Damage Quantification Using Mode Converted Guided Wave Based 1D Damage-Spectral Element

Quantifying the sizes of the damages in structures using guided waves is an emerging technology. It needs a suitable mathematical model that represents the behavior of the guided waves as they travel through the structure. Though finite element based theoretical models can provide insight into the behavior, they are computationally very costly. Spectral element is a promising solution in this regard. Quantifying the damage using a mode-converted wave based spectral element has not been reported yet. In this work, a spectral element that represents the characteristics of wave propagation, scattering and mode conversion caused by asymmetric notch-type damage in an isotropic waveguide is presented. This frequency domain damage-spectral element is formulated through a combination of three structural waveguides by enforcing appropriate force equilibrium conditions. The spectral element is able to represent the wave scattering and mode conversion due to the presence of the damage. This spectral element is employed in analyzing the wave propagation in a beam that has damage and the characteristics obtained are in agreement with the results expected based on time-of-flight calculations and those obtained using the finite element method. The relation between the depth of the damage and the magnitude of the mode-converted wave for notch-type damage is established using this spectral element and compared with the experimental result. Usage of the same spectral element in quantifying the length of the damage based on the reflections of the primary propagating wave from the damage ends is also demonstrated.