Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered beams; a mechanical solution

This paper deals with enhancing the existing Finite Element formulations through employing basic principles of structural mechanics accompanied with mathematical techniques. Introducing the concept of Basic Displacement Functions (BDFs), the free vibration analysis of rotating tapered beams is studied from a mechanical point of view. It is shown that exact shape functions could be derived in terms of BDFs. The new shape functions turn out to be dependent on the rotational speed, circular frequency, the position of element along the beam and variation of cross-sectional dimensions along the element. Dynamic BDFs are obtained by applying Adomian Modified Decomposition Method (AMDM) to the governing differential equation of motion. Carrying out numerical examples, the competency of the method is verified.