixtures (RM) techniques. The dispersion relation for the torsional wave under nonclassical boundary conditions is determined using surface/interface theory. The effects of surface/interface, fiber volume fractions, and heterogeneities on the phase velocity and the mode shapes of the wave have been demonstrated graphically.

A micromechanical modeling approach for predicting the piezoelectric and mechanical properties of piezoelectric fiber-reinforced multiphase composites containing CNT/GNP hybrids

This paper focuses on the prediction of piezoelectric coefficients, Young’s moduli and shear moduli of unidirectional piezoelectric fiber/carbon nanotube (CNT)/graphene nanoplatelet (GNP)-reinforced polymer composites using a novel micromechanics modeling technique. The multiphase composite configuration is that piezoelectric fibers are embedded within a polymer matrix filled by CNT/GNP hybrids. Agglomeration of hybrid nanofillers as a significant factor is identified and incorporated in the micromechanical calculation. Parametric studies are carried out to understand the effect of volume fraction, size and dispersion type of carbonous nanofillers as well as the piezoelectric fiber volume fraction on the effective material constants of multiphase composites. It is found that in comparison with the piezoelectric fibrous composite, the piezoelectric fiber multiphase composite containing CNT/GNP hybrids shows better elastic and piezoelectric properties. Also, further improvement in effective properties can be obtained by increasing the length and percentage of CNTs and GNPs. But, degradation in the elastic and piezoelectric constants is observed by the agglomeration of CNT/GNP hybrids. The current results are found to be in close proximity with the experimental data and other numerical results available in the literature.

An investigation of torsional surface wave in a piezoelectric fiber-reinforced composite layer imperfectly bonded to a functionally graded half-space

This article presents a comprehensive study of torsional surface wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer bonded to functionally graded (FG) half-space considering electrically short and open boundary conditions. The Strength of Materials (SM) and Rule of Mixtures (ROM) approaches have been adopted to determine the effective properties of the PFRC. The non-ideal mechanical and electrical interfacial boundary has been considered for the problem which appears in various realistic scenarios. For the torsional surface wave propagation through PFRC bonded to FG half-space, the dispersion equation has been derived analytically using Whittaker function. The obtained results are validated and matched with existing results by considering special cases. The variation of phase velocity due to the influence of fiber volume fraction, interfacial imperfection parameters and functionally grading parameters have been analyzed and illustrated by means of graphs. Furthermore, the distribution of the field variables, stress and electric displacements across the composite are presented through surface plots. The model holds potential applications in designing and manufacturing transducers, actuators and sensors. The use of PFRC can be found in a wide range of cutting-edge technology, including vibration-canceling gadgets, energy harvesters, and pressure sensors.

Theoretical and numerical analysis of free vibrations of piezoelectric circular plate reinforced with boron nitride

PurposeThe purpose of this research is to extract the natural frequencies of a circular plate containing a central hole reinforced with boron nitride nanotubes (BNNTs) and containing piezoelectric layers.Design/methodology/approachA unit cell shall be taken into account for the simulation of BNNT's volume fraction. A rectangular micromechanical model is used to obtain the mechanical properties of unit cell of piezoelectric fiber-reinforced composite (PFRC). The three-dimensional (3D) elasticity method is presented to provide the relationship between displacements and stresses. The one-dimensional differential quadrature method (1D-DQM) and the state-space methodology are combined to create the semi-analytical technique. The state-space approach is utilized to implement an analytical resolution in the thickness direction, and 1D-DQM is used to implement an approximation solution in the radial direction. The composite consists of a polyvinylidene fluoride (PVDF) matrix and BNNTs as reinforcement.FindingsA study on the PFRC is carried, likewise, the coefficients of its properties are obtained using a micro-electromechanical model known as the rectangular model. To implement the DQM, the plate was radially divided into sample points, each with eight state variables. The boundary situation and DQM are used to discretize the state-space equations, and the top and bottom application surface conditions are used to determine the natural frequencies of the plate. The model's convergence is assessed. Additionally, the dimensionless frequency is compared to earlier works and ABAQUS simulation in order to validate the model. Finally, the effects of the thickness, lateral wavenumber, boundary conditions and BNNT volume fraction on the annular plate's free vibration are investigated. The important achievements are that increasing the volume fraction of BNNTs increases the natural frequency.Originality/valueThe micromechanical “XY rectangle” model in PFRC along with the three-dimensional elasticity model is used in this literature to assess how the piezoelectric capabilities of BNNTs affect the free vibration of polymer-based composite annular plates under various boundary conditions.

