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1
Astride Localization in Cavities Filled with an
Irregular Absorber
Anna Rozanova-Pierrat, Bernard Sapoval, Simon
Félix, Marcel Filoche PMC, Ecole Polytechnique,
Palaiseau Cedex
Porous Media
Silent wall
Question why does it work?
Answer the irregular surface induces  astride
modes  which are both coupled to external
sources and dissipative
the ambient atmospheric pressure,
, where
density of the air,
tortuosity, characterizes the sinuous appearance
and variations in pore section,
raport of specific heats,
the Prandtl number,
porosity, ratio of the volume occupied by the
porous air to the total volume,
resistivity with the passage of air, linked to
the role of obstacle held by the solide in the
material
Examples of cavities
Damped Wave Equation
Eigenvalue problem
For the solutions in the form
We have
Approximation of the Acoustic System (1) for the
Porous Medium by the Damped Wave Equation
Astride in a simplified model
5
4.5
porous material
4
air
3.5
3
2.5
A) Supposing that
and
we obtain
2
1.5
which is the eigenvalue problem of the damped
Eq. with
1
0.5
B) Supposing that
we find
0
is small enough
0
0.5
1
1.5
2
2.5
Existence surface of a mode i
which is the eigenvalue problem of the damped
Eq. with
Astride localization
Energy Decay
Astrideness index
Astride in the damped wave equation
Astrideness index
Log(E(t))
E(t)
t0.054 c
t 0 c
t 0.0245 c
t0.0698 c
t0.0849 c
Spectrum
Most dissipative eigenvalues
Fractal 0
t0.1151 c
t0.1302 c
t0.1447 c
t1.0091 c
t2 c
Fractal 1
Fractal 2
3) B. Sapoval, S. Félix, M. Filoche, Localization
and damping in resonators with complex geometry.
Summited. 4) J.-F. Allard, Propagation of sound
in porous media Modelling sound absorbing
materials. ChapmannHall, London,1993.

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