1. Reference problem#

1.1. Geometry#

\(L=50m\) \(l=5m\)

fluid thickness \(e=0.5m\)

plate thickness \(h=0.5m\)

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

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

Fluid:

to simulate the permanent flow, a normal speed of \(–4m/s\) is imposed on the fluid inlet face, a normal speed of, the fluid inlet speed \({\overrightarrow{V}}_{0}\) being in the opposite direction to the normal inlet (by analogy with thermal analysis, a normal heat flow equivalent to \(–4\) is imposed),
To calculate the fluid disturbance caused by the movement of the plate, a Dirichlet boundary condition is imposed at a fluid node.
In \(x=\frac{e}{2}\), condition \({\phi }_{1}={\phi }_{2}=0\) is imposed, which corresponds to a zero flow rate through the upper fluid wall.

Structure:

the plate is subjected to an imposed displacement corresponding to a first mode of flexure [bib2] _:

\({X}_{1}\mathrm{=}\text{sin}\frac{\pi y}{L}\text{}\)