4. Summary of results

The difference in natural frequencies increases because when the critical buckling speed is close to the critical buckling speed, the stiffness of the equivalent system must tend towards zero. However, with rounding errors (since the values of added stiffness calculated by the operator are assigned « by hand » to a discrete model), it is not possible to obtain a natural pulsation of the zero system at the critical speed.

Discrepancies in the added stiffness values also remain because the reference solution is built on a semi-analytical solution that starts from the approximation according to which the separation of variables between the y dimension and the orthoradial coordinates is possible. It will be noted that the potentials chosen to describe the disturbance generated by the vibration of the structure in the fluid do not verify the complete Laplace equation but only in a transverse section of the fluid in orthoradial coordinates. This approximation made on the reference solution may explain some differences with the numerical calculation.