I'm doing a modal analysis of a submarine piping system (jumper). I calculated the natrual frequencies and I extract relevant modal shape. On this base I have to perform a VIV fatigue analysis (by means another software). For this scope I have to calculate the stress on the jumper relevant to a maximum displacement of 1 diameter.
1)Considering the mode mass normalized I divided all displacements, rotation included, for the maximum displacements. So doing I obtained a mode unity normalized.
2)I multiplied all displacements for the pipe external diameter. I get a deformed shape relevant to a maximum displacement of 1 diameter and I can calculate the relevant stresses.

My doubt is this about of the dimension to be used in the above operation. No problem for the displacement but for the rotations. Supposing the dimension of the terms in the mode mass normalized are: meter for the displacement and degree for the rotation it is:

m/m
degree/m

In the mode unity normalized the displacement are dimensionless while the rotation have a properly dimension.

Multiplying the mode unity normalized displacement for the pipe diameter the result are depending from the dimension used for the diameter. For example if I use mm instead m I obtain rotation 1000 times grater,

To conclude I would know at what dimension are referred the displacements and rotations in the mode mass normalized.

Tanks very much