The invention provides a cross-scale optimal scale ratio
selection method for a transient strong nonlinear
scale model test, and belongs to the field of
engineering structures. The problem of large similarity conversion error caused by theoretical inapplicability of the existing method is solved. The method comprises the following steps: based on a model component test of a classical
similarity theory, introducing a first-order derivative relationship that a variable pi item changes along with a scale ratio, establishing a micro-grouping
similarity model and carrying out Taylor expansion to obtain an iterative relationship that the variable pi item changes along with the scale ratio; setting a scale
ratio sequence, and converting the iterative relationship into a parabola mapping model representing the dynamic behavior of the
system; the method comprises the steps of determining a pervasive constant and a scale-
free interval corresponding to the pervasive constant on the basis of a reformation group theory, selecting a cross-scale optimal scale ratio according to the number of iterations, carrying out a
model test, obtaining a model change pi
time sequence, and carrying out similarity conversion on a
model test result to a prototype on the basis of a parabola mapping model and the reformation group theory. The method is used in the field of transient strong
nonlinear system dynamic
response analysis.