Modified analytical model for water entry of two-dimensional elastic cylinders based on continuum theory

This paper is devoted to the modification of analytical model for the water entry of two-dimensional cylinders. Compared with the conventional analytical model, the modified analytical model includes the effect of specific acoustic impedance. Firstly, based on the continuum theory, the mathematical relationship between the water impact on an elastic cylinder and that on a rigid cylinder is deduced, and the influence of specific acoustic impedance on water entry is introduced. Then, the steel cylinder, aluminum alloy cylinder, magnesium alloy cylinder and polyamide cylinder are taken as examples to compare the modified analytical results, conventional analytical results and SPH-FEM results. Among these four materials, the specific acoustic impedance of steel is large, while those of aluminum alloy, magnesium alloy and polyamide are small. The results show that only the conventional analytical results of the steel cylinder are in good agreement with the SPH-FEM results; in contrast, the modified analytical results of all the cylinders are in good agreement with their SPH-FEM results. Finally, the effect of specific acoustic impedance on water entry is validated by existing experimental data. It indicates that the modified analytical model can be used to solve the water entry problems of elastic cylinders of different materials.