Free vibration of a 2D-FGSW beam based on a shear deformation theory

In this paper, a two-dimensional functionally graded sandwich (2D-FGSW) beam model formed from three constituent materials is proposed and its free vibration analysis is carried out for the first time. The beam consists of three layers, a homogeneous core and two skin layers of 2D-FGM. The material properties of the skin layers are considered to vary in both the thickness and longitudinal directions by power gradation laws. Based on a third-order shear deformation theory, a beam element using the transverse rotation as an independent variable is formulated and employed to compute vibration characteristics. Numerical investigation is carried out to show the accuracy of the derived element and to illustrate the effects of the material distribution and layer thickness ratio on vibration frequencies and vibration modes of the beam.