Acoustic energy flux analysis of the bifurcated waveguide by varying outlet boundaries

Abstract

This communication is devoted to the analysis of the energy flux of a two-dimensional waveguide with planar and non-planar surfaces. The main goal is to analyze the effects of reflected and transmitted energy fluxes of the bifurcated waveguide by varying the different types of outlet boundaries. The upper and lower boundaries of the inlet are taken as flexural in nature, whilst the outlet of the duct is varied by soft, rigid and impedance boundary conditions. The benchmark Mode-Matching (MM) technique is applied to solve the underlying boundary value problem (BVP). The system is excited with two types of incident forcing: fluid-borne incident and structure-borne incident. For a flexible inlet bounded by a membrane, the obtained eigenfunctions are linearly dependent and non-orthogonal in character. For sake of this, generalized orthogonality relations (OR) are developed. Additionally, the application of generalized OR led to the appearance of some dependent sums that are tackled using the fixed membrane edge conditions. The application of edge conditions led to the unique solution of the BVP. In the end, the expressions of reflected and transmitted energy fluxes are obtained and analyzed graphically against frequencies for different structural properties of the waveguide. Furthermore, it is shown that the conserved energy flux is valid, and reconstructed matching conditions are found in good accord.