Free vibration of bidirectional functionally graded sandwich beams partially restin on pasternak foundation based on a sinusoidal theory

Abstract

In this paper, free vibration of a bidirectional functionally graded sandwich (BFGSW) beams partially resting on a Pasternak foundation is studied. The beams with three layers, an axially functionally graded core and two bidirectional functionally graded face sheets, are made from a mixture of metal and ceramic. The material properties of the face sheets are considered to vary continuously in both the thickness and length directions by the power-law distributions, and they are estimated by Mori-Tanaka scheme. A sinusoidal shear deformation theory, in which the transverse displacement is split into bending and shear parts, is employed to derive energy expressions of the beam. A finite element formulation is formulated and employed to compute vibration characteristics. Numerical result reveals that the ratio of foundation support to the beam length plays an important role on the vibration behaviour, and the dependence of the frequencies upon the material grading indexes is governed by this ratio. Numerical investigation is carried out to highlight the effects of the material distribution, the layer thickness ratio, the foundation stiffness on the vibration characteristics of the beams. The influence of the aspect ratio on the frequencies of the beams and is also examined and discussed.