Towards an analytical formulation for fluid structure tank vibration analysis: Modal equivalency using granular materials

•Liquid Hydrogen (LH2) used in cryogenic engines is too dangerous and expensive to be performed in vibratory tests.•We suggest the idea that pre-stressed grain systems maybe a surrogate materials to overcome the aforementioned issue.•Mathematical formulations of the new methodology are introduced. This paper focuses on a new methodology for substitution of Liquid Hydrogen (LH2) contained in cryogenic tank in vibration analysis by using surrogate granular materials. Our analysis is limited to a 3D tank that is supposed to be fully filled with granular grains and tries to establish a modal equivalence between (tank fully filled with LH2) and (tank fully filled with granular grains) systems. For this, we determine required pre-stresses based on a homogenization technique from properties of grains. After reviewing some important mathematical formulations of vibration and homogenization model, an example of modal equivalence between these two systems is presented. Analytical results are also compared with numerical simulations in order to prove the suitability of the new method.