Free vibration of symmetric FG sandwich Timoshenko beam with simply supported edges

Abstract

In this study, free vibration behaviors of a multilayered symmetric sandwich beam made of functionally graded materials are investigated. The material properties of the functionally graded sandwich beam are assumed to vary through the thickness according to the power and exponential laws. In order to provide this, fifty layered beam is considered. Each layer is isotropic and homogeneous although the volume fractions of the constituents of the layers are different. The effect of variation of mass density is also taken into account in addition to Young’s modulus by using mixture rules and laminate theory. Furthermore, natural frequencies are computed for simply-supported boundary conditions of FG sandwich beam using theoretical procedure based on Timoshenko and Euler-Bernoulli theorems. The effects of slenderness ratio and power index are also discussed. Finally, the obtained results are compared with the reported studies and ANSYS^® and found to be consistent with each other.