Research on similarity law of nonlinear shock response of ship plate frame structure under underwater explosion

                                
==Abstract==

The anti-explosion ability of ship grillage structure is an important index to evaluate the vitality of ships. Its model test is a low-cost and effective method to evaluate the vitality of ships and guide the design of ship anti impact structures. In view of the nonlinear and nonstationary process of underwater explosion damage to ship grillage, this paper breaks through the nonlinear effect of transient explosion impact that is not considered in the traditional scale model design, focuses on the one-dimensional nonlinear impact response of ship grillage structure, and carries out the characterization study of the similarity between model experiments and real ships. Considering that the vertical motion of the prototype and the model grillage structure in the model test obey the random walking model, the vertical impact response of the deck grillage is characterized as one-dimensional nonlinear non-stationary Brownian motion, which is described by Hurst index. Based on the classical similarity law, the similarity transformation relationship between the range R and the mean square deviation S is derived, and the Hurst index of the model and the prototype meets the equal relationship; Take a section of grillage structure on a real ship and conduct prototype, 1/2, 1/3, 1/4 and 1/5 one-dimensional nonlinear explosion impact scale simulation tests respectively. The numerical response results show obvious nonlinear characteristics, and the Hurst index of displacement, velocity and acceleration response of the model within the pulse width range is less than 5% compared with the prototype. According to the scale invariance of fractional Brownian motion, the similarity conversion relationship of multiple parameters (displacement, velocity, acceleration and mean square response) is obtained. With the mean square response as the characteristic parameter, the response value of the prototype is converted through this relationship, and compared with the model simulation results, the multi parameter response error under each scale ratio is less than 20%. It provides theoretical and technical support for conducting similar experiments on nonlinear response of underwater explosion shock of ships