Linear Theory Of Piezoelectricity Research Articles

Thermo-electro-elastic analysis of piezoelectric hollow cylinder with thermopolarization effect

Thermopolarization effect, refers to the coupling between electric polarization and temperature gradient, represents the linear response of electric polarization to temperature gradient. Although the thermal polarization effect was observed in many experiments, the qualitative and quantitative effects of thermal polarization on solids have not been studied. Thus, to clarify the quantitative impact of thermopolarization effect, based on the linear piezoelectric theory, the fundamental equations of the thermal-piezoelectric dielectric with the thermopolarization effect were derived, and a hollow piezoelectric cylinder was analyzed. The results show that the increasing thermopolarization coefficient can change the radial stress and circumferential stress sign, which is helpful to regulate the stress distribution in the cylinder. Besides, an interesting result shows that the increasing thermopolarization coefficient can shorten the time of the coupling process to the steady state. These results are useful for understanding the basic mechanical and physical properties of the thermo-electro-elastic multi-field coupling of piezoelectric cylinders. It helps to provide useful guidance for the design of microelectronic devices working in harsh environments.

An integrated modeling method for piezo-actuated compliant mechanisms

Piezo-actuated compliant mechanisms are widely employed in precision positioning and micro/nano manipulation due to their advantages of compact structure, high displacement resolution, and fast response. However, it is still challenging to accurately analyze the designed mechanisms due to the complicated coupled electromechanical behaviors of piezoelectric actuators and compliant mechanisms, which prevents further performance improvement by configuration design and optimization. A novel modeling method is developed in this paper for the kinetostatic and dynamic analyses of piezoelectric actuators and their comprised systems with compliant mechanisms. The electromechanical model of piezoelectric actuators is derived from linear piezoelectric vibration theory and further simplified as a practical equivalent model in the form of dynamic stiffness matrices. With the proposed actuator model, an integrated modeling method based on the dynamic stiffness matrix method is proposed for analyses of the piezo-actuated compliant mechanism with complicated configurations of piezoelectric actuators and flexible structures. Two case studies, including a piezoelectric actuator and a fast scanning stage, are analyzed to verify the effectiveness of the proposed approach. Both finite element analysis and experimental results validate that the presented modeling method can be used to resolve the kinetostatics and dynamics of complex piezo-actuated compliant mechanisms efficiently and effectively.

Mathematical modeling of electro‐elastic dislocations in piezoelectric materials

AbstractIn this work, based on the theory of linear incompatible piezoelectricity with eigendistortion and eigenelectric field, the concept of electro‐elastic dislocations is presented. Both field variables, the displacement vector u and the electrostatic potential φ, possess a jump discontinuity at the dislocation surface. Electro‐elastic dislocations are described not only by the dislocation density tensor but also by a new introduced field, the so‐called electric dislocation density vector. In addition to electro‐elastic dislocations, inhomogeneities, body forces and body charges are also considered. Within this framework, material balance laws that correspond to the symmetries of translation, scaling and rotation are derived. All fundamental fields of configurational mechanics like the Eshelby stress tensor, the electro‐elastic Peach‐Koehler force, the Cherepanov force, the Eshelby force among others, which take place in the broken (translational, scaling and rotational) conservation laws anymore are given.

Analysis of surface effect and flexoelectric effect on the electromechanical responses of bilayered transversely isotropic rectangular micro-plate

A new model of a bilayered transversely isotropic piezoelectric rectangular micro-plate with a distributed load is developed on the basis of Kirchhoff's plate theory and the extended linear piezoelectricity theory to characterize the piezoelectric micromachined ultrasonic transducer. The model takes into account both the surface effect and the flexoelectricity effect. The governing equation at the simply supported boundary condition is derived according to the variation principle. Based on the new model, the size dependent electromechanical coupling behaviors of the bilayered piezoelectric rectangular micro-plate are investigated. Considering the flexoelectric effect and surface effect synchronously, the numerical result indicates that the size dependence of the normalized central deflection decreases as the residual surface stress increases. For negative residual stress, the surface effect is the main influencing factor. While for positive residual stress, the surface effect dominates only when the ratio of thickness to length is smaller than about 25; otherwise, the flexoelectric effect will be more crucial. Moreover, if the thickness of the piezoelectric layer is less than about 40 nm, the electrical potential and polarization show a stronger size dependence. These results will be helpful to design and manufacture a piezoelectric micromachined ultrasonic transducer.