Rayleigh wave in a piezoelectric micro-mechanical bi-material system with mechanically and dielectrically imperfect interfaces

The present work investigates the propagation behavior of Rayleigh waves in a piezoelectric fiber-reinforced composite (PFRC) material stratum lying over a PFRC substrate with mechanically and dielectrically imperfect interfaces. The PFRC material structure is micro-mechanically modeled using the analytical techniques of the Strength of Materials (SM) and Rule of Mixtures (RM). Dispersion equations are obtained by employing suitable boundary conditions for electrically open and short conditions. The data of CdSe-epoxy and PZT-5A-epoxy materials as PFRC materials have been taken into account for fiber volume fraction to investigate the latent characteristics of Rayleigh wave propagation. Numerical calculations have been carried out to study the influence of mechanically compliant and dielectrically weakly (MCDW)/highly (MCDH) conducting imperfect interfaces on Rayleigh wave propagation in the considered structure. A comparative study has also been carried out to exhibit the concealed characteristics of Rayleigh wave propagation for various distinct cases in both the electrical conditions and manifested graphically for the fundamental mode of Rayleigh wave.

Reliability analysis of smart laminated composite plates under static loads using artificial neural networks

The applications of smart structures with integrated piezoelectric elements have been expanding in the last few decades due to the abilities of such structures to withstand mechanical loads and operate as sensors or actuators using their electromechanical coupling. The available manufacturing techniques can result in uncertainties in the structure's geometric parameters, which, coupled with uncertainties in material properties, can lead to unexpected failures or unreliable performance. This paper presents a reliability analysis of a smart laminated composite plate made of a graphite/epoxy cross-ply substrate with a piezoelectric fiber-reinforced composite (PFRC) actuator layer under static electrical and mechanical loads. A coupled finite element (FE) model was developed in COMSOL Multiphysics, from which nondimensional stresses and displacements were calculated. To investigate the effects of randomness in the material and geometric properties, an artificial neural network (ANN) model was developed and trained using generated FE data. Monte Carlo Simulation (MCS) and First- and Second-Order Reliability Methods (FORM/SORM) were then used to shed light on the significance of considering randomness in the various material and geometric parameters and the effect of such uncertainty on the resulting nondimensional stresses and displacements. A coefficient of variation (CV) study identified the piezoelectric stress coefficient as the most significant contributing factor to the variation of all nondimensional parameters. Variation in the nondimensional parameters also increases under the application of an electric load. ANN-based FORM, SORM, and MCS all indicate a pattern of low probability of failure until a threshold value of about 3% of input parameter variation is reached, beyond which there is a rapid nonlinear increase in failure probability with increasing input parameter variation.

Transference of SH waves in a piezoelectric fiber-reinforced composite layered structure employing perfectly matched layer and infinite element techniques coupled with finite elements

Most commercially used piezoelectric materials suffer from certain drawbacks like low piezoelectric output, brittle nature, etc. Thus, they cannot be utilized to their fullest extent in dynamic applications involving actuators, transducers, Surface Acoustic Wave (SAW) devices, and Love wave sensors, among others. The present work focuses on the transference attributes of anti-plane SH wave in a layered structure composed of a piezoelectric fiber-reinforced composite (PFRC) layer lying over a piezoelectric half-space. The PFRC composed of PZT-5A-epoxy is micro-mechanically modeled using Strength of Materials and Rule of Mixtures, and some of its electro-mechanical advantages over monolithic PZT-5A are discussed. The dispersion relation is obtained by analytical means, as well as two numerical techniques, viz., Semi-Analytical Finite Element - Perfectly Matched Layer (SAFE-PML) technique and Semi Analytical Infinite Element (SAIFE) technique with (1/r) type decay. The Rayleigh–Ritz method and Gauss 3-point quadrature formula are employed to derive the dispersion relation numerically. The effects of the existing parameters, viz. fiber volume fraction, PML length, PML function, etc., on the dispersion curves are graphically demonstrated and discussed. The present work is validated by matching the obtained results with the ones found in the extant literature.

