A semi-analytical model of guided wave with variable section under inhomogeneous prestress

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.