Basic displacement functions for centrifugally stiffened tapered beams

Introducing the concept of basic displacement functions (BDFs), free vibration analysis of rotating tapered beams is studied from a mechanical point of view. Holding pure structural/mechanical interpretations, BDFs are obtained by solving the governing static differential equation of flapwise motion of rotating Euler–Bernoulli beams and imposing appropriate boundary conditions. Following the principles of structural mechanics, it is shown that exact shape functions and consequently structural matrices could be derived in terms of BDFs. The new shape functions capture the effects of variation of both cross‐sectional area and moment of inertia along the element and the stiffening effect of centrifugal force. The method is employed to determine the natural frequencies of tapered rotating beams with different variations of cross‐sectional dimensions and the results are in good agreement with those in the literature. Finally, the effects of rotational speed and taper ratio on the natural frequencies are investigated.