Stochastic Stability of Linear Gyroscopic Systems: Application to Pipes Conveying Fluid

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 ε^1/3 when the damping and noise respectively are of O(ε) and O(⁠$ε$⁠). These results, pertaining to p^th moment stability and almost-sure stability of the trivial solution, are applied to study the stochastic stability of a pipe conveying pulsating fluid.