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This paper presents elasticity solutions for functionally graded piezoelectric plates under electric fields in cylindrical bending. Based on the generalized Mian and Spencer plate theory, the assumption of the material parameters which can vary along the thickness direction of the plate in an arbitrary fashion is kept; however, the materials are extended from elastic materials to piezoelectric materials. The electric potential function is constructed following the forms of the displacement functions in Mian and Spencer plate theory. The essential idea of Mian and Spencer plate theory (J Mech Phys Solids 46:2283–2295, 1998) is that the three-dimensional elasticity equations for inhomogeneous materials can be obtained by two-dimensional solution for homogeneous materials by straightforward substitutions. Through rigorous derivation, the corresponding elasticity solutions of cylindrical bending of functionally graded piezoelectric plates under electric fields are obtained. In the numerical examples, the accuracy of the present solutions is verified and the responses of plates subjected to electrical potential difference and electrical displacement are investigated, respectively. [ABSTRACT FROM AUTHOR]

The paper investigates the static, bending and vibration responses of the functionally graded piezoelectric plate (FGPP) resting on the two/three-parameter foundation under a thermo-electro environment. Hamilton's principles are used with first-order shear deformation theory to obtain the governing equations. They are solved using nine noded interpolation functions with 63 degrees of freedom (DOFs) per element. It is observed that the two-parameter foundation has a shear layer dominant, and the three-parameter foundation has an additional layer of spring that plays a significant role in the static bending and vibrational behavior of the CB/UCB conditions FGPP. The applied electrical voltage and the temperature change affect the static bending, and vibrational results as the rise in temperature lead to the plate's softening. An increase in voltage leads to a reduction in the stiffness of the plate. Also, Sg-law significantly influences the dimensionless frequency, center deflection, and axial stress compared to other laws. [ABSTRACT FROM AUTHOR]

In this paper, a functionally graded piezoelectric plate on an elastic foundation composed of two different piezoelectric materials bonded together in the form of plate is studied, and its static bending and fundamental frequencies are analyzed. First, based on Kirchhoff plate theory and the Hamilton principle, the governing equations and corresponding boundary conditions of the model are derived, and then the equations are discretized and solved by the differential quadrature method (DQM). Finally, the effects of physical parameters such as length-to-height ratio, length-to-width ratio, material graded index, foundation stiffness coefficient, temperature change value and external voltage value on static bending deflection, and fundamental frequency value of the functionally graded piezoelectric plate with four sides simply supported are discussed. The calculated results are in good agreement with those in the literature. The data results show that the increase in the elastic foundation stiffness coefficient will increase the equivalent stiffness of the plate. In the process of work, due to the equivalent pressure value generated by the influence of the external voltage, it will lead to unstable phenomena. [ABSTRACT FROM AUTHOR]

This work focuses on the free vibration characteristics of the functionally graded piezoelectric (FGPE) plate with classical and elastic constraints. First, the analytical model is established for the FGPE plate on the basis of the first-order shear deformation theory (FSDT). Besides, different distribution profiles of the material constituent are considered for the FGPE plate model, and various external initial voltages are also considered for modeling the piezoelectric effect. The displacement functions for the FGPE plate are then given in the form of third-kind orthogonal polynomials. Ultimately, the solution of the FGPE plate model is resolved by means of the Ritz method. Convergence and accuracy of the presented model are verified, and a series of parametric investigations are given. [ABSTRACT FROM AUTHOR]

In this paper, a functionally graded piezoelectric plate on an elastic foundation composed of two different piezoelectric materials bonded together in the form of plate is studied, and its static bending and fundamental frequencies are analyzed. First, based on Kirchhoff plate theory and the Hamilton principle, the governing equations and corresponding boundary conditions of the model are derived, and then the equations are discretized and solved by the differential quadrature method (DQM). Finally, the effects of physical parameters such as length-to-height ratio, length-to-width ratio, material graded index, foundation stiffness coefficient, temperature change value and external voltage value on static bending deflection, and fundamental frequency value of the functionally graded piezoelectric plate with four sides simply supported are discussed. The calculated results are in good agreement with those in the literature. The data results show that the increase in the elastic foundation stiffness coefficient will increase the equivalent stiffness of the plate. In the process of work, due to the equivalent pressure value generated by the influence of the external voltage, it will lead to unstable phenomena.

The improvement of the resolution and energy conversion efficiency of piezoelectric devices requires a thorough study of guided wave, especially the evanescent wave modes with high-phase speed and low attenuation. Due to the computation difficulties, investigations about the evanescent wave in piezoelectric structures are rather limited. In this article, an analytic method based on the orthogonal function technique is presented to investigate the complex dispersion relations and the evanescent guided wave in functionally graded piezoelectric plates, which can convert the complex partial differential equations with variable coefficients into an eigenvalue problem and obtain all solutions. Comparisons with other related studies are conducted to validate the correctness of the presented method. Three-dimensional full dispersion curves are plotted to gain a better insight into the nature of the evanescent waves. The influences of piezoelectricity and graded fields and electrical boundary conditions on evanescent waves are illustrated. The electromechanical coupling factors of the functionally graded piezoelectric material plates with different gradient fields are also investigated. Furthermore, the displacement amplitude and electric potential distributions are also discussed to illustrate the specificities of evanescent guided waves. The corresponding results presented in this work are promised to be used to improve the resolution of piezoelectric transducers. [ABSTRACT FROM AUTHOR]

