Free Vibration Analysis of a Functionally Graded Micro-Beam with Tapered Cross Section

In this study, the free vibration analysis of a functionally graded (FG) micro-beam with tapered cross-section is carried out theoretically. The beam has material distribution according to power law throughout thickness. governing equation reduced an ordinary differential for cross-sectional geometry whose width varies exponentially. Vibrations microbeams were analyzed analytically in elastic variation range based on modified stress couple theory. Motion equations and boundary conditions are derived from Hamilton principle. Analytical results natural frequencies calculated cantilever exponential FG beams. Solutions obtained as ratio beam's characteristic size internal length parameter FGM function characteristics.