Study of the dynamic behavior of plates in gradient properties with logarithmic and exponential porosity

Abstract

In this paper, we are interested in the dynamic behavior of porous plates in property gradient, the property gradient material is a new generation of composite material, which is characterized by a gradual and continuous variation of physical properties, in order to attenuate the major singularity of laminar materials, which is the direct transition from one material to another. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments.In order to model our plate as well as possible, we will use a high-order theory with four variables only, by injecting the exact position of the neutral surface. The originality of this work lies in the consideration of two types of porosity distribution “logarithmic and exponential” in the calculation of the position of the neutral surface.The plate is subjected to a vertical load of sinusoidal distribution expressed in double series of Fourier. The equation of motion for FG rectangular plates is obtained through Hamilton’s principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigen value problems.The object of this work is to study the influence of the variation of the volume fraction, the power index and The dimension ratio on the response of  the frequency , and ,the constraints , and and the dimensionless deflection and the dimensionless displacement obtained in the presence of porosity with logarithmic and exponential distribution compared to those uniformly distributed.