Compound influence of surface and flexoelectric effects on static bending response of hybrid composite nanorod

Nanoscale beams and rods are extensively used in several nano-electro-mechanical systems (NEMS) and their applications such as sensors and actuators. The surface and flexoelectricity phenomena have an extensive effect on nanosized structures and are related to their scale-dependent characteristics. This article presents the effect of different surface parameters and flexoelectricity on the electrostatic response of graphene-reinforced hybrid composite (GRHC) nanorods (NRs) using the theory of linear piezoelectricity, Euler-Bernoulli (EB), and Galerkin residual method. Based on these theories, the theoretical and finite element (FE) model is produced to investigate the static bending deflection of GRHC NRs when subjected to point and uniformly distributed load (UDL) considering different boundary conditions: cantilever (FC), fixed-fixed (FF), and simply supported (SS). This proposed FE model provides a useful tool for analyzing and investigating the outcomes of analytical models, which are found to be in good agreement. Our results presented in this article reveal that the effect of surface and flexoelectricity on the static bending response of GRHC NRs is noteworthy. These effects diminish with increased thickness/diameter of NR, and hence, these effects can be neglected for large-sized structures. The results presented here would help to identify the desired electrostatic response of GRHC NRs in terms of static bending response for a range of NEMS using different loading and boundary conditions as well as graphene volume fraction. This current study offers pathways for developing new proficient novel GRHC materials with enhanced control authority and present models can be exploited for numerous other materials as well as line-type structural systems such as beams, wires, rods, column/piers, and piles to study their global response.

In-plane-dominated vibration characteristics of piezoelectric thick circular plates based on higher-order plate theories

ABSTRACT Numerous engineering applications exist for the piezoelectric effect, which results from the electromechanical coupling between electrical and mechanical fields. In-plane vibrations of piezoelectric plates’ resonance frequencies and associated mode shapes have been thoroughly investigated. However, analytical solutions for in-plane-dominated vibrations of thick piezoelectric circular plates are limited. In this paper, higher-order plate theories for the in-plane-dominated vibration characteristics of piezoelectric circular thick plates under fully clamped and completely free boundary conditions are presented. The resonant frequencies and associated mode shapes were investigated based on two higher-order plate theories: second-order shear deformation plate theory and third-order shear deformation plate theory, as well as simplified third-order linear piezoelectric theory. Hamilton's principle was applied to derive equations of motion and boundary conditions. In the theoretical analysis, the resonant frequencies, associated mode shapes and distribution of electric displacements for various radius-to-thickness ratios were calculated. The numerical results obtained by the finite element method were compared with those obtained from theoretical analysis. Excellent agreement was found between the theoretical and numerical results for the thick piezoelectric circular plates.

Electromechanical behaviors in piezotronic quantum wells based on a quantum-corrected phenomenological theory

Piezotronic devices have attracted a great deal of attention due to their potential applications in self-powered tactile sensing, nano-device memory, human-electronic interface, etc. As the size of piezotronic devices shrinks, some interesting quantum effects begin to appear. In this paper, we establish a theory oriented to the engineering application of piezoelectric semiconductors, called quantum-corrected phenomenological (QCP) theory, by coupling the density-gradient theory and the linear piezoelectricity theory through Gauss's law. For numerical verification, we specifically studied the electromechanical behaviors in GaN/AlGaN heterostructure quantum wells (QWs) with both infinite and finite barrier height. The results of electron density, electric potential, and quantum potential are provided, and their dependence on the doping density, the applied stress, and the Al mole fraction is investigated. Some interesting quantum effects are revealed, and their influencing mechanisms are well investigated from a macroscopic perspective. Not only do the conclusions drawn in this paper enrich the fundamental understanding of the piezotronic effect in a QW structure, but also the proposed QCP theory can serve as a valuable tool for future device engineering.

