Elastic bending wave on the edge of a semi-infinite plate reinforced by a strip plate

Elastic waves localised near the edge of a semi-infinite plate reinforced by a strip plate are considered within the framework of the 2D classical theory for plate bending. The boundary value problem for the strip plate is subject to asymptotic analysis, assuming that a typical wavelength is much greater than the strip thickness. As a result, effective conditions along the interface corresponding to a plate reinforced by a beam with a narrow rectangular cross-section are established. They support an approximate dispersion relation perturbing that for a homogeneous plate with a free edge. The accuracy of the approximate dispersion relation is tested by comparison with the numerical data obtained from the 'exact' matrix relation for a composite plate. The effect of the problem parameters on the localisation rate is studied.