Dynamic instability of an eccentrically rotating ring-shaped structure

Abstract

Ring-shaped structures are widely used in engineering. However, their rotation axes are typically not coincident with the geometric axes, thus resulting in a rotational centrifugal force and significant vibration. This study focuses on the dynamic instability caused by constant and time-varying eccentricities. An analytical model is established using Hamilton’s principle and the Galerkin method, in which the rotational centrifugal forces resulting from constant and time-varying eccentricities are incorporated. Based on this model, the effects of rotation, revolution, eccentricity ratio, and damping on instability behaviors are examined. The instabilities caused by constant eccentricity are predicted using eigensolutions, whereas those caused by time-varying eccentricity with single- and multifrequency components are estimated by applying the Floquét theory. The results show that the instability domains from the multifrequency eccentricity are not a simple superposition of those from the single-frequency eccentricity but contain more instability domains originating from their combinations. The instability suppressions imposed by damping and gyroscopic effects are compared. Finally, the instability domains from constant and time-varying eccentricities are verified via numerical calculations.