This article presents a dispersion analysis of flexural trifurcated dominants acoustic wave mode propagating out of the mouth of a semi-rigid waveguide. The problem mainly concerns the study of the scattering characteristics of the structure subject to different material properties. The governing non Sturm-Liouville problem is approached through eigenfunction expansions while equating the orthogonal and non-orthogonal duct modes across the interface. Due to the multiple non-planar surfaces, the essential difficulty of root findings versus the respective scattering relationships is accomplished by proper justification. The uniqueness of the solution is assured while considering connections clamped and pinned on bending surfaces. In addition, the energy fluxes for each region of the duct are formulated in terms of scattered fields to analyze the energy distribution subject to different properties of the waveguide material. The results are well supported for different mathematical and physical reasons.

The current study models and explains the fluid–structure coupled response of a flexible shell connected with two rigid coaxial shells via circular step discontinuities. Radiations from annular and inner regions of inlet rigid shells scatter on interfaces after interaction with the geometric variations and change of material properties. The flexible shell that supports vibrations along the shell is expressed though the Donnell–Mushtari formulation in the differential system. The mode‐matching technique is applied to solve the governing boundary value problem. The solution is projected on the orthogonal characteristics which in flexible casing is generalized as compared with the properties of acoustically rigid setting. The implication of generalized orthogonality relations governs additional constants that are found by defining the physical connection of shell with rigid disc. The clamped and pin‐jointed conditions are considered in this article. The scattering powers and transmission loss are analyzed against frequency, chamber length, and radii of shells for clamped and pin‐jointed edge conditions. It is found that the power propagation in annular shell and inner shell behave conversely. Moreover, configuration can be attenuated through the variation of dimensions of chamber and edge conditions.

The present study examines the fluid-coupled wave response of a stepped elastic membrane discontinuity connecting a flexible shell to the annular rigid shell. The acoustic radiation from the internal and annular regions propagates along the flexible boundaries as well as through the compressible fluid that fills the interior of the shell and scatters at geometric discontinuity and edges. In contrast to previous studies, an elastic membrane disc with different boundary conditions is considered as the geometric discontinuity rather than an acoustically rigid step-discontinuity in a cylindrical waveguide. The problem governed by the rigid step-discontinuity is solved using the mode matching technique, while the Galerkin procedure is used for the elastic membrane discontinuity. The truncated form of both solutions reconstructs the matching conditions and satisfies the conservation laws, which further authenticate the correctness of the solutions and the validity of the obtained numerical results based on these solutions. It is worth noting that the parametric configuration of the elastic membranes, the edge conditions and the radii of the shells have a significant impact on the attenuation of the noise control device.