Stability domains of wind-excited random nonlinear systems through Lyapunov function

The movement of a system modelled by one degree of freedom, vibrating perpendicularly to an air flow, may proceed on various levels of stochastic stability. The paper investigates the stochastic stability of the movement influenced by parametric noises generated by the interaction of a moving bluff body and an air flow. Conditions of the loss or resumption of movement stability by means of the stochastic version of Lyapunov function are derived. Sub-critical and various types of the super-critical modes of system response combining the deterministic and the stochastic response components are investigated. These effects are verified by several mathematical models of nonlinear damping. The author shows a different response sensitivity to the mathematical model in the individual domains of stochastic instability which makes it possible to explain some paradoxes known from wind tunnel tests.