Short-Term Instability in Stochastic Aeroelasticity

Dynamic systems with lumped parameters are considered which interact with fluid flow with random temporal variations of speed. The variations may lead to “short-term” dynamic instability of a system — which is nominally stable in the classical sense — whereby occasional random excursions beyond neutral stability boundary result in rare short outbreaks in response. As long as it may be impractical to preclude completely such outbreaks for a designed system, subject to highly uncertain dynamic loads, the corresponding system’s response should be analyzed to evaluate its reliability. Linear models of the systems are studied to this end for the case of slow variations in the flow speed using parabolic approximation for the variations during the excursions together with Krylov-Bogoliubov (KB) averaging for the transient response. This results in a solution for probability density function (PDF) of the response in terms of PDF of the flow speed; the results may be of importance for predicting fatigue life. First-passage problem for the random response is also reduced to that for the flow speed. The analysis is used also to derive on-line identification procedure for the system from its observed intermittent response with set of rare outbreaks. Specific examples for analytical and numerical solutions for systems with random temporal variations of flow speed include: 1D and 2D galloping of elastically suspended rigid bodies in cross-flow; classical two-degrees-of-freedom flutter; bundles of heat exchanger tubes in cross-flow with potential for flutter-type instability.