In this article, electro-thermo-mechanical vibrational behavior of functionally graded piezoelectric (FGP) plates with porosities is explored via a refined four-variable plate theory for the first time. Uniform, linear and nonlinear temperature changes are considered in this study. Electro-elastic material properties of porous FGP plate vary across the thickness based on modified power-law model. The governing equations derived from Hamilton's principle are solved analytically. The exactness of solution is confirmed by comparing obtained results with those provided in the literature. Influences of applied voltage, porosity distribution, thermal loadings, material gradation, plate geometrical parameters and boundary conditions on the vibrational behavior of FGP plates are discussed. These results can be applied for accurate design of smart structures made of functionally graded piezoelectric materials by considering porosity distribution. [ABSTRACT FROM AUTHOR]

To provide reference for aerospace structural design, electro-mechanical vibrations of functionally graded piezoelectric material (FGPM) plates carrying porosities in the translation state are investigated. A modified power law formulation is employed to depict the material properties of the plates in the thickness direction. Three terms of inertial forces are taken into account due to the translation of plates. The geometrical nonlinearity is considered by adopting the von Kármán non-linear relations. Using the d’Alembert's principle, the nonlinear governing equation of the out-of-plane motion of the plates is derived. The equation is further discretized to a system of ordinary differential equations using the Galerkin method, which are subsequently solved via the harmonic balance method. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge-Kutta technique. Additionally, the stability of the steady state responses is examined by means of the perturbation technique. Linear and nonlinear vibration analyses are both carried out and results display some interesting dynamic phenomenon for translational porous FGPM plates. Parametric study shows that the vibration characteristics of the present inhomogeneous structure depend on several key physical parameters. [ABSTRACT FROM AUTHOR]

Here, free vibration analysis of functionally graded piezoelectric (FGP) plates with porosities is carried out based on refined four-unknown plate theory. The present plate theory captures shear deformation impacts needless of shear correction factor. A modified power-law model is adopted to describe the graded material properties of a functionally graded piezoelectric plate. Implementing an analytical approach, which satisfies different boundary conditions, governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in the literature. The impacts of applied voltage, porosity distribution, material graduation, plate geometrical parameters, and boundary conditions on vibration of porous FGP plate are discussed. [ABSTRACT FROM PUBLISHER]

This article deals with the sampling surfaces method developed recently by the authors and its implementation for the three-dimensional coupled steady-state thermoelectroelastic analysis of functionally graded piezoelectric laminated plates subjected to thermal loading. The sampling surfaces formulation is based on choosing inside the nth layer I n not equally spaced sampling surfaces parallel to the middle surface of the plate in order to introduce temperatures, electric potentials, and displacements of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree I n − 1 in the thickness direction for each layer permits the presentation of the proposed functionally graded piezoelectric plate formulation in a very compact form. The sampling surfaces are located inside each layer at Chebyshev polynomial nodes that allow one to minimize uniformly the error due to the Lagrange interpolation. As a result, the sampling surfaces method can be applied efficiently to analytical solutions for functionally graded piezoelectric laminated plates, which asymptotically approach the three-dimensional exact solutions of thermoelectroelasticity as I n → ∞ . [ABSTRACT FROM AUTHOR]

In this study, examination of buckling behavior of functionally graded piezoelectric (FGP) plates with porosities is conducted employing a refined four-variable plate theory. By capturing shear deformation effects, the present inverse trigonometric theory is needless of shear correction factor. Electro-elastic material properties of porous FGP plate vary across the thickness based on modified power-law model. Implementing an analytical approach which satisfies different boundary conditions, governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in literature. It is indicated that the buckling behavior of piezoelectric plates is significantly influenced by elastic foundation parameters, external voltage, porosity distribution, power-law index, boundary conditions and aspect ratio [ABSTRACT FROM AUTHOR]

Abstract: A paper presents the sampling surfaces (SaS) method and its implementation for the three-dimensional (3D) exact analysis of functionally graded (FG) piezoelectric laminated plates. According to this method, we introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the plate and choose displacement vectors and electric potentials of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In −1 in the thickness direction for each layer leads to a very compact form of governing equations of the FG piezoelectric plate formulation. This fact gives an opportunity to derive the 3D exact solutions of electroelasticity for thick and thin FG piezoelectric laminated plates with a specified accuracy utilizing a sufficient number of SaS, which are located at interfaces and Chebyshev polynomial nodes. [Copyright &y& Elsevier]

Abstract: The dynamic fracture problem for a functionally graded piezoelectric plate containing a crack perpendicular to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the medium vary continuously in the thickness direction. Integral transform techniques and dislocation density function are employed to reduce the problem to the solution of a singular integral equation. Mode I dynamic energy density factors are presented for an internal crack as well as an edge crack for various values of dimensionless parameters representing the size and location of the crack and the material nonhomogeneity. [Copyright &y& Elsevier]