How to analyse periodic data obtained from a vibration experiment?
Remember that you are observing a system (the structure) driven by an input (shake table).  Assuming linearity, the FFT result was caused by the shake table and the structure.  You should be able to pick out the various components to identify mechanical resonances in the structure.  For instance, you should see a strong component at the frequency of the shake table.  Exactly how to do this in more detail is out of my domain, as I am an electrical, not mechanical, engineer.