A new electro-mechanical finite formulation for functionally graded graphene reinforced composite laminated thick plates with piezoelectric actuator

Graphene is regarded as one of the most attractive reinforcements for composite materials attributing to the extraordinary physical characteristics. However, existing models in the literatures might meet severe challenges for the interlaminar stress prediction of functionally graded graphene reinforced composite (FG-GRC) laminated thick plate integrated with piezoelectric fiber reinforced composite (PFRC) actuator under electro-mechanical loadings. If transverse shear deformations cannot be described accurately, the mechanical performance of FG-GRC laminated plate with PFRC actuator will be significantly impacted by the electro-mechanical coupling effect and the sudden change of material characteristics at the interfaces. Thereby, a new electro-mechanical coupled plate model with only seven independent displacement variables is to be proposed in this paper. Employing the Reissner mixed variational theorem (RMVT), the precision of the transverse shear stresses considering the electro-mechanical coupling effect can be improved. Moreover, the second-order derivatives of in-plane displacement parameters have been removed from the transverse shear stress components, which can greatly simplify the finite element formulation. Thus, based on the proposed electro-mechanical coupled plate model, a simple C0-type finite element formulation is developed for interlaminar shear stress analysis of FG-GRC laminated thick plate with a PFRC actuator. The 3D elasticity solutions and the results obtained from other models are used to assess the performance of the proposed finite element formulation. Additionally, comprehensive parametric studies are achieved for the influences of graphene volume fraction, distribution pattern, electro-mechanical loading, boundary conditions, lamination scheme and geometrical parameters of the plate on the deformations and stresses of the FG-GRC laminated plate with a PFRC actuator.

Effective Coefficients of Piezoelectric Fiber Reinforced Composites Using Modified Strength of Materials and Energy Approaches

The effect of fiber cross-section on effective elastic and piezoelectric coefficients of piezoelectric fiber reinforced composites (PFRC) is investigated through two micromechanical analyzes viz. modified strength of materials (MSM) approach and energy approach. Results are verified with that of strength of materials (SM) approach available in the literature. A constant electric field is considered in the direction transverse to the fiber direction and is assumed to be same both in the fiber and matrix phases. It is observed that MSM and strength of materials (SM) approach predictions for the effective piezoelectric coefficient of the PFRC assessing the actuating capability in the fiber direction are in excellent agreement and also when the fiber volume fraction exceeds a critical value, this effective piezoelectric coefficient becomes significantly larger than the corresponding coefficient of the piezoelectric material of the fiber as investigated by both SM and MSM approaches. However, results of energy approach differ from both MSM and SM results and effective piezoelectric constant never exceeds to that of fiber as obtained by energy approach. It has been found for the piezoelectric fibers, cross-section of fiber has insignificant effect on the effective properties as predicted by MSM and energy approaches. Nomenclature

Propagation characteristics of love-type wave at the electro-mechanical imperfect interface of a piezoelectric fiber-reinforced composite layer overlying a piezoelectric half-space

In the present work, the micro-mechanical modeling of a piezoelectric fiber-reinforced composite (PFRC) is established using the analytical techniques of Strength of Materials and Rule of Mixtures, along with analyzing some of its electro-mechanical advantages over monolithic piezoelectric materials. Thereafter, the characteristics of a Love-type wave propagating at the imperfect interface of a layered structure comprising a PFRC layer overlying a piezoelectric half-space are analytically studied. The interface is classified into five exclusive types, viz. Mechanically compliant dielectrically weakly and highly conducting, welded interface, low dielectric interface, and grounded metallized interface, accounting for various realistic scenarios in different engineering applications. With the aid of suitable boundary conditions accounting for the different types of interfaces, the dispersion relations of the Love-type wave are derived considering both electrically open and short conditions at the free surface. The natures of phase velocity under the influence of the different interfacial imperfections and fiber volume fractions are graphically illustrated. The obtained results are validated by reducing and matching them with some results in the extant literature on Love wave propagation in terms of mathematical equations and graphs. The influences of the material parameters on the electromechanical coupling factor and piezoelectric coupling parameter are meticulously analyzed as these are vital properties that govern the efficiency of transducers and sensors. The outcomes of the present work may be applied in several scientific and engineering disciplines utilizing electroelastic transducers, sensors, capacitors, actuators, and in applications involving SAW devices and Love wave sensors to enhance their performance for obtaining high output in the long run.

