Mindlin plate theory for damage detection: imaging of flexural inhomogeneities

The scattering of plate waves by localized damage or defects that can be modeled as flexural inhomogeneities is examined within the framework of Mindlin plate theory. These inhomogeneities are characterized by variations in one or more of the four plate-theory parameters: the bending stiffness, shear stiffness, rotary inertia, and transverse inertia. It is shown that the Born approximation for the scattered field leads to a plate-theory analog of the Fourier diffraction theorem, which relates the far-field scattering amplitude to the spatial Fourier transform of the inhomogeneity variations. The application of this result is illustrated by using synthetic data derived for an idealized model of a delamination as a flexural inhomogeneity, ignoring mode coupling effects. A computationally efficient implementation of the filtered back-propagation algorithm, based on the eigensystem of the scattering operator, is employed for image reconstruction. The implications for in-situ imaging of structural damage in plate-like structures are briefly discussed, and some directions for further work are indicated.