Analytical and Numerical Investigation of Free Vibration Behavior for Sandwich Plate with Functionally Graded Porous Metal Core

The current work presents a free vibration analysis of a simply supported rectangular functionally graded sandwich plate using a new analytical model. The core of the sandwich plate is made up of porous metal, and the top and bottom faces are made up of homogenous materials. The core metal properties are assumed to be porosity dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The contribution of this paper is to evaluate the performance of functionally graded porous materials (FGPMs) as it is used for many biomedical applications, particularly in tissue engineering. Theoretical formulations are based on the classical plate theory to find the free vibration characteristics of the imperfect FGM sandwich plate and include different parameters. Parameters included are graded distributions of porosity, power-law index, core metal type, and aspect ratios. A numerical investigation using finite element analysis (FEA) and the modal analysis was conducted with the assistance of the commercial ANSYS-2020-R2 software to validate the analytical solution. To detect the various parameters influencing the fundamental frequencies of sandwich plate comprehensive numerical results are presented in dimensionless tabular and graphical forms. The results reveal that the frequency parameter of the sandwich plate increases with the increase of the porosity parameter and number of the constraints in the boundary conditions. Furthermore, the increase in the number of layers leads to an increase in the accuracy of the results for the same FGM core thickness. An accepted agreement can be observed between the proposed analytical solution and numerical results with a maximum error discrepancy of 8%.