Effect of Elastically Restrained Edges on Free Transverse Vibration of Functionally Graded Porous Rectangular Plate

Abstract

In this paper, the author studied free transverse vibration of a thin isotropic simply-supported functionally graded (FG) rectangular plate with porosity effect based on classical plate theory. The plate is considered to be elastically restrained against rotation. It is assumed that the material properties of the graded plate are porosity-dependent. An even porosity distribution is considered for analysis purposes. Due to the asymmetry of material in the thickness direction, the neutral surface is not the same as the geometrical mid-plane of the plate. The concept of the physical neutral surface of the FG plate along with classical plate theory is used to formulate the problem. Hence, the physical neutral surface is taken as the reference plane. The first three dimensionless frequencies of the plate are obtained using the Rayleigh-Ritz method. Boundary characteristic orthogonal polynomials (eigenfunctions), generated using the Gram-Schmidt process, are used in the Rayleigh-Ritz method. A parametric study shows that porosity and material distribution parameters have remarkable effects on the free vibration response of the plate. Results are compared with those of simply-supported FG plates.

Keywords

• functionally graded
• porous rectangular
• restrained
• physical neutral surface
• rayleigh-ritz