Three-Dimensional Free Vibration Analysis of Sandwich Plates with VSCL Face Sheets and Porous Functionally Graded Core

Abstract

This paper focuses on the free vibration analysis of sandwich plates with variable stiffness composite laminated (VSCL) face sheets and a functionally graded (FG) porous core. The problem is solved using the hierarchical finite element method (FEM) based on the three-dimensional (3-D) elasticity theory. The use of an FG material core in a VSCL sandwich plate offers many advantages in terms of lightweight properties, high stiffness, as well as high strength and toughness. The sandwich plate is modeled by an assembly of 3-D p-elements, where each element or layer has an independent thickness and material properties. The layers of the sandwich plate are assumed to be perfectly bonded between the interfaces. The present 3-D solutions are validated through convergence and comparison studies with the published results of various sandwich plates that employ different theories and methods. A parametric study is performed to investigate the effects of several factors, including the volume fraction function index, porosity, core-to-face sheet thickness ratio, plate thickness, fiber orientation angles and boundary conditions on the vibrational frequencies. The results show that the incorporation of composite curvilinear fibers in the face sheets, combined with a porous FG core, significantly enhances the stiffness of the sandwich plate. These results can be used to establish benchmarks for future comparisons.