An exact transfer matrix expression for bending vibration analysis of a rotating tapered beam

This paper presents a transfer matrix expression that can be used to determine the eigenpairs of a rotating beam with a cross section height that linearly decreases along the length of the beam element. The proposed method considers the effect of centrifugal force, including the effects of the axial force, hub radius, and taper ratio. Differential equations are solved for the in-plane bending vibration using the Frobenius method for a power series. The effect of the rotational speed on the eigenpairs of a rotating tapered beam is first investigated, followed by an examination of the contribution rates of the bending strain and additional strain energies generated by centrifugal forces for each mode by analyzing the variation of the energies computed from the strain and kinetic energies. To compute these contribution rates, we used a shape function that was defined by the displacement at both ends of the beam elements. The effect of tapering on the eigenfrequencies of the transverse vibration of rotating beams is analyzed by using various examples, and the contribution rates are examined by using taper ratios of 0 and 0.5.