Fonksiyonel Derecelendirilmiş Konik Kesitli Mikro Kirişlerin Serbest Titreşim Analizi

Abstract

In this thesis a theoretical investigation in free vibration of a functionally graded tapered (FG) micro beam is presented. It is assumed that material properties vary along the beam thickness according to power law distributions. The governing equation is reduced to an ordinary differential equation in spatial coordinate for cross-section geometries with exponentially varying width. The vibration behaviors of micro-beams made of functionally graded materials are analytically investigated on the basis of the modified couple stress theory in the elastic range. The governing equations of motion and boundary conditions are derived on the basis of Hamilton principle. Analytical solutions of the natural frequencies are obtained for exponential FG beams with hinged-hinged, clamped-clamped and clamped-free end supports. Solutions for the natural frequencies are obtained FGM distribution functions of properties and as a function of the ratio of the beam characteristic size to the internal material length scale parameter.