An analytical approach to evaluate effective coefficients of 1–3 piezoelectric composites

In this paper, a micromechanics method is developed to evaluate effective coefficients of piezoelectric fiber-reinforced composites. An exact solution is derived for effective elastic, piezoelectric and dielectric coefficients of such piezocomposites subjected to the applied load in the direction transverse to the fiber orientation. Simultaneously, based on finite element method, a numerical study is performed on a representative volume element of such piezo composite containing fiber in square packing arrangement. The finite element method provides a numerical solution to evaluate effective elastic, piezoelectric and dielectric coefficients for discrete volume fraction of fiber, the range being 0.1–0.6 for this study. The results are interpolated to understand the overall behavior of such piezocomposites. The results obtained from the micromechanics method and the finite element method are compared with the results obtained from other models based on strength of materials method given in the literature. It is observed that the method developed in this study provides better results for effective coefficients susceptible to fiber packing arrangements.

Influence of varying fiber volume fractions on plane waves reflecting from the stress-free/rigid surface of a piezoelectric fiber-reinforced composite half-space

Wave reflection phenomenon at the stress-free/rigid surface of a piezoelectric fiber-reinforced composite (PFRC) half-space is studied. The PFRC is micro-mechanically modeled using Strength of Materials (SM) and Rule of Mixtures (RM). Some of its electro-mechanical data are graphically shown and its advantages are discussed. An incident quasi-longitudinal (qP) wave generates reflected quasi-longitudinal (qP), quasi-transverse (qSV), and electroacoustic (EA) waves, whose propagation angles are graphically demonstrated. Closed-form expressions of energy ratios of reflected waves and interaction energy are obtained, which satisfy the Law of Conservation of Energy, thus validating this problem. Influences of incident angle, varying fiber volume fractions, and stress-free/rigid surfaces on amplitude/energy ratios are discussed.

A refined plate theory for functionally graded carbon nanotube-reinforced plates with piezoelectric actuator

With the advantage of outstanding mechanical characteristics, carbon nanotube (CNT) is nowadays considered as one of the most ideal reinforcements for composite materials. Mechanical properties of functionally graded carbon nanotube reinforced composite (FG-CNTRC) structures have been extensively investigated in the published literature. However, analytical results on transverse shear stresses of smart FG-CNTRC plates subjected to electro-mechanical loadings are scarce in literature. To fill this gap, a refined plate theory is proposed for bending analysis of laminated FG-CNTRC plates integrated with a piezoelectric fiber reinforced composite (PFRC) actuator. The kinematic assumptions of the proposed plate theory are obtained by superimposing an efficient zigzag function on the first-order shear deformation theory. Laminated FG-CNTRC plates with four distribution types of CNT through the thickness are considered. The governing equations are obtained by using the principle of minimum potential energy and the Navier's method is used to solve the boundary value problem. The present results are compared with the three-dimensional (3D) elasticity solutions and the results computed by using the chosen models. Numerical results show that the proposed zigzag function can effectively improve the accuracy of proposed plate model in predicting the displacements and stresses. In order to understand clearly the static behaviors of smart FG-CNTRC plates, the influences of electro-mechanical loading, CNT distribution through the thickness direction, CNT volume fraction and span-to-thickness ratio are thoroughly investigated.

An electromechanical model for functionally graded porous plates attached to piezoelectric layer based on hyperbolic shear and normal deformation theory

In this work, the bending behavior of functionally graded (FG) porous plates connected with a layer made of piezoelectric fiber-reinforced composite (PFRC) on the upper surface is presented via a quasi-three dimensional (3D) refined shear and normal deformation theory. The shear strains and normal deformation are both studied and so, the shear correction operator is not needed. The plate is under sinusoidal electro-mechanical loads. The material characteristics of the FG porous plate have continuous variation in the direction of thickness relying on a modified exponential function. The equilibrium equations will be established by utilizing the principle of virtual work and will be solved by considering Navier’s solution method. The electric potential effects on the present analyses are studied. The influence of porosity coefficient, inhomogeneity parameter, applied voltage, length-to-thickness ratio, and length-to-width ratio parameters will be discussed. By comparing it with other published studies, the efficiency of the current theory is verified.

An analytical approach to evaluate the effective coefficients of piezoelectric composites

In this paper, the effective coefficients of piezoelectric fiber-reinforced composites are determined through two micromechanics methods. The exact solutions are derived to predict the effective electro-elastic coefficients with modifications in the conventional strength of materials approach and strain energy approach to account for the effects of fiber packing arrangements and orientations on these properties. A representative volume element subjected to a mechanical loading in the longitudinal direction to the fiber and an electrical loading in the transverse direction to the fiber is used to model the problem mathematically and derive the results. The effective elastic, piezoelectric and dielectric coefficients are estimated by these two methods, and the results are compared with those predicted by the strength of materials method of the literature. From the results, it is observed that results obtained for the elastic, piezoelectric and dielectric coefficients by the strength of materials method and modified strength of materials method are in good agreement with each other in a useful range of fiber volume fractions, while the results obtained through the energy approach shows some deviations when compared with previously stated two methods. The strength of actuation capabilities in the direction longitudinal to the fiber shows significant improvements in the results obtained with the strain energy approach compared with those of the other two micromechanics methods.

