Dimensionless number for dynamic response analysis of box-shaped structures under internal blast loading

•Obtained a dimensionless governing equation of fixed plates.•Proposed a dimensionless number Din for internal blast.•Applied Din to analyze fully confined explosion.•Empirical expression on deflection–thickness ratio and Din.

Based on the governing equations of a fully clamped plate, a new dimensionless number for the dynamic response of box-shaped structures subjected to internal blast loading was suggested in this paper. The dimensionless number considered the influence of blast load, the strength of material and the structural dimensions. The parameters in the proposed dimensionless number can be easily obtained in practice. The dimensionless number has clear physical meaning and leads to good correlation between the response of box-shaped structures and the blast energy. It was also found that the structural response is inversely proportional to the material strength and the volume of the structure. The dimensionless number was applied to analyze the experimental data of box-shaped structures under internal explosion. The validity and efficiency of the dimensionless number were discussed, and an empirical expression was obtained which can be applied to the prediction of dynamic response of similar box-shaped structure under different internal explosive loads.