1. Reference problem#

1.1. Geometry#

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

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

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

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 \(x\).