Forced Vibration Responses of Smart Composite Plates using Trigonometric Zigzag Theory

The Trigonometric Zigzag theory is utilized in this research for analytically evaluating the forced vibration responses of smart multilayered laminated composite plates with piezoelectric actuators and sensors. This theory, as the name suggests, incorporates a trigonometric function, namely the secant function for describing the nonlinear behavior of transverse shear stresses through the thickness of the smart composite plates. The kinematics for the in-plane displacement components are obtained by superposing a globally varying nonlinear field through the thickness of the plate structure on a piecewise linearly varying zigzag field with slope discontinuities at the layer interfaces. The model also satisfies the inter-laminar continuity conditions of tractions at the interfaces of the multilayered plate. The equations of motion are derived using Hamilton’s principle, and the separation of the variables technique is extended to assume the solutions for the primary variables in space and time and solved analytically using Navier’s solution technique along with Newmark’s time integration scheme. A detailed analytical investigation of the dynamic behavior of the smart laminated plate coupled with piezoelectric materials like PVDF and piezoelectric fiber-reinforced composite (PFRC) is carried out by considering several forms of the time-dependent electromechanical excitations and also covering different geometrical and material features of the smart plate structure. The responses are found to be in close agreement with the elasticity solutions and some new results are also presented to show the dynamic controlling capacity of the piezoelectric layers.

Optimization of thermal buckling control for composite laminates with PFRC actuators using trigonometric shear deformation theory

This work aims to explore optimal design and control of thermal buckling for composite laminates with piezoelectric fiber reinforced composite (PFRC) actuators. Four-variable trigonometric shear deformation theory without introduction of a shear correction factor is used in the structural modeling. The high accuracy of the present approach is examined by analyzing the critical buckling temperature and natural frequency compared with references results. A temperature feedback control approach is proposed in designing the controller. Taking fiber angle as the optimization design variable, layerwise optimization approach (LOA) is applied to maximize critical buckling temperature of piezolaminated plate and a set of stacking sequences are obtained. The resulting analysis demonstrates that the proposed control approach can clearly increase the critical buckling temperature of piezo-laminated plates. The optimization process developed is useful in devising stacking sequences for the piezo-laminated structures in thermal environments.

Flexural Behavior of Functionally Graded Plates with Piezoelectric Materials

In the perspective of significant industrial applications and research works being conducted on functionally graded materials (FGMs), the present article seeks to demonstrate the flexural behavior of smart functionally graded plate with the use of recently developed inverse hyperbolic shear deformation theory. The kinematic field of this theory consists of five independent primary variables and inherently satisfies the traction-free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plate. The piezoelectric fiber-reinforced composite (PFRC) lamina is considered as the actuator of the smart structure. The Navier’s solution technique is used to convert the system of partial differential equations derived from the virtual work principle to a set of five algebraic equations. The response of the smart plate is determined in the form of deflection and stresses subjected to electromechanical load. The three-dimensional equilibrium equations of elasticity are used to accurately determine the transverse shear stresses. The responses obtained from the numerical examples of FGM plate integrated with PFRC layer are compared with the elasticity solutions and with the various kinematic models available in the existing literature. The actuation in the response of the smart FGM plate due to the PFRC layer is also presented in the form of graphs for verifying the controlling capacity.

Active vibration control of smart laminated beams using PFRC patches as sensors and actuators

Abstract The aim of this paper is to present the performance of piezoelectric fiber-reinforced composite (PFRC) sensors and actuators in active vibration suppression of smart laminated beams. Finite element based on an efficient layerwise theory has been selected for the kinematic modelling of smart beam. Both classical (CGVF) and optimal (LQR and LQG) feedback control systems are employed to actively suppress the vibration. The effects of fiber volume fraction and fiber direction of PFRC on the settling time, active damping ratios, peak tip deflection and peak control voltage are studied. The effectiveness of control strategies in terms of minimum control voltage for a given settling time is presented