Scattering of flexural waves by an inhomogeneity in a thin plate

The characteristics of defects in plate-like structures can be extracted from the scattered flexural waves. The scattering of flexural waves is studied in this paper, using the integral equation method in the framework of the Mindlin plate theory. Using the Born approximation, the expression for the flexural waves scattered by an inhomogeneity can be obtained, in which the Hankel function, rather than the exponential function, is involved in the integral kernel. Therefore, the far-field assumptions for the scatterer are not needed. The closed form for the singular integration of the Hankel function is solved, and hence, the complete scattered field near as well as inside the scatter can be calculated. The effective range of the far-field approximation is obtained by investigating the scattering amplitude of a circular inhomogeneity. In the case where the inhomogeneity diameter (2a) is less than one wavelength (λ), the far-field approximation achieves an accuracy of 1% at a distance greater than 2λ. If the inhomogeneity diameter is larger than λ, 1% accuracy will be achieved by the far-field approximation at a distance greater than 3ka.