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.
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