How about this approach: Random vibration analysis of a cantilever beam - #2 by FEAnalyst ?
Might be good to ask on the CalculiX forum too. Some guys there dealt with similar issues. Here’s an example (response spectrum analyses): Shock Response Spectrum - Is there a workaround? - CalculiX (official versions are on www.calculix.de, the official GitHub repository is at https://github.com/Dhondtguido/CalculiX).
Also, it seems that Code_Aster supports random vibration analyses.