1. Reference problem#

1.1. Geometry#

_images/1000246E0000267300000F4C2D8EFD6EA689E23E.svg

\({L}_{a}=0.075\), \({L}_{s}=0.025\), \({L}_{e}=0.05m\)

constant square section, \(a=0.05m\) or circular cross section (in the axisymmetric case) constant with radius \(R=a=0.05m\).

1.2. Material properties#

solid: \(E={2.10}^{11}\mathrm{Pa}\)

\({\rho }_{s}=7800\mathrm{kg}/{m}^{3}\)

\(\nu =0.3\)

air: \({c}_{a}=340m/s\)

\({\rho }_{a}=1.2\mathrm{kg}/{m}^{3}\)

water: \({c}_{e}=1400m/s\)

\({\rho }_{e}=1000\mathrm{kg}/{m}^{3}\)

\(c=\mathrm{célérité}\mathrm{du}\mathrm{son}\)

\(c=\) Speed of sound in the fluid

1.3. Boundary conditions and loading#

  • For all points \(M\) on face \((\mathrm{M1}\mathrm{M2}\mathrm{M3}\mathrm{M4})\) the pressure and the displacement potential are zero (free surface condition),

  • for the points \(P\) of the solid, we block all the degrees of freedom except the translation in \(x\) so that this solid behaves like a piston along the axis \(x\).