In-plane vibration of a rigid body attached to a flexible rotating beam

Abstract

The dynamics of rotating systems are conventionally analyzed using models that assume the axis of rotation to be stationary. However, in instances such as helicopters and gas turbines with contra-rotating rotors such models which neglect the complexity arising from the coupling between the stator and the rotor due to their comparable masses can lead to inaccurate predictions. This paper examines the coupled stator-rotor dynamics of a model comprising a rigid (but non-stationary) body which is excited with a flexible rotating beam. Equations of motion governing the model's dynamics are developed and are found to have time-periodic boundary conditions. For the axisymmetric case the system loses its time dependence; the natural frequencies and the mode shapes vary with rotation speed. Specific modes soften within certain speed regimes, while other modes stiffen. Instabilities such as divergence and flutter are observed, and the effects of parameters on the critical speeds are investigated. The non-axisymmetric case is parametrically excited at twice the rotation speed. Floquet theory is employed to develop stability charts; regimes of instability exhibit a definitive structure comprising simple and combination parametric resonances. Temporal responses are modulated, and they exhibit characteristic side-banded frequency spectra.