Research Of Stochastic Stability And Reliability On The Casing Pipe Of Flying Boom

Aerial refueling by flying boom is one of the most efficient ways to transport fuel.It has the advantage of fast refueling and low docking difficulty. The key structural ofrefueling is the casing pipe. The stability of the pipe has a great influence on oildelivery. Scholars all around the world have done a lot of research on the dynamics ofthe casing pipe, but the study is focus on the casing pipe subjected to deterministicexcitation. Actually, there are a lot of random factors when the casing pipe istransporting oil. It is likely to be the main reason of the destruction. Therefore, it isnecessary to study the dynamics and control strategy of the refueling boom affectedby random factors. In this paper, we have finished the following works applyingStochastic Nonlinear Dynamics Theory.1. Considering the impact of the axial random excitation to the air refuelingcasing boom, simplifying the excitation as stationary random process (gauss whitenoise). Build casing structural vibration model according to the theory of elasticityand Galerkin method. The max Lyapunov exponent is obtained by quasinon-integrable Hamiltonian theory. The local stability has been analyzed by usingOseledec multiplicative ergodic theory, while the global stability has been analyzedby judging the modality of the singular boundary. The stationary probability densityfunction and the joint probability density function are obtained by solving the FPK(Fokker-Planck-Kolmogorov) equation. Meanwhile, we studied when the stochasticHopf bifurcation would turn out and how structural parameters affected the behaviorof stochastic Hopf bifurcation.2. The movement of the casing pipe structural can be described by a group ofHamilton regularization equations, and can be expressed as a one-dimensionaldiffusion process. Then, the BK (Backward Kolmogorov) equation for reliability andthe first-passage time was established. What’s more, the numerical results wereobtained under specific initial and boundary conditions. Finally, we studied the pipe’sfirst-passage, as well as the impact of structural parameters on the behavior of thefirst-passage.3. The optimal control strategy aimed to get maximum reliability was accessed bydynamic programming principle. If the control force is a bounded function, the optimal control laws are "bang-bang" controls. The controlled Hamilton system canbe showed by a one-dimensional diffusion process. The reliability function and thefirst-passage time probability density function were calculated in numerical method.The results show that the pipe’s reliability will be higher and the damage time will belonger as the control force increasing.