Complex modes expansion with vector projection using power flow to simulate Lamb waves scattering from horizontal cracks and disbonds

This paper presents an inexpensive but accurate analytical method to calculate the scattering of straight-crested Lamb waves from cracks parallel to the plate surface. The same method is applicable for the disbond problem. In this method, the scatter field is expanded in terms of complex Lamb wave modes with unknown amplitudes. These unknown amplitudes are obtained from the boundary conditions using vector projection utilizing the power expression. The process works by projecting the stress conditions onto the displacement eigen-spaces of complex Lamb wave modes and vice versa. The authors call this technique “complex modes expansion with vector projection” (CMEP). The CMEP approach is versatile and can be readily applied to corrosion, cracks, or disbonds. In this paper, the CMEP method is applied to a horizontal crack in a plate. For verification of the results the authors compared them with the results obtained by using the finite element method (FEM) and literature. The FEM analysis was conducted in the frequency domain with non-reflecting boundaries. It was found that CMEP results correspond very well with FEM results over a wide frequency-thickness range up to 1.5 MHz mm with CMEP being orders of magnitude faster than FEM.