Scattering Analysis of Acoustic Waves in Waveguides Containing Partitioned Wave-Bearing Cavities
The present thesis addresses a class of boundary value problems arising in the modelling of scattering of acoustic waves in ducts or channels comprising partitioning of guiding structure along with abrupt geometric changes and material contrast. The mathematical formulation of such problems includes Helmholtz’s type governing equation and involves Dirichlet, Neumann, Robin type, and/or higher order boundary conditions. The envisaged problems are solved by using the mode-matching (MM) scheme. This approach relies on the eigenfunction expansions of propagating modes of duct regions, the orthogonal characteristics of eigenfunctions and the matching conditions at interfaces. The eigenvalue problems with higher order boundary conditions, the eigen-sub systems are of and non-Sturm Liouville category whereby the use of generalized orthogonal characteristics is indispensable. Such eigenfunction characteristics are incorporated in the process of conversion of differential systems into linear algebraic systems and ensure the convergence of the systems. Moreover, the low frequency approximation solution is developed for some cases and is compared with MM. For each physical problem, the solution schemes are validated through opposite mathematical and physical argument. To analyze the physical consequences of each model problem as a noise control measure, the transmission loss and/or scattering powers in different regimes are discussed numerically.