I recommend you build the modal analysis model using remote displacement BCs and see how close it comes to the lab results of the rail resting on the sleepers. I expect it will be closer than the first trial you did with contact.

Then you can do all the work needed to simulate a full Structural Transient model and strike the rail with a hammer and simulate the ringing while extracting all the vertical displacements to feed that simulation data into the software that computes mode shapes and frequencies.