See my last post on structural damping. If there are ways to compute this,I am unaware; I have often done it experimentally. For a clamped or any beam frequencies define the mode shape but not amplitude, as you indicate, since amplitude is a function of output to input, or Q. Metals have a Q of about 50 (about 1% damping) while some brittle materials have a Q of 100 or more. Rubber has a Q of 3-10 or so.
Once you introduce joints, Q drops significantly, so for structures with a lot of joints this can drop to from the 50-100 values to 10-25 values, but you have to determine this experimentally. Also, as you increase the load input (energy) damping also increases (lowers the Q).