Buckling Analysis of Axially Functionally Graded and Non-Uniform Beams Based on Timoshenko Theory

In this paper, the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated. Based on the auxiliary function and power series, the coupled governing equations were converted into a system of linear algebraic equations. With various end conditions, the characteristic polynomial equations in the buckling loads were obtained for axially inhomogeneous beams. The lower and higher-order eigenvalues were calculated simultaneously from the multi-roots due to the fact that the derived characteristic equation was a polynomial one. The computed results were in good agreement with those analytical and numerical ones in literature.