Abstract
The similarity test of ship stiffened plate structures under underwater explosions is a cost-effective and efficient method to evaluate the vitality of ships and guide the design of their shock resistance. This study focuses on the nonlinear impact response model tests of ship stiffened plate structures and their similarity laws with actual ships. The vertical motion of the ship stiffened plate structure is characterized by the Hurst index, and an equivalent relationship between the Hurst index of the model and the prototype is derived from classical similarity law. Based on the Hurst index, a similarity transformation relationship between the strain signals of the model and prototype is established. To verify the conclusions, similarity experiments of underwater explosions were conducted on both the model and the prototype. The original signals were grouped by the natural vibration period to determine the variation of the Hurst index over time. The model experiment strain signals for each natural vibration period were converted and compared with the prototype experiment results to verify the method's effectiveness. Simultaneously, the Hurst index of the stiffened plate structure under explosive shock load and its similarity transformation relationship with the prototype were simulated and analyzed. This provides theoretical and technical support for conducting analogous nonlinear response experiments for ship underwater explosions.