Periodically Perturbed Linear Gyroscopic Systems*

ABSTRACT

This paper presents an analytical method to examine the dynamical behavior of periodically perturbed linear conservative gyroscopic systems. Explicit stability conditions for perturbations of small intensity are obtained using the method of averaging. The existence of combination resonance in addition to subharmonic parametric resonance is established. For large periodic excitation, a numerical method based on the Floquet theory is used to extend the stability boundaries. These results are applied to the problem of flow-induced vibration in a supported cylindrical pipe conveying fluid with pulsating velocity. The effects of the mean flow velocity, dissipative forces, boundary conditions, and virtual mass on the extent of the parametric instability regions are then discussed.