Implicit non-ordinary state-based peridynamics model for linear piezoelectricity

In the present work, the development and analysis of linear piezoelectricity in the peridynamics framework is presented. The model is developed using non-ordinary state-based Peridynamics. The equations of motion are derived using Hamilton’s principle and the correspondence material model is developed by establishing the connection between the classical theory of linear piezoelectricity and the newly proposed peridynamic linear piezoelectricity framework. An implicit implementation is proposed for two-dimensional linear piezoelectricity. Moreover, for the stabilization of the proposed scheme, the bond-associated correspondence model is used. We demonstrate the capabilities of the proposed model by presenting some 2 D numerical examples.

Anti-plane shear wave motion in a composite layered structure with slit

Anti-plane shear wave propagation in a functionally graded piezoelectric substrate and a piezoelectric substrate guided by a slit is analyzed theoretically. The equations of motion are taken from the linear theory of piezoelectricity for polarized ceramics. The dispersion relation is obtained by applying appropriate boundary conditions on the derived solutions. PZT-5 and ZnO are taken as numerical examples to manifest the effect of different material parameters (gradient factor, slit width etc.) graphically on the phase and group velocity of the considered wave. LiI O 3 and BaTi O 3 materials are taken separately to compare the results. Also, graphs are plotted for different modes of the wave as well as for different frequency ranges and for the case when slit is absent. As a special case, it is remarked that the present study has resemblance with one of the existing works. The highlights of the study are to characterize the anti-plane wave propagation within a functionally graded piezoelectric substrate/gap/piezoelectric substrate coupled structure, to show the effect of different parameters, modes, frequency, etc. on the velocity profile of the considered wave and to show the effect of gap layer. The outcomes of this study may be used to enhance the sensitivity of acoustic wave devices and sensors.

Analytical solution of the electro-mechanical flexural coupling between piezoelectric actuators and flexible-spring boundary structure in smart composite plates

An analytical solution has been developed developed in this research for electro-mechanical flexural response of smart laminated piezoelectric composite rectangular plates encompassing flexible-spring boundary conditions at two opposite edges. Flexible-spring boundary structure is introduced to the system by inclusion of rotational springs of adjustable stiffness which can vary depending on changes in the rotational fixity factor of the springs. To add to the case study complexity, the two other edges are kept free. Three advantages of employing the proposed analytical method include: (1) the electro-mechanical flexural coupling between the piezoelectric actuators and the plate’s rotational springs of adjustable stiffness is addressed; (2) there is no need for trial deformation and characteristic function—therefore, it has higher accuracy than conventional semi-inverse methods; (3) there is no restriction imposed to the position, type, and number of applied loads. The Linear Theory of Piezoelectricity and Classical Plate Theory are adopted to derive the exact elasticity equation. The higher-order Fourier integral and higher-order unit step function differential equations are combined to derive the analytical equations. The analytical results are validated against those obtained from Abaqus Finite Element (FE) package. The results comparison showed good agreement. The proposed smart plates can potentially be applied to real-life structural systems such as smart floors and bridges and the proposed analytical solution can be used to analyze the flexural deformation response.

Electro-elastic dislocations in piezoelectric materials

ABSTRACTIn this paper, dislocations in piezoelectric materials are studied in the framework of linear incompatible theory of piezoelectricity with eigendistortion and eigenelectric field. We consider that both field variables, the displacement vector and the electrostatic potential ϕ, possess a jump discontinuity at the dislocation surface. This leads to the appearance of two eigenfields, the eigendistortion or plastic distortion tensor and the eigenelectric field vector providing the terminology of electro-elastic dislocations. These two eigenfields give rise to the well-known concept of dislocation density tensor and the new-introduced concept of the electric dislocation density vector, respectively, completing the basic framework of the mathematical modelling of electro-elastic dislocations in piezoelectric materials. Material balance (or broken conservation) laws which correspond to translation, scaling and rotation groups of transformations are derived for piezoelectric materials with electro-elastic dislocations considering additionally inhomogeneities, body forces and body charges. The terms breaking the translational, scaling and rotational symmetries, that is, the configurational or material forces (electro-elastic Peach–Koehler force, Cherepanov force, electrostatic part of the Lorentz force, piezoelectric inhomogeneity force or Eshelby force), the corresponding total configurational work and total configurational vector moment which give rise to the non-conserved -, M- and -integrals, respectively, are obtained.

