1. Reference problem#

1.1. Geometry#

\(L=50m\)

\(I=5m\)

fluid thickness \(e=0.5m\)

plate thickness \(h=0.5m\)

The coordinate \(\mathrm{Oxyz}\) is located at a distance of \(\frac{e}{2}\) from the plate

Fluid: density \(\rho =1000{\mathrm{kg.m}}^{-3}\) (water).

Structure: \({\rho }_{s}=7800\mathrm{kg}/{m}^{3}\); \(E=2.1{10}^{11}\mathrm{Pa}\); \(\nu =0.3\) (steel).

Fluid:

to simulate the permanent flow, a normal speed of \(–4m/s\) is imposed on the fluid inlet face (by thermal analysis, a normal heat flow equivalent to —4 is imposed),
To calculate the fluid disturbance caused by the movement of the external cylinder, a Dirichlet boundary condition is imposed at a fluid node.
we impose in

The condition

which corresponds to a zero flow through the upper fluid wall.

Structure:

the plate is subjected to a displacement corresponding to its first two modes of flexure [bib2]: