Dear Neelabh,
Regarding your first question, I see very little difference in the natural frequencies between these two cases – most of the differences are in the third significant digit or higher. I’m not surprised by these results because I wouldn’t expect a rotor mass imbalance to impact the natural frequencies much.
Regarding your second question, here’s how I interepret your linearization output:
Mode → Description
1/2 → Generator rigid body
3 → 1st Tower Side-to-Side
4 → 1st Tower Fore-Aft
5 → 1st Blade Flap Asymmetric - Sine
6 → 1st Blade Flap Collective
7 → 1st Blade Flap Asymmetric - Cosine
8 → 1st Blade Edgewise Asymmetric - Sine
9 → 1st Blade Edgewise Asymmetric - Cosine
10 → Drivetrain torsion
11 → 2nd Tower Fore-Aft
12 → 2nd Tower Side-to-Side
13 → Other
14 → 2nd Blade Flap Asymmetric - Sine
15 → 2nd Blade Flap Collective
16 → 2nd Blade Flap Asymmetric - Cosine
17 → Nacelle yaw
When the rotor is spinning (as in your example), it is not proper to refer to an asymmetric mode as “pitch” or “yaw” as is common with a nonspinning rotor. So, above, I simply referred to the asymmetric modes with “sine” or “cosine” as used by MBC3.
Regarding your third question, a mass imbalance in the rotor may cause a problem with resonance, not instability. A “resonance” typically refers to excitation forces occuring at or near natural frequencies (as would be the case for a rotor imbalance). An “instability” typically refers to negative damping.
Best regards,