Propagation of fluid-loaded structural waves along a duct with smoothly varying bending characteristics

This article is concerned with the sound field generated by a fluid-loaded structural wave travelling along the boundary of a two-dimensional duct with walls that have smoothly varying elastic properties. It is the field within the duct that is of interest and the exterior region is assumed to be in vacuo. By recourse to a modified form of the two-dimensional plate equation the boundary-value problem is posed in terms of the fluid velocity potential. A functional difference equation method is used to obtain an explicit integral solution from which the reflection and transmission coefficients are determined. Various limiting forms of the modified plate equation are discussed together with the implications each has on both the analytic method used herein and the physical situation it describes.