Two load cases
W+P1
WNC

The natural frequencies from both case are identical. So liquid weight is not counted into the mass-spring system?

I highly appreciate if someone can explain me this issue.

Hyong

Those are static load cases, and don't have any affect on dynamics (unless you have a non-linear system, and you have to reference a static case for non-linear boundary conditions).

Your test/study should be setup as follows:

1) Build your model and define the fluid density on the 1st element.
- run the static analysis
- setup the dynamic model analysis and run
- note the natural frequencies

2) Go back the the model input and delete the fluid density
- run the static analysis
- setup the dynamic model analysis and run
- note the natural frequencies

3) Compare the two sets of frequencies.