An efficient analytical global–local (AGL) analysis of the Lamb wave scattering problem for detecting a horizontal crack in a stiffened plate

Abstract

This paper addresses a forward problem using an analytical global–local (AGL) method based on the physics of the Lamb wave propagation in the presence of a crack in the complex structure which would be beneficial for the inverse problem of damage detection. Discontinuity in a structure acts as a damage source and interacts with a Lamb wave. The global analytical solution determines the wave generation by a transmitter, wave propagation through the structure, and detection by a receiver. The local analytical solution determines the scattering coefficients for the Lamb waves at the discontinuity location. These frequency-dependent scatter coefficients are calculated considering transmission, reflection, and mode conversion. An analytical method called “complex mode expansion with vector projection (CMEP)” is used to calculate the scattering coefficients of Lamb wave modes from geometric discontinuities. The scattered wave field from a discontinuity is expanded in terms of complex Lamb wave modes with unknown scatter coefficients. These unknown coefficients are obtained from the boundary conditions using a vector projection utilizing the power expression. Two test cases are considered in this paper: (a) a plate with a pristine stiffener and (b) a plate with a cracked stiffener. Complex-valued scattering coefficients are calculated from 50 to 350 kHz for S0 incident waves. Scatter coefficients are compared for both cases to identify the suitable frequency range to excite a Lamb wave to detect the crack. The frequency-dependent complex-valued scattering coefficients are then inserted into the global analytical model. Therefore, in combination AGL method provides the exact analytical Lamb wave solution for the simulation of Lamb wave propagation and interaction with a discontinuity. By comparing the waveforms for both pristine stiffener and cracked stiffener, the crack can be detected. An FEM transient analysis was also performed to calculate the scattered wave signals. FEM results agree well with the AGL predicted results. An experiment was also performed to validate the AGL result. The obtained experimental results match well with the CMEP analytical predictions. The present AGL method is a highly computationally efficient simulation approach which allows performing virtual experiments for structural health monitoring applications.