Derivation of an efficient element for free vibration analysis of rotating tapered Timoshenko beams using basic displacement functions

The accuracy of results predicted by finite element method considerably depends on the shape functions used to formulate the displacement field along the element. In this article, a novel approach is introduced to derive an efficient beam element. Special functions, namely Basic Displacement Functions (BDFs), are introduced and derived through power series solution of the static part of the governing differential equations for rotating tapered Timoshenko beams. It is shown that the shape functions could be derived in terms of BDFs through basic principles of structural mechanics. It is shown that the proposed shape functions have the advantage of including the effect of the rotational speed, hub radius, and varying cross-sectional dimensions. In order to verify the competency of the present element in the determination of natural frequencies, several numerical examples are carried out, and the results compared with those in the literature.