Effective sound absorbing boundary conditions for complex geometries
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Date
2024-05
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Abstract
We analyze a system of equations that describes the propagation
of sound waves. We are interested in complex constructions along a
part of the boundary of the domain, for example constructions with small
chambers that are connected to the domain. We also allow that different
flow equations are used in the chambers, e.g., modelling a damping material.
In addition to the complex geometry, we assume that the viscosity
vanishes in the limit. The limiting system is given by wave equations,
we derive these equations and determine the effective boundary conditions.
The effective boundary conditions replace the large number of
small chambers. We provide examples for sound absorbing constructions
and their Dirichlet-to-Neumann boundary conditions.
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Keywords
wave equations, boundary conditions