Comparative Study of Dispersion Curves for LAMB Waves Using Analytical Solutions and Semi-Analytical Methods

Abstract

Lamb wave dispersion curves are useful for optimizing the inspection scanning distance that can be covered with good sensitivity in many current applications. However, one of the main problems concerning this calculation lies in selecting a numerical method that is computationally accurate and efficient. In this paper, Lamb waves dispersion curves are generated by the Scaled Boundary Finite Element Method, and by the Rayleigh–Lamb equation. For the semi-analytical case, waveguide cross-section discretization was performed using isoparametric elements and high-order spectral elements. The semi-analytical formulations lead to an eigenvalue problem that can be solved efficiently by calculating the couples of wavenumbers and frequencies that guarantee the wave mode propagation, the basis for generating the dispersion curves. These are compared with those obtained from the analytical solution for the symmetric and antisymmetric modes; in both cases, homogeneous plates of constant thickness are considered. The numerical results show good agreement when using a low number of isoparametric elements, or a single spectral element with shape functions of the order of six for computing the dispersion curves and wave structure. The calculation is given with low computational effort, and the relative variation with respect to the analytical reference values is less than 2%.