Scattering of obliquely incident waves by straight features in a plate

• The scattering of obliquely incident plate modes from straight features is solved analytically.
• For the propagating modes, the scattering matrices are proven to be Hermitian.
• A real orthogonal relation applicable to the oblique incidence problems is derived.

The scattering of obliquely incident waves by straight features in a plate is solved analytically. The reflection matrix of a free straight edge and the scattering matrix of a straight thickness step are obtained respectively by modal decomposition based on a real orthogonal relation. The formulas are illustrated through numerical examples. The matrices are found to be Hermitian for the propagating modes; thus, the mode conversions are reciprocal in terms of energy. The matrices can be used to determine the scattering from more complicated straight features if the cross sections are approximated as sequences of stairs and steps.