Influence of Porosity on Vibration of Porous FG Plates Resting on an Arbitrarily Orthotropic Winkler-Pasternak Foundation by PDDO

Abstract

This paper studies the vibration responses of porous functionally graded (FG) thin plates with four various types of porous distribution based on the physical neutral plane by employing the peridynamic differential operator (PDDO). It is assumed that density and elastic modulus continuously vary along the transverse direction following the power law distribution for porous FG plates. The governing differential equation of free vibration for a porous rectangular FG plate and its associated boundary conditions are expressed by a Lévy-type solution based on nonlinear von Karman plate theory. Dimensionless frequencies and mode shapes are obtained after solving the characteristic equations established by PDDO. The results of the current method are validated through comparison with existing literature. The effects of geometric parameters, material properties, elastic foundation, porosity distribution, and boundary conditions on the frequency are investigated and discussed in detail. The highest fundamental dimensionless frequency occurs under SCSC boundary conditions, while the lowest is under SFSF boundary conditions. The porous FG plate with the fourth pore type, featuring high density of porosity at the top and low at the bottom, exhibits the highest fundamental frequency under SSSS, SFSF, and SCSC boundary conditions. The dimensionless frequency increases with an increase in the elastic foundation stiffness coefficient.