Flow-induced instability under bounded noise excitation in cross-flow

Flow-induced vibration of a single cylinder in a cross-flow is mainly due to vortex shedding, which is usually considered as a forced vibration problem. It is shown that flow-induced vibration of a cylinder in the lock-in region is a combination of forced resonant vibration and fluid-damping-induced instability, which leads to time-dependent-fluid-damping-induced parametric resonance and constant-negative-damping-induced instability. The time-dependent fluid damping can be modeled as a bounded noise. The dynamic stability of a two-dimensional system under bounded noise excitation with a narrow-band characteristic is studied through the determination of the moment Lyapunov exponent and the Lyapunov exponent. The case when the system is in primary parametric resonance in the absence of noise is considered and the effect of noise on the parametric resonance is investigated. For small amplitudes of the bounded noise, analytical expansions of the moment Lyapunov exponents and Lyapunov exponents are obtained, which are shown to be in excellent agreement with those obtained using Monte Carlo simulation. The theory of stochastic stability is applied to explore the stability of a cylinder in a cross-flow. The analytical and numerical results show that the time-dependent-fluid-damping-induced parametric resonance could occur, which suggests that parametric resonance also contributes to the vibration of the cylinder in the lock-in range.