1. Reference problem#

1.1. Geometry#

_images/1000000000000306000002F4DFDF82EB0FB3D248.png

Figure 1.1 Problem geometry and loading system

Parallelipipedic cavity:

  • length: \({l}_{x}=1.0m\)

  • height: \({l}_{y}=1.0m\)

  • width: \({l}_{z}=2.0m\)

Coordinates of the points:

  • \(\mathit{N1}\): \(x=0.6\), \(y=0.4\), \(z=0.0\)

  • \(\mathit{N2}\): \(x=0.5\), \(y=0.5\), \(z=1.0\)

  • \(\mathit{N3}\): \(x=0.5\), \(y=0.5\), \(z=2.0\)

1.2. Material properties#

The material properties of the fluid are those of air:

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

Sound speed

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

Density

The material properties of the plate are those of steel:

\(E=2.1\times {10}^{11}\text{Pa}\)

Young’s module

\(\nu =0.3\)

Poisson’s ratio

\({\rho }_{S}=7800.0{\text{kg.m}}^{-3}\)

Density

\(t=0.005\text{m}\)

Thickness

1.3. Boundary conditions and loads#

Imposed displacement:

Plate wall

\(\mathit{DX}=0\), \(\mathit{DY}=0\), \(\mathit{DZ}=0\)

Imposed loading:

\[\]

: label: EQ-None

textrm {Point} mathit {N1}