Vibration Analysis of Functionally Graded Sandwich Beam with Variable Cross-Section

In this study, free vibration behavior of a multilayered symmetric sandwich beam made of Functionally Graded Material (FGM) with variable cross-section is investigated. The elasticity and density of the Functionally Graded (FG) sandwich beam vary through the thickness according to the power and exponential laws by using mixture rules and laminate theory. 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. Furthermore, the width of the beam varies exponentially along the length of the beam with rectangular cross-section. The natural frequencies are computed for conventional boundary conditions of the FG sandwich beam using theoretical procedure. The effects of material index, geometric index and slenderness ratio are also discussed. Finally, the obtained results are compared with those in literature and a finite element based commercial program ANSYS® and found to be consistent with each other.