Abstract

The Green’s functions for a given medium are defined to be the solution of the wave propagation problem in presence of a concentrated force. Two analytical methods to derive the elastodynamic Green’s functions using guided waves in layered structures are proposed. The dispersion relations and modal functions were obtained using the global matrix method and singular value decomposition (SVD) to find the null space vector. In the first approach, the representation theorem for elastodynamics was introduced to develop the modal expansion of the Green’s function in terms of the analytical mode shapes normalized by a factor related to the power flow in the layered structure. In the second approach, temporal and spatial Fourier transforms were applied to the field variables and the boundary conditions. Application of the interface conditions and discontinuity conditions across the force lead to a system of linear equations for the calculation of the unknown constants. The residue theorem was applied for inverse Fourier transform of the matrix-form Green’s function to recover the frequency domain expressions. In this paper, the displacements and stresses in a three-layered structure with different materials produced by a concentrated impulse load were obtained by the two methods. The problem was also solved using the conventional Finite Element Method (Abaqus). All three results were in a good agreement.

How to Cite:

Araque, L. ., Wang, L. . & Mal, A. ., (2019) “Elastodynamic Green’s functions for layered structures”, Review of Progress in Quantitative Nondestructive Evaluation .