Free vibration of a rotating tapered Rayleigh beam: A dynamic stiffness method of solution

The dynamic stiffness method for free vibration analysis of a rotating tapered Rayleigh beam is developed to investigate its free vibration characteristics. The type of taper considered covers a majority of practical cross-sections. The effects of centrifugal stiffening, an outboard force, an arbitrary hub radius and importantly, the rotatory inertia (Rayleigh beam) are included in the analysis. Natural frequencies and mode shapes of some examples are illustrated by using the developed dynamic stiffness matrix and applying the Wittrick–Williams algorithm. The theory is validated by using comparative results in the literature. The effects of slenderness ratio, rotational speed and taper ratio on results are discussed. This is followed by some concluding remarks.