Piezoelectric Nanoplates Research Articles

Porosity effect on thermal buckling behavior of actuated functionally graded piezoelectric nanoplates

This paper addresses the thermal buckling of actuated functionally graded piezoelectric porous nanoplates. Eringen's nonlocal elasticity theory with a higher-order shear deformation theory are used to obtain the analytical solution. The FGP porous nanoscale plate material possesses smooth continuous gradient transition of properties between materials as the dimension varies according to a modified power law function. The plate is under the influence of several thermal loadings (uniform, linear, nonlinear thermal difference) and electric voltages. A closed form solution of simply-supported FGP porous nanoplates is obtained using Navier's method. The critical thermal buckling of FGP porous nanoplates subjected to several thermal loadings and electric voltages is investigated. Numerical examples are presented to validate the present formulation. The influence of several porosity coefficients, small-scale parameters, thermal loadings, geometric parameters, power law exponents and external electrical voltages on the thermal buckling of FGP porous nanoplates are discussed.

Buckling analysis of piezoelectric cut out nanoplates using numerical method

Buckling analysis of the nanocomposite piezoelectric nanoplate with cut out resting in elastic foundation is presented in this article. In order to enhance mechanical properties of nanoplate with central cut out, carbon nanotubes (CNTs) are distributed as uniform distribution (UD) through thickness. For defining the shape function of cut out, the domain decomposition method and orthogonal polynomials are used. At last, to obtain critical buckling load of system, Rayleigh-Ritz method is provided. The impacts of the length and width of nanoplate, dimension of square cut out and elastic medium on the piezoelectric nanoplate are presented in this study. The results show that considering cut out in nanoplate, the buckling load is decreased.

Size-dependent thermo-electromechanical responses analysis of multi-layered piezoelectric nanoplates for vibration control

Multi-layered piezoelectric nanostructures stand as one the most promising candidates for smart nanodevices and nanocomposites which are widely used as sensors and actuators in nano-electromechanical systems due to their excellent performances in fabrication, design and energy conversion (i.e. electrical and mechanical energy). The inherent nano-sized piezoelectricity properties (e.g. enhanced piezoelectric effect and novel electrical/chemical/physical properties) enable them to be regarded as the next-generation piezoelectric materials. Present study aims to investigate the size-dependent thermo-electromechanical responses of multi-layered piezoelectric nanoplates under heating loads. In the context of nonlocal piezoelectric thermoelastic theory, a composite laminated piezoelectric plate is chosen as the analytical model whilst the coupled governing equations for each layer with size-dependent characteristic lengths of thermal, electric and elastic fields as well as non-idealized interfacial conditions are obtained, and then solved by using Laplace transformation techniques. The transient solutions obtained are applied to bi-layered piezoelectric nanoplates and the effects of size-dependent characteristic lengths and material constants ratio on structural responses are evaluated and discussed to provide a comprehensive understanding and design insights of piezoelectric nanocomposites.

A generalized dynamic model of nanoscale surface acoustic wave sensors and its applications in Love wave propagation and shear-horizontal vibration

• A generalized dynamic model based on the Hamilton's principle and variational approach is established. • The model is applied to depict the wave propagation in SAW nano-devices or vibration of piezoelectric nanoplates. • The surface effect is included with the aid of the surface elasticity , surface piezoelectricity and surface permittivity. • A critical thickness value of surface acoustic wave nano-devices or piezoelectric nanoplates can be obtained. • Below the critical thickness, the size-dependent properties will become evident and should be taken into account. A generalized dynamic model to depict the wave propagation properties in surface acoustic wave nano-devices is established based on the Hamilton's principle and variational approach. The surface effect, equivalent to additional thin films, is included with the aid of the surface elasticity, surface piezoelectricity and surface permittivity. It is demonstrated that this generalized dynamic model can be reduced into some classical cases, suitable for macro-scale and nano-scale, if some specific assumptions are utilized. In numerical simulations, Love wave propagation in a typical surface acoustic wave device composed of a piezoelectric ceramic transducer film and an aluminum substrate, as well as the shear-horizontal vibration of a piezoelectric plate, is investigated consequently to qualitatively and quantitatively analyze the surface effect. Correspondingly, a critical thickness that distinguishes surface effect from macro-mechanical behaviors is proposed, below which the size-dependent properties must be considered. Not limited as Love waves, the theoretical model will provide us a useful mathematical tool to analyze surface effect in nano-devices, which can be easily extended to other type of waves, such as Bleustein-Gulyaev waves and general Rayleigh waves.

