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SUMMARY:Sound absorption by perforated walls along boundaries - Agnes Lama
 cz-Keymling (Universität Duisburg-Essen)
DTSTART:20230322T120000Z
DTEND:20230322T123000Z
UID:TALK195745@talks.cam.ac.uk
DESCRIPTION:Asymptotic analysis of multiscale models with periodically het
 erogeneous coefficients became possible with the development of the method
  of homogenization in the 1970s.&nbsp\;If the periodicity length is small 
 compared to the size of the sample of the medium it turns out that the ori
 ginal equation is approximated well by an effective model with constant co
 efficients. &nbsp\;\nIn this talk our interest lies in the mathematical an
 alysis of a sound absorbing perforated plate\, e.g. along the wall or ceil
 ing of a room.To this end we analyze the Helmholtz equation in a complex d
 omain where a sound absorbing structure at a part of the boundary is model
 led by a periodic geometry with periodicity $\\varepsilon>0$. A resonator 
 volume of thickness $\\varepsilon$ is connected with the main part of the 
 macroscopic domain by thin channels (opening $\\varepsilon^3$).&nbsp\;We a
 nalyze solutions in the limit $\\varepsilon\\to 0$ to find that while the 
 lowest order approximation is trivial the effective system at order $\\var
 epsilon$ indeed describes sound absorption.\nThe talk is based on a joint 
 work with P. Donato and B. Schweizer.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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