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[FAQ]

No. For a single mode, the ratio to critical is greater at frequencies below resonance and smaller at frequencies above resonance. This is documented in the Structural Analysis Guide Section 1.2.4. You can find the complete equation in the ANSYS Help documentation, under “Mechanical APDL -> Theory Reference -> 14.3.3 equation 14-22 parameter g, mj, gEj”.
The damping contribution g is related to the damping matrix by
[C]=(2*g/Omega)*K
Omega is the excitation frequency. So (2*g/Omega) is a coefficient times the stiffness matrix like Beta damping.
Beta = 2*eta/omega
omega is the natural frequency while
2*g/Omega = 2*eta/omega:
eta (ratio to critical) = g(omega/Omega)
In a single degree of freedom test you will see the ratio to critical be higher at low excitation frequencies and lower at high excitation frequencies.