Bending stress analysis of a piezoelectric nanoplate with flexoelectricity under inhomogeneous electric fields

Flexoelectricity has been found as an unneglectable electro-mechanical coupling effect in micro/nanoscale dielectric materials. We present a stress function based bending stress analysis method for piezoelectric nanoplate under inhomogeneous electric fields considering both piezoelectric effect and flexoelectric effect in this work. A Ritz type solution procedure is developed by means of the quasi-three dimensional stress functions with the initial assumption of out-of-plane stress functions. A standard eigenvalue problem is constructed to obtain the general solutions of governing equations which are obtained by the principle of complementary virtual work. For the numerical analysis, we investigate the bending stresses in laminated piezoelectric nanoplate with or without flexoelectricity and the size-dependent effect on the bending stress distributions. Two kinds of inhomogeneous electric fields are considered for discussion. The present work is expected to help understanding the influence of flexoelectric effect on the bending stress distributions for the future design and application of piezoelectric nanostructures.

Analytical modeling for vibrating piezoelectric nanoplates in interaction with inviscid fluid using various modified plate theories

This study aimed to investigate the fluid-structure interaction of a piezoelectric nanoplate using the analytical method. For the purpose of the study, nonlocal elasticity theory is employed for capturing the small-scale effects of the structure. The structure is modeled based upon several theories including classical plate theory, Mindlin plate theory, third-order shear deformation theory and six different types of modified shear deformation theory. These modified shear deformation theories devote various nonlinear distributions for transverse shear stress along the thickness of nanoplate. Two new distributions for transverse shear stress are proposed for the first time in this article. The fluid is considered to be incompressible, inviscid and irrotational. Fluid velocity potential associated with bulging and sloshing modes are obtained with satisfying Laplace's equation and fluid boundary conditions. Governing equations of fluid-structure interaction are derived with Hamilton's principle and Galerkin approach is applied to solve them. After validation of the present study with the available results in the literature, the effects of various parameters such as dimensions of fluid, nonlocal parameter and dimensions of piezoelectric nanoplate on the wet frequencies and mode shapes of the system are illustrated.

PROPAGATION CHARACTERISTICS OF SH GUIDED WAVES IN A PIEZOELECTRIC NANOPLATE

Piezoelectric nanomaterials have many unique properties, such as enhanced electromechanical coupling, low power dissipation and sensitive response, etc. Also such materials can meet the demand of microminiaturization of piezoelectric devices. These advantages make them strong candidates for applications in the fields of sensing, nanoelectromechanical systems (NEMS), flexible electronic device, and so on. As one of the most important features of nanomaterials, surface effect which resulted from the high ratio of surface to volume commonly plays a dominant role in the overall mechanical properties of piezoelectric nanomaterials. Due to the presence of surface effect, the bulk stress and bulk electric displacement jump across the piezoelectric surface, thus the classical continuity conditions are invalid. In this paper, the dispersion characteristics of SH guided waves propagating in a monolayer piezoelectric nanoplate are investigated with consideration of the surface effect. A surface is regarded as a two-dimensional continuum of zero thickness which possesses own material properties, and the influences of surface elasticity, surface piezoelectricity, surface permittivity and surface density are accounted into the non-classical boundary conditions of the piezoelectric nanoplate via the surface piezoelectricity model. The analytical expressions of dispersion relations are derived, and the numerical examples are provided to discuss the impacts of surface material parameters and nanoplate thickness on the symmetric and antisymmetric modes. Analysis results show that the propagation characteristics of SH guided waves exhibit obvious size-dependence. The surface effect has a significant impact on dispersion behaviors when the nanoplate thickness is small enough, while they may become more and more negligible as the thickness increases.

Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers

In the present paper, the nonlocal strain gradient refined model is used to study the thermal stability of sandwich nanoplates integrated with piezoelectric layers for the first time. The influence of Kerr elastic foundation is also studied. The present model incorporates two small-scale coefficients to examine the size-dependent thermal stability response. Elastic properties of nanoplate made of functionally graded materials (FGMs) are supposed to vary through the thickness direction and are estimated employing a modified power-law rule in which the porosity with even type of distribution is approximated. The governing differential equations of embedded sandwich piezoelectric porous nanoplates under hygrothermal loading are derived through Hamilton\'s principle where the Galerkin method is applied to solve the stability problem of the nanoplates with simply-supported edges. It is indicated that the thermal stability characteristics of the porous nanoplates are obviously influenced by the porosity volume fraction and material variation, nonlocal parameter, strain gradient parameter, geometry of the nanoplate, external voltage, temperature and humidity variations, and elastic foundation parameters.

Nonlocal analytical solution of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal nanoplates

Based on the nonlocal elasticity theory, the static bending deformation of a functionally graded multilayered one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) simply supported nanoplate is investigated under surface mechanical loadings. The functionally graded material is assumed to be exponential along the thickness direction. By utilizing the pseudo-Stroh formalism and propagator matrix method, exact closed-form solutions of functionally graded multilayered 1D hexagonal PQC nanoplates are then obtained by assuming that the layer interfaces are perfectly contacted. Numerical examples for six kinds of sandwich functionally graded nanoplates made up of piezoelectric crystals, quasicrystal and PQC are presented to illustrate the influence of the exponential factor, nonlocal parameter and stacking sequence on the phonon, phason and electric fields, which play an important role in designing new composite structures in engineering.