Size-dependent electromechanical coupling in functionally graded flexoelectric nanocylinders

Flexoelectricity is an electromechanical coupling between polarization and strain gradient, which not only exhibits strong size dependency but is structure associated (geometry or microstructure). By the definition of flexoelectric coefficients, the flexoelectricity-related strain gradients can be generated by tailoring mechanical structures, such as the traditional designed truncated pyramid. In this work, a novel asymmetric nanocylinder is composed of functionally graded materials presented with uniform pressures on the top surface to create a relatively large inhomogeneous strain field for the achievement of obvious flexoelectric polarization. Based on the power-law-distributed material property assumption, we investigate the flexoelectricity of the proposed functionally graded nanocylinder. Based on the extended linear theory of piezoelectricity, the closed-form solutions are obtained, which can specifically characterize the size-dependent flexoelectricity. The most common setups are applied to quantify the flexoelectric response. From the numerical results, we can conclude that the electromechanical properties can be significantly influenced by the given FG configuration with graded material parameters, which can be a guideline for the design of novel flexoelectric devices.

Static and dynamic response of graphene nanocomposite plates with flexoelectric effect

In this work, the electromechanical behaviors of graphene reinforced nanocomposite (GRNC) plates with flexoelectric effect were studied by using Kirchhoff's plate theory, Navier's solution and extended linear piezoelectricity theory in conjunction with the mechanics of materials (MOM) and finite element models. The static and dynamic responses of simply supported flexoelectric GRNC nanoplates under different loadings such as uniformly distributed, varying distributed, inline and point loads were investigated. The developed MOM and FE models envisage that the effective piezoelectric constants of a GRNC account for the actuating capability in its transverse direction due to the applied electric field in the plane. The elastic properties of pristine and defective graphene sheets were also estimated via molecular dynamics (MD) simulations and the obtained results are found in good agreement with the existing experimental and numerical results. Our results reveal that the flexoelectric effect on the static and dynamic responses of GRNC nanoplate is substantial and cannot be neglected. The electromechanical response of GRNC plates can be engineered to attain the desired deflection characteristics and resonant frequencies for a range of nanoelectromechanical systems using different boundary conditions as well as geometrical parameters such as aspect ratio/thickness of nanoplate and volume fraction of graphene.

Dispersion Waves in a Submerged Thermo-Piezoelectric Membrane

Abstract Wave propagation in a thermo piezoelectric membrane immersed in an infinite fluid medium is discussed using three-dimensional linear theory of elasticity and thermos piezoelectricity. Three displacement potential functions are introduced to uncouple the equations of motion, heat and electric conduction equations. The frequency equations are obtained for longitudinal and flexural modes at the solid fluid interfacial boundary conditions. The numerical results are analyzed for PZT-4 material and the computed stress, strain, electric displacement and temperature distribution are presented in the form of dispersion curves and its characteristics are studied.

Bending of piezoelectric beams with the flexoelectric effect under applied load at any position

Flexoelectricity describes the coupling between polarization and strain gradients and presents a strong size dependence at nanoscale. In the current work, based on the extended linear piezoelectricity theory with flexoelectricity, we study bending of piezoelectric beams with consideration of flexoelectric effect. When a concentrated force at any position and electric voltage is exerted, the expression for bending deflection of simply-supported and clamped beams is derived. The obtained results show that flexoelectric effect can cause a softer elastic behavior of simply-supported and clamped beams. Sensitivity analysis of the transverse deflection and bending moment is made for two typical boundary conditions. Flexoelectric effect has a more significant effect on the bending response of a piezoelectric beam with smaller thickness.

Improving piezoelectric and pyroelectric properties of electrospun PVDF nanofibers using nanofillers for energy harvesting application

