Defect localization in waveguide assemblies with curved joints via wave finite elements and time of flight analysis

A numerical approach is proposed to localize defects in elastic waveguides connected by curved elastic joints. 2D assemblies involving straight waveguides with a curved joint and a defect are specifically dealt with, where the joint is placed between the measurement point (output signals) and the defect. Such an analysis requires assessing wave conversion phenomena and times of flight for wave packets when they are transmitted through the joint and reflected by the defect. In this paper, the wave finite element (WFE) method is used to help understand these phenomena. An original strategy is proposed where the times of flight, for transmitted or reflected wave packets, are defined from the frequency derivatives of the arguments of the scattering matrices of the joint and the defect. The procedure to localize a defect follows from comparing the theoretical expressions of the times of flight with those recorded at the measurement point. Also, the proposed approach enables the identification of the types of waves which are truly transmitted through the joint and reflected by the defect. Numerical experiments are carried out which highlight the relevance, in terms of accuracy and robustness, of the proposed approach.