Feedback Stabilization of Distributed Parameter Gyroscopic Systems

2009 ◽  
pp. 85-97 ◽  
Author(s):  
Paweł Skruch
Keyword(s):  
Feedback Stabilization ◽  
Distributed Parameter ◽  
Gyroscopic Systems

Transient Vibration of Gyroscopic Systems With Unsteady Superposed Motion

1995 ◽  
Author(s):  
J. A. Wickert
Keyword(s):  
Equations Of Motion ◽  
Mathematical Structure ◽  
Time Dependent ◽  
Distributed Parameter ◽  
Rotating Shaft ◽  
Transient Vibration ◽  
Modal Amplitude ◽  
Technical Interest ◽  
Gyroscopic Systems ◽  
Two Degree Of Freedom

Abstract The equations of motion for a gyroscopic system with unsteady superposed motion are derived for the prototypical 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 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.

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