TRANSIENT VIBRATION OF GYROSCOPIC SYSTEMS WITH UNSTEADY SUPERPOSED MOTION

✍ Scribed by J.A. Wickert

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 263 KB
• Volume: 195
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0462

✦ Synopsis

The equation of motion for a gyroscopic system with unsteady superposed motion is derived for the prototypcial problem in which motion of an oscillating particle is measured relative to a non-inertial frame. The resulting coefficient matrices are time-dependent, and skew-symmetric acceleration terms are present both as Coriolis acceleration and as a component of net stiffness. Such mathematical structure is also demonstrated in the context of other unsteady gyroscopic systems, including flexible media that translate with time-dependent speed. Following the asymptotic approach of Krylov, Bogoliubov and Mitropolsky, a perturbation method is developed for the case in which the superposed motion varies slowly when viewed on the time scale of the system's natural periods of oscillation. First-order approximations for the modal amplitude and phase are obtained in closed form. The method is illustrated through two examples of technical interest: a two-degree-of-freedom model of a rotating shaft, and a distributed parameter model of a moving tape or web.