Energy distribution of bifurcated waveguide structure with planar and non-planar surfaces

The present communication addresses the reflection and transmission analysis of a two-dimensional waveguide structure with planar and non-planar surfaces. In the fields of physics, engineering and applied mathematics, research is being carried out to control or reduce unwanted and harmful noise to an acceptable level. Our aim is to solve the boundary value problem developed to simulate the transmission and reflection of a bifurcated waveguide structure in the channels or ducts that have abrupt changes in the height together with planar and non-planar surfaces. Furthermore, the eigenfunctions are linearly independent and non-orthogonal. To solve non-orthogonal eigenfunctions, a generalized orthogonality relation has been developed. Solution is obtained using mode matching technique (MMT) along with generalized orthogonal relations. In the last section, solution is viewed graphically in the inner and outer ducts or channels for different frequencies and height. The expressions for energy distribution in different duct regions are obtained and sketched subject to the various properties of the waveguide material. The results are well supported for a number of mathematical and physical reasons.