1. Reference problem#

1.1. Geometry#

_images/1000000000000554000002E7A0F250415844FC36.png

Figure 1.1 Problem geometry and loading system

Parallelipipedic cavity:

  • length: \(L={l}_{x}=1.0m\)

  • height: \(h={l}_{y}=0.1m\)

  • width: \(l={l}_{z}=0.2m\)

Coordinates of the points:

  • \(A\): \(x=0.\), \(y=0.05\), \(z=0.1\)

  • \(B\): \(x=0.\), \(y=0.1\), \(z=0.2\)

  • \(C\): \(x=1.\), \(y=0.1\), \(z=0.0\)

  • \(D\): \(x=1.\), \(y=0.05\), \(z=0.1\)

1.2. Material properties#

The material properties are those of air:

\(c=340{\text{m.s}}^{-1}\)

Sound speed

\(\rho =1.2{\text{kg.m}}^{-3}\)

Density

1.3. Boundary conditions and loads#

Uniform unit speed and impedance:

Inlet section \(x=0\)

\({V}_{n}=-1{\text{m.s}}^{-1}\text{à 500 Hz}\)

\({Z}_{n}=-1000{\text{kg.m}}^{-2}\mathrm{.}\text{s}\)

Input section \(x=1\)

\({Z}_{n}=-408{\text{kg.m}}^{-2}\mathrm{.}\text{s}\)