Analytical Estimates of the Motion and Elastic Vibrations of the Structures of Separated Fairing Flaps of Rocket-Space Systems

Equations are obtained, and a model is constructed for studying the dynamics of separation of fairing flaps of rocket and space systems. Based on the assumption that the angular velocity of rotation of fairing flaps during separation is small compared to the lower frequencies of their natural vibrations, two independent groups of analytical relations are obtained, one of which describes the spatial motion of the fairing flaps as a whole relative to the launch vehicle, and the second one describes elastic vibrations in the turn section relative to the axes fixed on the carrier. Based on the ratios of the first group, the trajectories of the motion of the fairing flaps in the process of separation are constructed. In the second group of equations, the dependences of the level of excitation of the flap vibrations on the different times of switching on the separation engines and/or the spread of the characteristics of pushers are studied. The mathematical model considered expands significantly the range of problems to be solved and allows for the first time to analyze the simultaneous influence of both types of motion, the spatial motion of the fairing flaps as a whole and the elastic relative vibrations, on the safety of the separation process, which means the guaranteed exclusion of their collisions with both the launch vehicle and the payload. A number of relevant analytical estimates are obtained for calculating the relative motion and the level of vibrations of the flaps during their separation.