A New Procedure for Exploring the Dispersion Characteristics of Longitudinal Guided Waves in a Multi-layered Tube with a Weak Interface

Dispersion characteristic of longitudinal guided wave plays an important role in detecting defect of multi-layered tube. Here, a new procedure is proposed to explore such dispersion characteristic in a kind of multi-layered tube with weak interface. The mathematical equations are firstly established, from which the spectral method is applied to get an approximate solution in the whole axial wave number range, and the customary root-finding approach is then developed to improve the solution’s accuracy in some local axial wave number regions. Based on the above procedure, an algorithm is designed and applied to several numerical examples for a two-layered tube with the intact and weak interfaces. The results show that the present procedure preserves both the efficiency of the spectral method and the accuracy of the root-finding approach, and can be employed in defect detection by longitudinal guided wave on the multi-layered tube with weak interface effectively.