Normal wave diffraction in the rounded section of a waveguide

Abstract

Basing on Sturm-Liouville’s method, a normal wave propagating in the curved section of the waveguide elbow with a constant cross-section was studied. When solving problems in rectangular or cylindrical coordinates, the variables may be distributed, therefore the m-th order wave for exciting an initial field may be investigated separately. Further, the boundary condition for a wave field problem for the curved section of the waveguide is written. The wave field in this curved section must satisfy the wave equations recorded in cylindrical coordinates at the given boundary conditions. Then wave equations are solved by integrating them taking into consideration the orthogonalities of equation forms. A convenient system of integral equations is obtained for computation of normal wave diffraction.