3. Implementation in Code_Aster

The approach to frequency dependent modes described above has been implemented in*Code_Aster* via a macro command, namely DYNA_VISCO. This script uses standard commands existing in*Code_Aster* for the conventional modal method. Python codes have been added for the new developments:

• definition of a frequency dependent behavior,

• computation of frequency dependent modes by the iterative algorithm,

• Frequency response computation with realization of the stiffness matrix at each frequency step.

In the iterations, modes are computed as solutions of Eq. () via the standard CALC_MODES command. The modal extraction method is described in [9]. Five eigensolutions are searched around \({\omega }_{p}\) for each iteration. This number is a good compromise between securing the convergence of the iterative algorithm and limiting the total computing time. In the case where the algorithm would not converge, the number of the searched eigensolutions will be automatically increased by the program.

The user can define several VEM with different behaviors and choose the frequency dependent modes to be used: real modes or beta-modes. At this time of the implementation, it is also possible to compute frequency dependent complex modes, but they cannot be used as a modal basis for response computation.