Dynamic response of a clamped/free hollow circular cylinder under travelling torsional impact loads

Impact-induced vibrations in the casing of a gas centrifuge due to a sudden failure of the spinning rotor (crash) can cause structural disintegrity of the casing. In order to study the influence of the rotor failure behaviour and the impact load histories on the dynamic response of the casing, a simple crash model is proposed in this paper to analyse the transient torsional response due to tangential components of the impact loads. The casing is modeled as a linear-elastic hollow circular cylinder, clamped at the lower end and free at the upper end. The rotor is thought to break up in identical sections in a sequence determined by its fracture behaviour. Each section is assumed to cause an axi-symmetric load distribution at the inner surface of the casing. Therefore the problem is essentially reduced to the analysis of a clamped/free cylinder under travelling torsional impact loads. The problem is solved by representing the impact loads as local pulses acting over the length of the sections. A perturbation method is used to show that the general two-dimensional theory of axi-symmetric torsional wave propagation in circular cylinders, for the problem under consideration, may be approximated by the elementary one-dimensional theory. Solutions are obtained according to the usual modal expansion approach. Measurements of transient torsional responses are shown to be in good agreement with the calculated responses by choosing a suitable shape of the pulses. The effects of travelling velocity and pulse shape are investigated. Finally the transfer of kinetic energy in the rotor to vibrational energy of torsion in the casing is studied.