Buckling analysis of piezoelectric cut out nanoplates using numerical method

Buckling analysis of the nanocomposite piezoelectric nanoplate with cut out resting in elastic foundation is presented in this article. In order to enhance mechanical properties of nanoplate with central cut out, carbon nanotubes (CNTs) are distributed as uniform distribution (UD) through thickness. For defining the shape function of cut out, the domain decomposition method and orthogonal polynomials are used. At last, to obtain critical buckling load of system, Rayleigh-Ritz method is provided. The impacts of the length and width of nanoplate, dimension of square cut out and elastic medium on the piezoelectric nanoplate are presented in this study. The results show that considering cut out in nanoplate, the buckling load is decreased.

Thermo-electro-mechanical vibration analysis of nonlocal piezoelectric nanoplates involving material uncertainties

This study aims to detect the influence of material uncertainties on the free vibration of nonlocal piezoelectric nanoplates under thermo-electro-mechanical loadings. The size-dependent governing equations are derived based on the nonlocal theory and Hamilton’s principle, and Navier method is used for the solution. Considering inadequate experimental data, uncertain-but-bounded parameters are used to quantify the uncertain nanomaterial properties. Based on the interval analysis theory, a novel hull iterative algorithm (HIA) is proposed to evaluate the thermo-electro-mechanical vibration behavior of piezoelectric nanoplates. The presented method is compared with Monte Carlo method and sensitivity based interval analysis method, and well agreements are achieved. A sensitivity analysis is performed to identify the most dominant uncertain parameters. Using the HIA, parametric studies are carried out to explore the combined effects of material uncertainties and temperature change, external electric voltage, biaxial force as well as nonlocal parameter on the natural frequency of piezoelectric nanoplates.

Correction to: Buckling of magneto-electro-hygro-thermal piezoelectric nanoplates system embedded in a visco-Pasternak medium based on nonlocal theory

The original version of this article unfortunately contained a mistake. Farzad Ebrahimi was not listed among the authors.

Nonlinear vibration of piezoelectric sandwich nanoplates with functionally graded porous core with consideration of flexoelectric effect

The porous materials become a new class of advanced engineering material due to their excellent advantage such as low specific weight, efficient capacity of energy dissipation, reduced thermal and electrical conductivity, enhanced recyclability and machinability. In this study, the nonlinear vibration of piezoelectric sandwich nanoplates with functionally graded (FG) porous core under electrical load is presented. The piezoelectric effect, flexoelectric effect and von Karman type large deformation are simultaneously taken into account. Results show that the piezoelectric and flexoelectric effects of the material reduce the vibration frequency of the sandwich nanoplate even there is no applied voltage on the piezoelectric layer. The natural frequency of the sandwich structure with porous core can be adjusted by controlling the porosity distribution and porous coefficients of the porous material, and the applied voltages on the piezoelectric layer.

Electroelastic biaxial compression of nanoplates considering piezoelectric effects

In the present theoretical work, it is assumed that a piezoelectric nanoplate is connected to the voltage meter which voltages have resulted from deformation of the plate due to in-plane compressive forces whether they are critical buckling loads or arbitrary forces. In order to derive governing equations, a simplified four-variable shear deformation plate theory has been employed using Hamilton’s principle and Von-Kármán assumptions. Modified couple stress theory has been applied to considering size-dependent effects in nano size. In order to compare the results, a validation has been done with the results of macroscopic. Results have been presented by changing some parameters, such as aspect ratio, various boundary conditions and length scale parameter influence on the produced voltage by the piezoelectric nanoplate. The most important outcomes show that an increase in length scale parameter leads to decreasing the produced voltage at constant in-plane arbitrary forces.

Buckling of magneto-electro-hygro-thermal piezoelectric nanoplates system embedded in a visco-Pasternak medium based on nonlocal theory

In this present work the critical loading of magneto-electro-viscoelastic-hygro-thermal (MEVHT) piezoelectric nanoplates embedded in a viscoelastic foundation are investigated. Via two variable shear deformation plate theory displacement are obtained. The governing equations of nonlocal viscoelastic nanoplate are driven by using Hamilton’s principle and solved by an analytical solution. A parametric study is presented to examine the effect of the nonlocal parameter, hygro-thermo-magneto-electro-mechanical loadings and aspect ratio on the critical loading of MEVHT nanoplates. It is found that the critical loading is quite important to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the hygro-thermal loading.

