Diffraction of normal modes in composite and stepped elastic waveguides

Abstract

A method of calculating the diffraction of Lamb waves at the vertical junctions of elastic waveguides is proposed, the effectiveness of which is ensured by taking into account the nature of the singularity of the solution at corner points. The property of the generalized orthogonality of normal modes plays a key role. It enables the coefficients of the expansion of the wave field in the modes to be expressed in terms of the displacements and stresses along the junction line. Numerical results are presented which show how the transmission coefficients and the energy distribution depend on the height of the step and frequency for a stepped waveguide, attached to an undeformed substrate.