Some Intriguing Results Pertaining to Functionally Graded Columns

Abstract

Some intriguing results are reported in conjunction with closed form solutions obtained for a clamped-free vibrating inhomogeneous column under an axial concentrated load using the semi-inverse method. Fourth order polynomial is postulated for both the vibration mode shape and buckling displacement. Solution is provided for the flexural rigidity and the natural fi'equency. It is shown that, for each level of axial loading, there may exist up to five flexural rigidities satisfying the governing differential equation and boundary conditions.

Archive of Mechanical Engineering

“…Free vibration and stability analyses of Timoshenko beams with nonuniform cross-sections were studied in [11] by employing an energy-based finite element solution. In [12], authors examined functionally graded column which have fixed-free end conditions and which is subjected to a compressive axial load. Free vibration and stability of axially functionally graded Euler-Bernoulli beams that taper in different planes are studied in [13].…”