In this study, it was aimed to increase the piezoelectric and pyroelectric properties of electrospun polyvinylidene fluoride (PVDF) nanofibers simultaneously by using specific nanofillers. Graphene oxide (GO), graphene, and halloysite nanotubes with different concentrations (0, 0.05, 0.4, and 1.6% wt/wt) were combined with PVDF solution and were fabricated in the form of nanofibers through electrospinning. Pyroelectric properties of samples were measured by submerging sealed samples in hot water (360°K) and ice (270°K). The piezoelectric properties of the samples were evaluated through bending tests. The microstructural, mechanical, and thermal properties of the electrospun PVDF nanocomposite were investigated using scanning electron microscope, Instron instrument, and thermogravimetric analysis, respectively. To further support the experimental observations for generating electric voltage in the bended nanogenerator, the PVDF nanogenerator (PNG) was also modeled by a finite element analysis based on the theory of linear piezoelectricity using COMSOL Multiphysics simulation software. Experimental results showed that adding nanofillers could improve the piezoelectric and pyroelectric properties of all samples, associated with the increment of β‐phase in the nanofibers. It was concluded that adding nanofillers could increase pyroelectricity about 50% more than piezoelectricity in pristine PVDF nanofiber web. The PNG containing 1.6 wt% GO showed the highest efficiency in terms of piezoelectricity and pyroelectricity. In addition, the results showed that the ratio of piezoelectric to pyroelectric coefficients was constant (~1.5) and it was independent of the nanofiller type and content. The effect of external force and vibration frequency on the output voltage was also investigated. Increasing the compressive force and vibration frequency caused a greater output voltage. Finally, the fabricated nanogenerator was integrated on insole and elbow to investigate its energy harvesting capabilities from body movement.

Optimal shape control of piezolaminated beams with different boundary condition and loading using genetic algorithm

Piezoelectric actuators are effectively used to control the response of light weight structures in shape, vibration and buckling. Optimization for the shape control of piezoelectric beam is the recent challenge which requires proper numerical technique to perform. The shape control of a composite beam using surface-bounded piezoelectric actuators has been investigated in the present work. The mathematical model is developed using two-node Timoshenko beam element coupling with the theory of linear piezoelectricity. First-order shear deformation theory is employed in the formulation to consider the effect of shear. In the analysis, the effect of the actuators position for different set of boundary conditions is investigated. For different boundary conditions which include clamped-free-, clamped–clamped- and simply supported beam, optimisation of piezoelectric patch location is investigated. Moreover, a genetic algorithm is adopted and implemented to optimize the required voltage to maintain the desired shape of the beam. This optimization technique is applied to different cases of composite beams with varying the boundary condition.

A Study of the Flexoelectric Effect on the Electroelastic Fields of a Cantilevered Piezoelectric Nanoplate

Flexoelectricity, a spontaneous polarization in linear response to strain gradients or non-uniform deformation, is believed to contribute to the size-dependent electromechanical coupling of piezoelectric materials at the nanoscale. In the current work, the flexoelectric effect upon the static bending behaviors of a cantilevered piezoelectric nanoplate (PNP) is studied. Based on the Kirchhoff plate model and the extended linear piezoelectric theory, the non-conventional governing equations and the boundary conditions of the PNP under both mechanical and electrical loads are derived with the incorporation of the flexoelectric effect. Finite difference method (FDM) is performed to get the numerical solution for the electroelastic fields of the plate. Simulation results show that the flexoelectric effect is more prominent for the thinner plates with smaller thickness. It is also found that the flexoelectric effect upon the electroelastic responses of the clamped PNP is also sensitive to some other factors, including the boundary conditions, the plate geometric ratio, and the applied mechanical and electrical loads. This work aims to provide an increased understanding of the size-dependent electromechanical coupling properties of a piezoelectric plate structure.

Dynamic electromechanical behavior of single-crystal α-quartz

Electrical response from dynamic compression tests on x-cut single crystal α-quartz specimens at strain rates of 103 s−1 reveal nonsimilar stress-charge behavior during damage evolution. Specifically, when quartz is undergoing extensive and irreversible dynamic brittle fracture under a compressive stress impulse of up to 1.8 GPa, the effective piezoelectric stress coefficient (d) exhibits approximately a 24% increase from loading to unloading. The experimental results are examined in the framework of the theory of linear piezoelectricity in order to understand the role of increasing crack density and crystal orientation on electroelastic properties.

Chiral effects in piezoelectricity

This paper is concerned with the linear theory of piezoelectricity for Cosserat continua. The deformation of homogeneous and isotropic chiral materials is investigated. First, a counterpart of the Boussinesq–Somigliana–Galerkin solution in the classical elastostatics is presented. Then, the fundamental solutions in the stationary theory are established. In contrast with the case of achiral solids, in the theory of isotropic chiral materials the displacement and microrotation fields are coupled with the electric field.