On the vibrational dynamics of rotating thin-walled cylinders: A theoretical and experimental study utilizing active magnetic bearings

This paper describes a theoretical and experimental study to establish the vibrational dynamics of a rotating thin-walled cylinder with radial bearing supports. The main focus is on the prediction of forced response, and the variation in response behaviour with rotational speed. A shell theory analysis is shown to provide a very complete description of rotordynamic behaviour that predicts various types of natural mode for free vibration. These include in-surface torsional and extensional modes, out-of-surface wall bending modes, as well as the classical beam bending modes exhibited by long flexible rotors. For exact solution of the free vibration problem, the coupled eigenproblems derived from the continuum equations and boundary constraints can be solved numerically. This approach can be applied for any given rotational speed. To avoid having to solve the equations repeatedly, an alternative model is formulated based on the zero-speed mode-shapes which has a simple parametric dependency on rotational speed. The method is applied to the dynamic modelling of an experimental system comprising a 0.8 m long steel rotor with outer diameter of 0.166 m and wall-thickness of 3.1 mm supported by two radial active magnetic bearings. The dynamic behaviour of the system is identified by frequency response testing at different rotational speeds, where excitation forces are applied through the bearings. The results confirm the accuracy and applicability of the developed shell theory model for practical use in rotordynamic prediction and analysis.