Numerical and Analytical Investigation of Free Vibration Behavior of Porous Functionally Graded Sandwich Plates

Abstract

This study investigates the free vibration analysis of a sandwich plate made of functionally graded materials (FGMs) with porosities to evaluate the natural frequency. Five parameters contribute to FGM: porous index, elastic parameters, porosity ratio, length-to-thickness ratio, and length-to-width ratio. Taking into account the thickness of the FGM plate, it is assumed that the plate has a new distribution of porosities. An investigation based on classical plate theory (CPT) examines kinematic relationships. This paper presents results for metal-ceramic functionally graded rectangular plates with a power law through the variation of volume fractions with porous ratio. A margin of error of not more than 5% applies to thin and thick plates. To validate the analytical results, a numerical investigation was conducted by employing the finite element method using ANSYS. This investigation was conducted on a 3D model of an FG system with SOLID186 an eight-noded element. Using various boundary conditions and selected models, illustrated the influence of porosity distribution characteristics on sandwich plate dynamic response. It was found that the frequency parameter of the plate increases with the increase in the sandwich structure mounting constraints. The plate thickness was divided into N layers to show the effect of several layers on the obtained results. It was found that the natural frequency for the FGM sandwich plate remains the same regardless of the number of layers for the same FGM thickness.