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 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 can be written in the case of the flexural movement of the plate [bib1]:

For the first mode:

For the second mode:

However, the added modal coefficients projected onto these flexure modes can be written as:

either:

• Digital applications:

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

Speed \({V}_{0}\) to \(4{\mathrm{m.s}}^{-1}\)

The values of the mechanical system are:

The mass added by the flow is equal to:

The depreciation added is equal with \({V}_{0}=4{\mathrm{m.s}}^{-1}\):

The added stiffness applies with \({V}_{0}=4{\mathrm{m.s}}^{-1}\):

2.2. Benchmark results

Analytical result.

2.3. Bibliographical references

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

• BLEVINS R.D: Formulas for natural frequency and mode shape. Ed. Krieger 1984