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The purpose of this document is to describe the macro commands needed to draw the Campbell diagram in*Code_Aster*. The approach is based on the one already developed in the software ROTORINSA [bib1].

The Campbell diagram is a graphical representation of the natural frequencies of a rotating system as a function of its rotation speed. The natural frequencies and modes of a rotating system are obtained by solving the dynamic equilibrium equation of a rotating shaft system, without a second member and including the effects due to damping.

\(M\ddot{\delta }+C(\Omega )\dot{\delta }+K\delta =0\) eq 1- 1-1

Where \(M\) is the mass matrix of the system, \(C(\Omega )\) is a non-symmetric matrix, a function of the speed of rotation, including the gyroscopic effect (antisymmetric) and the damping characteristics of the bearings, and \(K\) is the stiffness matrix of the system.

The data required to draw the Campbell Diagram are therefore the natural frequencies, as well as the corresponding modes, as a function of the rotation speed in table form. The step allowing the calculation of these modes is already developed in Code_Aster (cf. [R5.01.01]).

Two macro controls are developed. The first macro command CALC_MODE_ROTATION calculates the frequencies and modes on the complete system according to the rotation speeds. The second macro command IMPR_DIAG_CAMPBELL classifies the flexure, torsional, and traction/compression modes, standardizes these modes, determines the direction of precession of the flexure modes, sorts the frequencies according to different mode tracking methods, and then draws the Campbell diagram.