Data orbits similarity conversion law of scaled-down model tests of ship structures under strong impact loads

The model test under strong impact loads constitutes a transient, strongly nonlinear, and non-stationary physical process that exhibits extreme sensitivity to system parameters, boundary conditions, and initial conditions. A minor perturbation induces bifurcation and abrupt changes in system dynamics, resulting in output uncertainty for model tests and significant challenges in achieving similarity conversion between models and prototypes. In this paper, the second law of similarity is applied to construct data orbits of impact responses for characterizing kinematic system evolution, and a principle of topologically conjugate conversion for similar systems in phase space is proposed. Through phase space reconstruction methodology, the kinematic evolution patterns of acceleration responses in ship structures under strong impact loads are investigated, with mapping functions of acceleration response data orbits derived in phase space. A similarity equation for model-to-prototype conversion is established based on the topologically conjugate conversion principle. Theoretical analysis demonstrates the rationality of introducing prediction coefficients in distortion models, while fundamental conditions for achieving similarity conversion in nonlinear dynamical systems are formulated. Finally, the numerical results from the single-layer reinforced plate rack and cabin section show that the data orbits corresponding to the acceleration responses of the 1:2 scaled model and the prototype have the same symbol sequences in the phase space under satisfying the similarity conversion condition, which verifies the correctness of the similarity conversion of data orbits for the scaling model test of the ship structures under the strong impact loads.