Study on nonlinear vibration of simplified solid rocket motor model

The unstable combustion of the large aspect-ration solid rocket in the end phase flight is of great interest and importance to the solid rocket design. The large aspect-ratio solid rocket motor (SRM) tends to produce unstable combustion in flight. As shown in published literatures, it is believed that the main reason for this phenomenon is the internal flow field. However, in terms of the intense pressure oscillation, the contribution of the motor casing should not be ignored. In this paper, the nonlinear natural frequencies of different motor shells in flight are mainly concerned. The SRM model in the working state is simplified to a double-layer time-varying axially moving free-free beam. The governing equation of nonlinear lateral vibration is derived according to the Hamilton principle. The Galerkin method and multi-scale method are adopted to solve the governing equations. Firstly, to verify the accuracy of the presented method, the validating experiments base on the finite difference method are carried out. According to the comparison, the results obtained through the Galerkin method coupled with multi-scale method coincides well with the results obtained by the finite difference method as well as the results in the public literatures. The influence of structural change and axial velocity on the nonlinear coefficients and natural frequencies of the SRM shell is investigated by numerical experiments. The results show that the natural frequency of the SRM shell change during the whole flight and the increase of aspect ratio has a significant influence on the natural frequency. Under the initial excitation, the nonlinear natural frequency will change abruptly. Under some particular excitations, it is possible that the resonance coupling between the shell vibration and internal flow field occurs and it contributes to the amplification of the unstable combustion further. (C) 2019 Elsevier Masson SAS. All rights reserved.