On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

Nonlinear forced vibration of rectangular plates by modified multiple scale method

In the present study, the nonlinear forced vibration of a rectangular plate is investigated analytically using modified multiple scales method for the first time. The plate is subjected to transversal harmonic excitation, and the boundary condition is assumed to be simply supported. The von Karman nonlinear strain displacement relations are used. The extended Hamilton principle and classical plate theory are applied to derive the partial differential equations of motions. This research focuses on resonance case with 3:1 internal resonance. By applying Galerkin method, the nonlinear partial differential equations are transformed into time dependent nonlinear ordinary differential equations, which are then solved analytically by modified multiple scales method. This proposed approach is very simple and straightforward. The obtained results are then compared with both the traditional multiple scales method and previous studies, and excellent compatibility is noticed. The effect of some of the main parameters of the system is also examined.

Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to Non-Uniform Heating Using the Fourier Transform Method

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).