二元机翼模型在随机参数激励下的首次穿越问题

为研究机翼在随机参数激励下的稳定性和可靠性，建立了在一个随机气流速度影响下的二元机翼随机动力学模型．首先，利用拟不可积Hamilton系统的随机平均法，将系统的广义能量表示为一维Ito扩散过程；其次，利用奇异性边界理论讨论了系统的全局随机稳定性；最后，为研究机翼振动能量和噪声强度对机翼工作安全性能的影响，求得了系统可靠性函数和首次穿越（系统损坏）时间概率密度函数．结果表明：系统可靠性函数在接近安全工作域边界时降低得很快，能量初值远离安全域边界可降低损坏概率密度峰值并将对应的时刻推后；噪声强度的增大也会引起系统可靠性下降加快和首次穿越概率密度函数峰值上升．

First Passage of a Two-Dimensional Airfoil Model Subject to Stochastic Parametric Excitation

In order to study the stability and reliability of an airfoil subject to stochastic parametric excitation,a two- dimensional airfoil stochastic dynamical model in incompressible flow was derived. At first,the model was reduced to a one- dimensional Ito diffusion process by using stochastic average method of quasi non-integrable Hamittonian system. Secondly, the global stochastic stability of the system was studied by applying the boundary classification associated with diffusion process. Finally,the Backward Kolmogorov equation and the General Pontryagin equation were established to research the influence of the system＇s energy and noise intensity on the airfoil＇s safety. The results illustrate that system reliability decreased rapidly near the edge of the safe operation area,and when the initial value of energy was far away from the edge, the peak time of first damage probability densities was postponed and the peak value reduced. Further more ,the increasing noise intensity can cause a fast decrease of the system＇s reliability and a raise in the peak value of the first passage probability densities.