In order to accurately and effectively obtain the contact performance of the mating surface under the material surface topography characteristics, a numerical simulation method of rough surface based on the real topography characteristics and a multi-scale hierarchical algorithm of contact performance is studied in this paper. Firstly, the surface topography information of materials processed by different methods was obtained and characterized by a measuring equipment; Secondly, a non-Gaussian model considering kurtosis and skewness was established by Johnson transform based on Gaussian theory, and a rough surface digital simulation method based on real surface topography was formed; Thirdly, a multi-scale hierarchical algorithm is given to calculate the contact performance of different mating surfaces; Finally, taking the aeroengine rotor as the object, the non-Gaussian simulation method was used to simulate the mating surfaces with different topographies, and the multi-scale hierarchical algorithm was used to calculate the contact performance of different mating surfaces. Analysis results showed that the normal contact stiffness and elastic–plastic contact area between the mating surfaces of assembly 1 and assembly 2 are quite different, which further verifies the feasibility of the method. The contents of this paper allow to perform the fast and effective calculation of the mechanical properties of the mating surface, and provide a certain analysis basis for improving the surface microtopography characteristics of materials and the product performance.

The correlation of guided wave propagation characteristics with structural prestress is of paramount importance to the structural health monitoring of gas pipelines. A variable section structure and inhomogeneous prestress are common conditions in the pipeline. However, most of the existing guided wave finite element models focus on the structure size and stress distribution under two-dimensional conditions, and it is difficult to analyze the three-dimensional structure with non-uniform stress and variable cross section. In this paper, an acoustoelastic theory combined with a semi-analytical finite element based on the three-dimensional mapping method is proposed to investigate guided wave propagation. It provides a generalized tool to study guided waves in waveguides with a variable cross section under inhomogeneous prestress. Then it is applied to two cases, a hollow cylinder with a variable cross section subjected to axial force and radial force, to demonstrate the capability of the method. Dispersive solutions are obtained in terms of the three-dimensional dispersion surface and the change in phase velocity in a variable cross section. The results show that there is a propagation mode, which is insensitive to the change in the section but sensitive to the change in prestress. The effectiveness of the proposed method is verified by comparing with the experimental results. This study provides a good application prospect for the structural design and performance analysis of variable cross section waveguides.