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

OpenAlex İngilizce

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