2. Benchmark solution

2.1. Calculation method used for the reference solution

For the calculation of the added coefficients:

we show [bib1] that the added mass and damping coefficients depend, in each region where \(\rho\) is constant, on the permanent potential of the fluid velocities \(\stackrel{ˉ}{\phi }\) as well as on two fluctuating potentials \({\phi }_{1}\) and \({\phi }_{2}\): these potentials are written in the case of the rotational movement of the external cylinder around the pivot C [bib1]:

For the region relating to

:

For the region relating to

:

However, the added modal coefficients projected onto this mode of rotation can be written as:

Suppose by separating the integral on two half-cylinders:

1. Digital applications:

An added damping calculation was made which corresponds, for the given speed, to a damped vibratory behavior of the structure:

speed

To \(4{\mathrm{m.s}}^{-1}\)

The values of the mechanical system are:

The mass added by the flow is equal to:

(independent of the flow speed value)

The added damping applies with \({V}_{0}=4{\mathrm{m.s}}^{-1}\) (it is independent of the change in density):

Knowing that the amortization of the mechanical system is worth

, the total damping of the fluid/structure system is written as:

1. to

   

The flow does not amplify the vibrations. The internal structural damping is significant enough to dissipate the energy provided by the flow to the structure. The system is still depreciated.

2.2. Benchmark results

Analytical result.

2.3. Bibliographical references

1. ROUSSEAU G., LUU H.T.: Mass, damping and stiffness added for a vibrating structure placed in a potential flow - Bibliography and implementation in the*Code_Aster* - HP-61/95/064