Method for reducing the vibration levels of a propfan of contrarotating bladed disks of a turbine engine

1. A method for reducing the vibration levels in a turbine engine comprising a first moveable bladed disk and a second moveable bladed disk, forming a propfan of contrarotating disks, because of the turbulence of aerodynamic origin generated by the second bladed disk on the first bladed disk, said method comprising:

A—defining an initial configuration of the blades as a function of an expected performance of the turbine engine, with individual aerodynamic profiles of p sections (c 1 , c 2 , . . . cp) stacked radially between a root and a tip of said blades;

B—calculating, in a computer, a synchronous forced response y(ω) on the first bladed disk as a function of a harmonic excitation force f(ω) generated by the second bladed disk based on a relation y(ω)=F( τ y υ *f(ω), where F is a linear function of a generalized aerodynamic force τ y υ *f(ω) for a fundamental mode of vibration υ in question;

C—defining, in a computer, a coefficient (α<1) of reduction of the synchronous forced response y(ω);

D—determining, in a computer, for each of said p stacked sections (c 1 , c 2 , . . . cp) of one of the two disks, a tangential geometric offset value θ of the individual aerodynamic profile so as to reduce a term corresponding to the generalized aerodynamic force associated with the fundamental mode of vibration υ| τ y*f(ω)|, a temporal phase shift φ of an excitation pressure f(ω) being linked to a tangential geometric offset by a relation θ=N excit *φ where N excit is the number of exciter sources; the combination of the p sections with the tangential offsets therefore defines a new configuration of the blades of said one of the two disks;

E—calculating, in a computer, a synchronous forced response y′(ω) on the first bladed disk;

F—if |y′(ω)|>α*|y(ω)|, repeating, in a computer, the calculation at D with new tangential geometric offset values;

G—if |y′(ω)<α*|y(ω)|, manufacturing at least a portion of the blades of said one of the two disks with the new configuration and employing the blades in the propfan; and

H—operating the propfan with reduced vibration levels.

2. The method as claimed in the claim 1 , wherein

y

⁡

(

ω

)

=

F

⁢

⁢

(

y

υ

τ

*

f

⁡

(

ω

)

)

=

∑

υ

=

1

n

⁢

⁢

[

y

υ

*

y

υ

T

/

(

ω

υ

2

-

ω

2

+

j

*

ω

*

β

υ

)

]

*

f

⁡

(

ω

)

(

1

)

where

the symbol Σ means that the forced response y(ω) is the sum of the forced responses of each of the fundamental modes of vibration υ to the pulsation ω,

y υ corresponds to a mode shape of the mode υ under the hypothesis of a unit norm of Eigen vectors relative to a weightun,

T y υ corresponds to a transpose of the preceding vector,

ω υ corresponds to a pulsation associated with the mode υ,

ω corresponds to a pulsation of the excitation,

j 2 =−1,

β υ corresponds to a generalized modal damping for the mode,

and f(ω) is the harmonic excitation force in the form f*cos(ω*t+φ) where t is time and φ the temporal phase shift.

3. The method as claimed in claim 2 , wherein the first disk is in a wake of the second bladed disk.

4. The method as claimed in claim 2 , wherein the first bladed disk is upstream of the second bladed disk.

5. The method as claimed in claim 1 , wherein the first disk is in a wake of the second bladed disk.

6. The method as claimed in claim 1 , wherein the first bladed disk is upstream of the second bladed disk.