1. Reference problem

1.1. Geometry

The system consists of a circular piston vibrating in contact with an annular fluid column ending in a free surface:

Length: \(1m\)

width: \(0.03m\)

height: \(0.025m\)

the axis of revolution is axis \(\mathrm{OY}\) of the coordinate system. \(\mathrm{OX}\) refers to the radial axis.

1.2. Material properties

Structure: steel - elastic material

\(E={2.10}^{13}\mathrm{Pa}\)

\(\nu =0.3\)

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

The spring has a stiffness per radian of \(K=\frac{{10}^{5}}{2\pi }N/m/\mathrm{rad}\)

Fluid: equivalent thermal material

\(\lambda =1.\)

\({\rho }_{f}{C}_{p}=1000.\)

1.3. Boundary conditions and loads

On the structure side: the \(\mathrm{DX}\) degree of freedom of all the nodes in the structure is locked: DX: 0.0

On the fluid side: zero pressure (i.e. temperature) is imposed on the nodes of the free surface.