Resonance problems in acoustic waveguides

Abstract

Acoustic resonance problems in closed systems can be solved numerically with finite element methods. The resulting real resonances become complex, if the system changes to an open system with an unbounded domain. While for a completely open system only damped resonances exist, laterally confined domains can sustain localized, truly trapped modes with nominally zero radiation loss. These discrete resonant modes cannot be excited linearly by continuous propagating duct modes due to symmetry constraints. If the symmetry of the geometry is broken the trapped modes become highly localized quasi-trapped modes which can interfere with the propagating duct modes. Since standard finite element methods are restricted to bounded domains, in a numerical treatment of such problems so called transparent or non-reflecting boundary conditions are needed. In this paper two different types of transparent boundary conditions namely the complex scaling method and the Hardy space infinite element method, are used to compute resonances as well as transmission and reflection coefficients for symmetric obstacles in a two dimensional waveguide.