Mode coalescence and the Green’s function in a two-dimensional waveguide with arbitrary admittance boundary conditions

This study focuses on sound attenuation in a two-dimensional waveguide with arbitrary admittance boundary conditions on both sides of the guide. The emphasis is on understanding the formation and potential applications of the exceptional points (EPs) which arise when two (EP2) or three (EP3) modes d...

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Bibliographic Details
Published in:Journal of sound and vibration 2022-01, Vol.516, p.116510, Article 116510
Main Authors: Perrey-Debain, E., Nennig, B., Lawrie, J.B.
Format: Article
Language:English
Subjects:
Acoustics
Asymptotic methods
Boundary conditions
Coalescing
Duct acoustics
Electrical impedance
Exceptional point
Green's functions
Green’s function
Guided waves
Mechanics
Non-Hermitian physics
Numerical analysis
Perturbation
Physics
Puiseux series
Sound attenuation
Wave attenuation
Waveform analysis
Waveguides
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Summary:This study focuses on sound attenuation in a two-dimensional waveguide with arbitrary admittance boundary conditions on both sides of the guide. The emphasis is on understanding the formation and potential applications of the exceptional points (EPs) which arise when two (EP2) or three (EP3) modes degenerate into a single mode. A perturbation approach is used to obtain asymptotic expressions for the trajectories of the axial wavenumbers in the complex plane as they coalesce to form an EP. The numerical results presented herein suggest that the first triple root (EP3) assures maximum modal attenuation along the waveguide. Further, it is demonstrated that the classical Green’s function is degenerate at an EP. Modified Green’s functions which are valid at EP2 and EP3 are presented.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2021.116510