Torsional Vibration of Shafts with Varying Diameters.

The article is devoted to the study of the torsional vibrations of a shaft of varying cross section. The variation of the radius of the cross section is linear with respect to the abscissa. The study of real modes of vibration lead to the integration of differential equation with non-constant coefficients, without a second member. In the case of the variation previously defined, the differential equation lead to a Bessel equation of the order of 3/2. The equation of real pulsations is then determined from the general equation by the introduction of limiting conditions.