Hydrofoil vibration induced by a random flow: a stochastic perturbation approach

The problem of an elastic lifting hydrofoil in a randomly perturbed flow is considered. It appears that in these conditions the phenomenon of hydroelastic-induced vibrations is controlled by a stochastic differential operator. By using the theory of stochastic perturbation, a technique of solution for this class of problems is proposed, leading to an effective numerical solution. The fundamentals of the method are given and it is applied to the general problem of hydroelastic vibrations. A numerical application to the case of an elastic control surface for a prototype-high- speed marine vehicle is presented. Comparisons between the results obtained by the Stochastic Perturbation Method (SPM) and those provided by standard Monte Carlo simulations (MCS) show the accuracy of the proposed method and a useful saving in computational time. A method is given for comparing the computational time required by the two methods, for a given statistical accuracy.