Lamb wave propagation in a plate with step discontinuities

• Lamb wave-scattering at step discontinuities.
• Least-square solution by employing analytical expressions.
• Inclusion of nonpropagating and evanescent modes in near-field solutions.
• Good agreement between analytical and numerical findings.

Ultrasonic Lamb waves are affected by structural discontinuities (e.g. stiffeners, ribs or joints), and it is necessary to understand the quantitative characteristics of their influence on the waves so that the structural features are not misidentified as defects in nondestructive evaluation (NDE) applications. In this paper, the benchmark problem of Lamb wave reflection at a free end as well as the interaction of Lamb waves with upward and downward step discontinuities is solved using an analytical approach. The free-end problem is considered to show the influence of the decaying waves on the power flow in the plate. In all problems, a near-field solution is obtained, and power flows past the cross-sections of the plate are evaluated. Furthermore, amplitude spectra and results for different step sizes are presented. The analytically derived results are compared with those from transient finite element simulations, showing good agreement.