Vibration Analysis of Gyroscopic Systems

Mechanical structures which can vibrate about a state of mean rotation or translation may constitute gyroscopic dynamic systems that are related by the mathematical similarity of their governing equations of motion. Considering as examples a rotating circular ring and an axially travelling string, the analogy of those systems is demonstrated. The linear vibrations obtained by superposing small perturbations on the stationary solution are analyzed. Assuming time-varying speeds, the effect of non-constant stress resultants on the dynamic stability of gyroscopic systems is investigated and the results are compared to those found in literature where the stress resultants of axially moving continua are commonly taken as constant. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)