Abstract: The distortion similarity relation of thin-walled conical shells was established by using the natural frequency of transition model based on least square method， aiming at the limitation of traditional similarity model design method， dimension analysis method and equation analysis method in some cases， a method for determining the applicable interval of distortion model was also proposed. The boundary equation of the applicable interval of geometric structure of a single material thin-walled conical shell with similar distortion model of different orders was obtained by polynomial fitting method， based on the method for determining the applicable interval of distortion model size when the model and prototype are similar in natural characteristics (natural frequencies are proportional mapping relationship， and mode shapes are consistent). The accuracy of derivation of distortion similarity relation is proved by experiment verification， which provides theoretical basis for dynamic similarity of thin-walled conical shell structure test model.

Key words: conical shell, distortion model, dynamic similitude, applicable interval, natural frequercy