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In this study, we have introduced, for the first time, a novel integral quasi-3D higher-order shear deformation theory (HSDT) employing a third-order shape function. This approach is employed to analyze the free vibration characteristics of a cracked porous functionally graded material (FGM) beam supported on a three-parameter elastic foundation (Winkler/Pasternak/Kerr). This new Quasi HSDT introduces a stretching effect that surpasses the capabilities of FSDT and other HDST. The employed shape function satisfies the conditions of shear stress nullity at both the higher and lower facets without the need for correction factors. The study incorporates a mathematical model representing Winkler/Pasternak/Kerr foundation types into the Hamiltonian to derive the equations of motion. The FGM beam studied in this paper is assumed to be composed of materials with a distribution that varies according to a power law along its height. Our results are compared with previous studies and we reinforce our findings with a parametric study assessing the impact of crack attributes on the natural frequencies of the FG plate. This study presents an advanced integral quasi-3D HSDT, applied for the first time, to analyze the behavior of FG beams resting on a three-parameter foundation. [ABSTRACT FROM AUTHOR]

This article examines the impact of inclined transverse cracking on the natural frequency of Euler-Bernoulli-model imperfect FG beams on an elastic foundation, taking into account the pinned-pinned and clamped-clamped boundary conditions. The equations are diffused using the classic finite element method (h-version). Material properties are considered to vary in both directions of the beam; width and thickness, using the power-law formula. The approximate porosity model is adopted with a uniform distribution. Cracked element stiffness is determined by reducing the cross-section of a bi-directional FG beam. The numerical results are compared with those of previous convergence studies for dimensionless fundamental frequencies. Case studies were carried out to evaluate the effect of the porosity values, the crack depth, the crack location, slope angle, and the Winkler-elastic foundation parameters on the first three natural frequencies of a beam with different support conditions and material gradient. In addition, the results demonstrated that the two-way distribution function plays an important role in the convergence of frequencies. [ABSTRACT FROM AUTHOR]

In this paper, wave propagation in functionally graded (FG) porous plates resting on Winkler-Pasternak foundation is studied using a quasi-3D shear deformation theory. The proposed theory has a new displacement field that includes indeterminate integral terms and contains fewer unknown variables taking into account the effect of transverse shear and thickness stretching. The parameters of the elastic foundation are introduced in the present formulation following the mathematical model of Pasternak. In addition, the effect of porosity is studied. The material of the FG plate is inhomogeneous and the material properties are assumed to vary continuously in the thickness direction according to a power law of the volume fraction. The equations governing wave propagation in the plates resting on an elastic foundation are derived using Hamilton's principle. Then, the dispersion relationship between frequency and wave number is solved analytically. A comprehensive numerical result is accomplished to evaluate the effects of the volume fraction index, the porosity, thickness ratio (h/a), and the wave number on the wave propagation in functionally graded porous plates are discussed in detail. [ABSTRACT FROM AUTHOR]

This present paper concerned with the analytic modelling for vibration of the functionally graded (FG) plates resting on non-variable and variable two parameter elastic foundation, based on two-dimensional elasticity using higher shear deformation theory. Our present theory has four unknown, which mean that have less than other higher order and lower theory, and we denote do not require the factor of correction like the first shear deformation theory. The indeterminate integral are introduced in the fields of displacement, it is allowed to reduce the number from five unknown to only four variables. The elastic foundations are assumed a classical model of Winkler-Pasternak with uniform distribution stiffness of the Winkler coefficient (kw), or it is with variables distribution coefficient (kw). The variable's stiffness of elastic foundation is supposed linear, parabolic and trigonometry along the length of functionally plate. The properties of the FG plates vary according to the thickness, following a simple distribution of the power law in terms of volume fractions of the constituents of the material. The equations of motions for natural frequency of the functionally graded plates resting on variables elastic foundation are derived using Hamilton principal. The government equations are resolved, with respect boundary condition for simply supported FG plate, employing Navier series solution. The extensive validation with other works found in the literature and our results are present in this work to demonstrate the efficient and accuracy of this analytic model to predict free vibration of FG plates, with and without the effect of variables elastic foundations. [ABSTRACT FROM AUTHOR]

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGMplates are studied in detail. [ABSTRACT FROM AUTHOR]

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam. [ABSTRACT FROM AUTHOR]

Thermal buckling analysis of rectangular sigmoid functionally graded plates (S-FGPs) is investigated using first-order shear deformation theory. The sigmoid functionally graded material (S-FGM) system consists of ceramic (Al2O3) and metal (Al) phases varying through the thickness of plate according to a two power-law distribution. Material properties and thermal expansion coefficient of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The thermal loads are assumed to be uniform and sinusoidal distribution through-the-thickness. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and loading type on the critical buckling for S-FGM plates. [ABSTRACT FROM AUTHOR]