Bending-wave diffraction from strips and cracks on thin plates

Two canonical problems concerning scattering of bending waves in thin plates are solved. The scatterers are either a semi-infinite rigid strip or a semi-infinite crack in an otherwise uniform plate of infinite extent. The exact scattered waves are represented by Fourier integrals obtained using the Wiener-Hopf method. The far-field diffraction coefficient for the rigid strip is independent of the material parameters, and is thus a universal parameter. The crack diffraction coefficient depends upon Poisson's ratio but this dependence is weak. Guided waves are generated on the free edges of the crack, and can be defined in terms of a separate diffraction coefficient which vanishes if Poisson's ratio is zero.