Free vibration analysis of a rotating double-tapered beam using the transfer matrix method

In this study, a transfer matrix method is developed to analyze the effect of the centrifugal force on the natural frequencies of a rotating double-tapered beam, whose cross-sections have linearly reduced height and width. The root of the differential equation is determined based on the Bernoulli-Euler theory and the effects of the hub radius, taper ratio, and rotation speed, by applying the Frobenius method. In particular, the effect of the centrifugal forces is analyzed based on the relationship between the bending and additional strain energies generated by centrifugal stiffening. The shape function of the displacements depends on the variations in the taper ratio and rotation speed. In addition, the strain energies are varied. Various examples are presented to demonstrate the influences of the strain energies. Furthermore, the effects of the centrifugal force on the natural frequencies of the rotating double-tapered beam are investigated by analyzing the variation in the predicted strain energy.