Submerged circular cylindrical shell subjected to two consecutive shock waves: Resonance-like phenomena

A submerged evacuated circular cylindrical shell subjected to a sequence of two external shock waves generated at the same source is considered. A semi-analytical model combining the classical methods of mathematical physics with the finite-difference methodology is developed and employed to simulate the interaction. Both the hydrodynamic and structural aspects of the problem are considered, and it is demonstrated that varying the delay between the first and second wavefronts has a very significant effect on the stress–strain state of the structure. In particular, it is shown that for certain values of the delay, the constructive superposition of the elastic waves travelling around the shell results in a ‘resonance-like’ increase of the structural stress in certain regions. The respective stress can be so high that it sometimes exceeds the overall maximum stress observed in the same structure but subjected to a single-front shock wave with the same parameters, in some cases by as much as 50%. A detailed parametric analysis of the observed phenomenon is carried out, and an easy-to-use diagram summarizing the finding is proposed to aim the pre-design analysis of engineering structures.