Many codes use “Loss Tangent” to define damping. In Chapter 1 of the WB Mechanical Dynamics Training notes there is table of different damping specifications. Damping ratio is equal to (Loss Tangent) / 2. You can also see that in Theory Manual EQ 15-21. Damping input with TB,SDAMP (loss tangent) is multiplied by 1/OMEGA, damping input with MP,DMPR (damping ratio) is multiplied by 2/OMEGA. Note that in a harmonic analysis, damping ratio is not a constant ratio to critical. For a single mode it would be ratio to critical at resonance but become a smaller ratio to critical at lower frequencies and a higher ratio at higher frequencies. This effect isn’t very noticeable because the effect of damping decreases quickly away from resonance.