A reaction matrix method in waveguides with coupling resonances
Regular paper
LAUM, UMR CNRS 6613
Wednesday 3 june, 2015, 14:20 - 14:40
0.3 Copenhagen (49)
Abstract:
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.