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Dynamic stability of linear conservative gyroscopic systems under stochastic parametric excitations of small intensity is examined. Conditions for mean square stability of dynamic response are obtained. Results are shown to depend only on those values of the excitation spectral density near twice the natural frequencies and the combination frequencies of the system. These results are applied to the problem of flow induced vibration in a supported pipe conveying fluid with pulsating velocity. The effects of mean flow velocity and virtual mass on the extent of parametric instability regions are then discussed.

Turbulence in wind velocity is shown to change the stability condition for the motion of suspension bridges. When the turbulence is convected at a high velocity, the time variation of the random excitation field becomes fast as viewed by the nonmoving structure. In this case the structural response can be approximated by components of a Markov vector process. Modeling the structure as a linear system and considering only the dominant torsional mode, the stability boundaries for the first and the second stochastic moments are obtained in terms of the mean wind velocity and the spectral level of the turbulence component.

The dynamic stability of nongyroscopic, elastic structures under parametric random loading of small intensity is investigated. Conditions for stability in the second norm of the dynamic response are obtained and shown to depend only on those values of the excitation spectral density near twice the natural frequencies and the combination frequencies of the structure. As an application, the flexural-torsional stability of a simply supported thin elastic beam subjected to stochastically fluctuating end couples is studied.

In this paper bifurcation behavior of parametrically perturbed nonlinear gyroscopic systems is considered. Parametric excitations are assumed to be periodic and the method of averaging is used to examine bifurcation behavior. Explicit results for bifurcating paths in the presence of both subharmonic and combination resonance are obtained for certain classes of systems that commonly occur in practical situations. As an application, the stability of a light rotating shaft that carries a heavy rotor is discussed.

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.