Comparing Different Theories for Dynamic Behavior of a Functionally Graded Beam

Abstract

Theoretical formulation, Navier’s solutions of rectangular plates based on a new higher order shear deformation model are presented for the static and dynamic analysis of functionally graded plates (FGPs). This theory enforces traction free boundary conditions at plate surfaces. Shear correction factors are not required because a correct representation of transverse shearing strain is given. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concern flexural behavior of FG plates with Metal–Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. Results are verified with available results in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static and dynamic behavior of functionally graded plates. This paper presents a theoretical investigation in free vibration of simply supported FG beam. Young’s modulus of beam varies in the thickness direction according to power law. Governing equations were found by applying Hamilton’s principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. A free vibration frequency is given for different material properties.