Rigid-flexible-cavity coupling trajectory and uncertainty trajectory analysis of supercavitating projectiles

Structures of supercavitating projectiles operating at high underwater velocity are subjected to large deformations generated by high forces acting on the projectile. Moreover, it is widely that probabilistic and non-probabilistic uncertain information are coexisting. Therefore, flexible and uncertainty trajectory analysis of supercavitating projectiles are required. Formulae of flexible body motion and rigid-flexible coupling dynamic differential equations are introduced first. Then rigid-flexible coupling equations are decoupled. Flexible deformations are solved by modal superposition method; detailed rigid trajectory equations in vertical plane, supercavity equation and force formulae are presented, and calculation flowchart of rigid-flexible-cavity coupling trajectory is given. Third, by chaos method, the uncertainty rigid-flexible-cavity coupling trajectory simulation of supercavitating projectiles with uncertain launch parameters is performed, and parameters are described by random variables and non-probabilistic interval variables. Finally, The correctness of rigid-flexible-cavity coupling trajectory algorithm is validated by the experimental data provided by relevant literatures. To investigate the effect of flexible deformation of projectile on coupling trajectory, the variation of the resultant coupling trajectory was investigated by varying two important flexibility parameters - slenderness ratio and Young's modulus. The results of rigid-flexible-cavity coupling trajectory are compared with that of rigid-cavity trajectory through an engineering example. Trajectory curves sets and distribution of impact points are presented through uncertainty rigid-flexible-cavity coupling trajectory simulation.