Modeling of wave propagation in plate structures using three-dimensional spectral element method for damage detection

This paper presents the application of three-dimensional (3-D) spectral element method (SEM) to wave propagation problems in plate structures for the purpose of damage detection. The excellent characteristic of the SEM is that the mass matrix is diagonal because of the choice of Lagrange interpolation function supported on the Gauss–Lobatto–Legendre (GLL) points in conjunction with the GLL integration rule. Therefore, numerical calculation can be significantly efficient in comparison with the classical finite element method (FEM). By taking advantage of this characteristic, a 3-D spectral finite elements (SFEs)-based model is developed to simulate the wave propagation in plate structures. Lamb waves, propagating in aluminum plates with and without a crack are investigated. Responses from 3-D SFEs- and 2-D SFEs-based models are compared. Different Lamb wave modes are generated using different excitation approaches and, subsequently, characteristics of those modes are analyzed. The results demonstrate that the proposed model can offer efficient and realistic simulation for Lamb wave propagation in plate structures, so as to detect damages in those structures.