A reaction matrix method in waveguides with coupling resonances

Regular paper

Lei Xiong


Wednesday 3 june, 2015, 14:20 - 14:40

0.3 Copenhagen (49)

A Reaction Matrix Method is used to investigate wave propagation through locally perturbed acoustic waveguide. A coupling matrix is introduced to describe the coupling between the discrete modes and via the semi-infinite ducts. Two cases are considered: a waveguide coupled with cavity, and with impedance wall. In both cases, Fano resonances and trapped modes are all observed at some particular frequencies. Effective Hamiltonian is explored to locate the positions and widths of the resonances of the open system. By varying a parameter continuously, avoided crossings of the resonances in the complex plane are always observed. Because of the interference of two neighbor resonances via the duct, the width of one of the resonances will almost vanish, resulting in the strong localization of the pressure field in the waveguide. More importantly, the Reaction Matrix Method also allows an easy treatment of the non-separable problem along transverse and axial directions. This method is also applied to a lined wall with varying impedance along the axis. The effects of the Fano resonances and trapped modes on the transmission and reflection coefficients are analyzed. By tracing the motions of the eigenvalues of the effective Hamiltonian, the Fano line-shape transmission coefficients can be well predicted at some particular frequency.

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