In this article, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method. Introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions could be explicitly obtained in terms of BDFs via application of basic principles of structural mechanics. BDFs are obtained using the unit-dummy-load method. Carrying out static analysis, it is verified that exact results are provided by applying one or a few elements. The competency of the present element in stability and free vibration analyses is verified through several numerical examples.

In this article, free vibration characteristics of rotating axially functionally graded tapered beams with six different boundary conditions are studied through a finite-element approach. The beam element employed in this study is a two-noded element whose shape functions are obtained in terms of special functions namely basic displacement functions. Application of this beam element provides good results as the shape functions take the effects of variable centrifugal force, cross-sectional area, and mechanical properties of the material. In this study, the effects of material non-homogeneity, taper ratio, rotating speed parameter, hub radius, and tip mass are investigated. The results are given in tabular form so that they could be used as a means of comparison for future studies in this field.