A Mode-Matching Tailored-Galerkin Approach for Higher Order Interface Conditions and Geometric Variations

The current study focuses on the modeling and analysis of acoustic scattering from an elastic membrane disc located in a cylindrical waveguide that may involve structural discontinuities. The physical problem is governed by Helmholtz's equation and involves higher order boundary conditions at the interfaces. The Mode-Matching (MM) method in conjunction with Galerkin formulation is developed to solve the governing boundary value problems. The solution procedure is first applied on two prototype problems to formulate the theoretical frame work, which is then used to analyze the structural response of the elastic membranes attached at the mouth of the cylindrical expansion chamber. The aforementioned solution method yields the linear algebraic systems containing infinite equations. These systems are truncated first and then are numerically solved. From the numerical experiments, it is found that geometrical and material properties of the structure significantly affect the transmission loss as well as the scattering energies.