Sensitivity and Uncertainty Analysis of the Nonlinear Flight Dynamics System of the Flexible Body

Free flight of a flexible body, such as large slenderness missiles, is a complex process involving rigid-flexible coupling dynamics. The strong flexible effect and the sensitive rotational characteristics caused by large slenderness ratio provide an extreme environment for the rigid-flexible coupled system. To study the performance of nonlinear flight dynamics system of the flexible body under extreme conditions, the trajectory of javelin model with a slenderness ratio of 98.15 flying in vacuum condition is calculated, and the uncertainty and the sensitivity of the coupled system are analyzed for the first time. The Monte Carlo (MC) method and the non-intrusive polynomial chaos (NIPC) method are compared by quantifying the uncertainty in the coupled system with the random moment of inertia of principal axis (Ixx). The uncertainty in the coupled system is quantified using the second-order NIPC method. It is found that the decoupled method is sensitive to the time step due to the unsynchronization of status variables between the rotational equation and structural equation. In contrast, the coupled method is insensitive to the time step. Ixx, stiffness according to the primary modes, and the initial deformation have the largest influence on the uncertainty of the coupled system. The rotational velocity in x direction (ωx) is significantly sensitive to the random inputs. The total uncertainty region of the ωx gradually expands over time.