Abstract Summary
The reciprocity, orthogonality and bi-orthogonality relations are well established for symmetric waveguides, with the most known example being the Rayleigh-Lamb problem of wave propagation in an infinite elastic layer. In this paper, these relations are derived for non-symmetric waveguides using as an example the canonical problem of wave propagation in an infinite elastic plate loaded by a fluid layer of a finite height with uniform mean flow parallel to its surface. The links between formulations of dispersion equation, reciprocity/bi-orthogonality relations and energy flux are demonstrated and discussed. The Green’s function for stable regimes of wave motion in the presence of a flow is derived using the bi-orthogonality relation, and partition of the energy flux between transmission paths is analyzed.