Electro-thermal buckling of elastically supported double-layered piezoelectric nanoplates affected by an external electric voltage

PurposeThermal buckling of double-layered piezoelectric nanoplates has been analyzed by applying an external electric voltage on the nanoplates. The paper aims to discuss this issue.Design/methodology/approachDouble-layered nanoplates are connected to each other by considering linear van der Waals forces. Nanoplates are placed on a polymer matrix. A comprehensive thermal stress function is used for investigating thermal buckling. A linear electric function is used for taking external electric voltages into account. For considering the small-scale effect, the modified couple stress theory has been applied. An analytical solution has been used by taking various boundary conditions.FindingsEEV has a considerable impacted on the results of various half-waves in all boundary conditions. By increasing EEV, the reduction of critical buckling temperature in higher half-waves is remarkably slower than lower half-waves. By considering long lengths, the effect of EEV on the critical temperature will be markedly decreased.Originality/valueThis paper uses electro-thermal stability analysis. Double-layered piezoelectric nanoplates are analyzed. A comprehensive thermal stress function is applied for taking into account critical temperature.

Lamb wave propagation with flexoelectricity and strain gradient elasticity considered

In this paper, the effects of flexoelectricity and strain gradient elasticity on Lamb waves propagating in an infinite piezoelectric nanoplate are analytically investigated. The dispersion equations are obtained and numerically solved for both the electrically open and short cases. A detailed discussion about the dispersion relations of the lowest mode is subsequently presented. Numerical results indicate that flexoelectricity and strain gradient elasticity have a substantial effect on Lamb wave propagation. Compared with the phase velocity of classical piezoelectric Lamb waves, flexoelectricity could decrease the phase velocity, while strain gradient elasticity could increase it. The effects of flexoelectricity and strain gradient elasticity largely depend on the wave number, material properties and nanoplate thickness. In infinite PZT-5H ceramic nanoplates, the effects of flexoelectricity and strain gradient elasticity on the phase velocity are negligible for wave numbers less than 106 m−1. However, for larger wave numbers, not only the phase velocity but also the dispersion relations can be significantly changed with the introduction of flexoelectricity and strain gradient elasticity. In addition, the effects of flexoelectricity and strain gradient elasticity on the electromechanical coupling coefficient are significant and complicated. Since the flexoelectric effect and the strain gradient elasticity effect exist in almost all dielectric materials, the conclusions obtained in this paper are general and can be applied to the analysis and design of the acoustic devices based on Lamb wave propagation.

Dynamic modeling of embedded nanoplate systems incorporating flexoelectricity and surface effects

In this research, vibration characteristics of a flexoelectric nanoplate in contact with Winkler-Pasternak foundation are investigated based on nonlocal elasticity theory considering surface effects. This non-classical nanoplate model contains flexoelectric effect to capture coupling of strain gradients and electrical polarizations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, flexoelectric and surface effects are omitted. Hamilton’s principle is employed to derive the governing equations and the related boundary conditions which are solved applying a Galerkin-based solution. Natural frequencies are verified with those of previous papers on flexoelectric nanoplates. It is illustrated that flexoelectricity, nonlocality, surface stresses, elastic foundation and boundary conditions affects considerably the vibration frequencies of piezoelectric nanoplates.

Free vibration and buckling investigation of piezoelectric nano-plate in elastic medium considering nonlocal effects

In this paper, buckling and free vibration of piezoelectric nano-plate on elastic foundation are investigated. The assumptions of nonlocal elasticity and classical plate theory are considered. The simply supported boundary conditions are considered and plate is subjected to external electric voltage. The final equations of the motion are derived using Hamilton function and solved by Navier method to find the natural frequency and critical buckling force of the nano-plate. The effect of various parameters on the plate behavior, such as nonlocal parameter, electrical voltage, and Winkler and shear modulus, is investigated and results are compared with those reported in the literature. The results show that by increasing the small-scale effects, the natural frequency and buckling load decrease.

Cylindrical bending analysis of a layered two-dimensional piezoelectric quasicrystal nanoplate

The piezoelectric effect is a significant property of quasicrystal. In this article, the exact solution is derived for a layered piezoelectric quasicrystal nanoplate with nonlocal effect in cylindrical bending. Based on the nonlocal theory and the pseudo-Stroh formalism, the exact solution for a homogeneous simply supported nanoplate is obtained. With the aid of the propagator matrix, the exact solution for a multilayered nanoplate is achieved. Numerical examples are carried out to reveal the influences of span-to-thickness ratio, nonlocal parameter, and stacking sequence on piezoelectric quasicrystal nanoplates with their top surface subjected to two loadings. One is a z-direction mechanical loading and the other is an electric potential loading. These results can be served as benchmarks for the design, numerical modeling, and simulation of layered two-dimensional piezoelectric quasicrystal nanoplates under cylindrical bending.