Abstract: Simplified design method is studied based on the dynamical similarity theory due to the problem of vibration analysis experiments of thin-walled short cylindrical shell with annular labyrinth (TWSCSAL). The thin-walled short cylindrical shell with three annular labyrinths is a typical object. The mathematical model is set up by using Donnell type nonlinear strain-displacement relations, and the frequency equation of TWSCSAL is obtained. The dynamic similar law between model and prototype is solved with dimensional analysis method. The similar design method of incomplete geometric similar model is studied particularly, and the theoretical formula is obtained. In order to illustrate the similar design method, the three annular labyrinths thin-walled short cylindrical shell are simplified for T shapes. The similar methods such as one annular labyrinth simplified for T shapes, two annular labyrinths simplified for T shapes and three annular labyrinths simplified for T shapes are put forward respectively. The natural frequencies and mode shapes of model and prototype are compared by using the finite element method. And the correctness and effectiveness of the similarity design method is verified.

Key words: Dynamical similarity, Test model, Thin-walled short cylindrical shell with annular labyrinth, Vibration, laser welding, mechanical vibration, microhardness, microstructure