Guided Waves in Pipes Versus Lamb Waves in Plates - A Convergence Analysis

This work is concerned the with analysis of the convergence of guided waves in pipes to Lamb waves in plates for isotropic materials. The main goal is to be able to define a threshold frequency above which it is reasonable to approximate waves propagating in a pipe with a certain wall thickness to radius ratio as Lamb waves. The study involves a detailed comparison of velocity differences for symmetric and antisymmetric waves in plates versus longitudinal and flexural modes in pipes. Phase and group velocities of pipes with various wall thickness-to-radius ratios are compared to a plate of corresponding thickness. An empirical convergence criterion is defined to determine the frequency above which a pipe will have a plate-like response. It is shown that “convergence” may already be reached at frequencies commonly used for nondestructive testing purposes. Analytical considerations are supported and validated by experimental results, showing good agreement of predicted and measured wave velocities.