Natural frequencies of a functionally graded anisotropic rectangular plate

Abstract

We use the first-order shear deformation theory (FSDT) coupled with the finite element method (FEM) to study free vibrations of a functionally graded (FG) anisotropic rectangular plate with the objective of maximizing one of its first five natural frequencies. The following edge conditions are considered: (i) all edges clamped, (ii) all edges simply supported, (iii) two opposite edges clamped and the other two free, and (iv) two opposite edges simply supported and the other two free. An advantage of a functionally graded plate over a laminated plate is that material properties vary continuously through the plate thickness. Thus no sudden discontinuities in stresses occur across an interface between any two adjoining laminae thereby eliminating the delamination mode of failure. Whereas there have been numerous works on studying the response of FG plates made of isotropic elastic constituents with the homogenized material also modeled as isotropic elastic (e.g., see Refs. [1,2] and references cited therein), the only other study on FG anisotropic plate [3] has assumed that all elastic constants vary exponentially through the plate thickness at the same rate. It is highly unlikely that elastic moduli of a FG anisotropic plate will exhibit this property. Here we consider a FG anisotropic plate in which the fiber orientation varies smoothly through the plate thickness.