Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method

This paper studies the vibration characteristics of a rotating tapered cantilever Bernoulli-Euler beam with linearly varying rectangular cross-section of area proportional to xⁿ, where n equals to 1 or 2 covers the most practical cases. In this work, the differential transform method (DTM) is used to find the nondimensional natural frequencies of the tapered beam. Numerical results are tabulated for different taper ratios, nondimensional angular velocities and nondimensional hub radius. The effects of the taper ratio, nondimensional angular velocity and nondimensional hub radius are discussed. The accuracy is assured from the convergence of the natural frequencies and from the comparisons made with the studies in the open literature. It is shown that the natural frequencies of a rotating tapered cantilever Bernoulli-Euler beam can be obtained with high accuracy by using DTM.