Research on the similarity of ship structure's shock response under underwater explosion based on scaling theory

The impact response of a ship's hull structure to an underwater explosion is a typical transient and strongly nonlinear process, characterized by bifurcations and abrupt changes in its dynamic response, leading to uncertainties in the system's dynamical behavior. Traditional prediction methods based on classical similarity theory struggle to provide accurate forecasts. To address the issue of similarity transformation in underwater explosion model tests, this paper introduces scaling theory on the basis of classical similarity theory. It explains the distortion phenomena observed in classical similarity theory and derives a similarity scaling transformation equation for model tests that satisfies scaling theory. The paper also delves into the scope of application of this scaling transformation equation. To describe the similarity ratio characteristics between models and prototypes, the paper introduces the renormalization group theory based on fractal and self-similarity principles, defining large, medium, and small scale ratios for model tests. Taking the frame and section structures of a certain ship as prototypes, a series of model tests are designed according to the large, medium, and small scale ratios established in this paper. Through same-scale and cross-scale model tests, the effectiveness and universality of the similarity scaling transformation equation for the impact response of a ship's hull structure to underwater explosions, based on scaling theory, are fully verified. The research results indicate that the large, medium, and small scale ratios defined based on the renormalization group theory can clearly specify the range of scale ratios in model test design. Compared to classical similarity theory, the similarity scaling transformation equation for the impact response of a ship's hull structure model test to underwater explosions, derived based on scaling theory, can be effectively applied to prototypes under both same-scale and cross-scale conditions, breaking through the limitations of parameter variation ranges in model tests.