In this paper we obtain asymptotic approximations for the moment Lyapunov exponent, g(p), and the Lyapunov exponent,λ, for a two-degree-of-freedom gyroscopic system close to a double zero resonance and subjected to small damping and noisy disturbances. Using a perturbation approach, we show analytically that the moment and the top Lyapunov exponent grow in proportion to ε1/3 when the damping and noise respectively are of O(ε) and O(). These results, pertaining to pth moment stability and almost-sure stability of the trivial solution, are applied to study the stochastic stability of a pipe conveying pulsating fluid.
- Applied Mechanics Division
Stochastic Stability of Linear Gyroscopic Systems: Application to Pipes Conveying Fluid
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Vedula, L, & Sri Namachchivaya, N. "Stochastic Stability of Linear Gyroscopic Systems: Application to Pipes Conveying Fluid." Proceedings of the ASME 2002 International Mechanical Engineering Congress and Exposition. 5th International Symposium on Fluid Structure Interaction, Aeroelasticity, and Flow Induced Vibration and Noise. New Orleans, Louisiana, USA. November 17–22, 2002. pp. 1233-1241. ASME. https://doi.org/10.1115/IMECE2002-39024
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