Scattering of guided waves propagating through pipe bends based on normal mode expansion

The scattering of guided waves propagating through pipe bends is studied by means of normal mode expansion. First, the bi-orthogonality relationship for normal modes in pipe bends is derived, based on which the displacement and stress fields at the interfaces between the straight and curved parts are expanded with the normal modes in both parts. Then, based on the displacement and stress field continuity principle, the scattering problem is regarded as an eigenproblem of a transfer matrix, the solution of which gives the mode conversions at the interfaces. A case study is presented of the low-frequency longitudinal mode incident on a pipe bend, and it is found that the dominant mode conversions are L(0,1) reflection and mode conversion from L(0,1) to F(1,1). Finite element simulations and experiments are also conducted. L(0,1) bend reflection and mode-converted F(1,1) are clearly observed, which agrees well with the theoretical predictions.