Study on dynamic response of multi-degree-of-freedom explosion vessel system under impact load

In order to study the dynamic response and calculate the axial dynamic coefficient of the monolayer cylindrical explosion vessel, the wall of vessel is simplified as a multi-degree-of-freedom (MDoF) undamped elastic foundation beam. Decoupling the coupled motion equation and using Duhamel's integrals, the solutions in generalized coordinates of the equations under exponentially decaying loads, square wave loads and triangular wave loads are calculated. These solutions are consistent in form with the solutions of single-degree-of-freedom (SDoF) undamped forced vibration simplified model. Based on the model, equivalent MDoF design method (also called MDoF dynamic coefficient method) of cylindrical explosion vessel is proposed. The traditional method can only predict the dynamic coefficient of torus portion around the explosion center, but this method can predict that of the vessel wall at any axial n dividing point position. It is verified that the prediction accuracy of this model is greatly improved compared with the SDoF model by comparing the results of this model with SDoF model and numerical simulation in different working conditions. However, the prediction accuracy decreases as the scaled distance decreases and approaches the end of the vessel, which is related to the accuracy of the empirical formula of the implosion load, the simplification of the explosion load direction, the boundary conditions, and the loading time difference.