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

The modal analysis is a solution of an eigenvalue problem.Since it is not possible to get absolute values of the eigenvectors, it is a done based on "scaling".One way of scaling is considering the maximum value as unity and the other is the so called mass normalization i.e. taking PHI TRANSPOSE* M *PHI=1 where PHI signifies eigenvectors.So these are relative magnitudes.

Since rotational vibration is not very significant in structural systems, rotational DOFs are condensed out by "static condensation".

I am not sure if I have answered the question that you have asked. Kindly revert back if that is not so .

Regards

I don’t believe that the rotations change when the length units change. In fact, the mass normalized mode shapes are always reported identically (for both displacements and rotations) regardless of what the units are.

The units for mass normalized modes are inches and radians. So if you need to get a maximum displacement of 219 mm, you would need to:

• Determine the maximum displacement in the mass normalized mode shape (I assume that this would be the maximum RESULTANT displacement at a node as opposed to in one particular DOF).
• Multiply all displacements in the mass normalized mode shape by the ratio of [219 / max displ].
• Multiply all rotations by [219 / (max displ * 25.4)] * 57.295 to adjust for the original inches and to further convert from radians to degrees. (Of course if you want to use meters instead of mm, than you would use 0.0254 instead of 25.4).