What units and factors are applicable in order to convert rotations from an AutoPIPE modal analysis report into actual rotations?
Example:
Performed a modal analysis to capture a piping systems natural frequency. Physical field measurements of the amplitude of vibration have been recorded from the actual piping which is vibrating at the natural frequency. Using these measurements of amplitudes of measurements find a ratio between the unit-less amplitudes of the modal analysis and the actual amplitude of vibration (at the same points). Using this factor, find the actual amplitude of all points from the modal analysis. However also need the angle of rotation at each point, Tried applying the same factor to the unit-less rotation but results are too high to be correct.
How to convert from modal rotation to actual rotation?
The mode shapes and frequencies are not unit dependent since they are scaled. However in order to understand the rotation units you would need to make a simple system and test this relationship. For a simple cantilever model (restrained in x-direction) with 5 nodes at 1.0ft or 304.8mm distance (total of 5ft) and rigid anchor at one end
MODE SHAPE Point
MODE SHAPE
Point
Frequency TRANSLATIONS ROTATIONS
name Mode (Hertz) X Y Z X Y Z
------ ---- --------- ------- ------- ------- ------- ------- -------
*** Segment A begin ***
A00 1 67.6917 0.000 0.000 0.000 0.000 0.000 0.000
A01 1 67.6917 0.000 0.000 0.270 2.212 0.000 0.000
A02 1 67.6917 0.000 0.000 0.931 3.739 0.000 0.000
A03 1 67.6917 0.000 0.000 1.841 4.636 0.000 0.000
A04 1 67.6917 0.000 0.000 2.876 5.024 0.000 0.000
A05 1 67.6917 0.000 0.000 3.947 5.111 0.000 0.000
In English units:
If length in ft:
Rotation at A05 = (3.947-2.876)/1.0ft = 1.071 * 4.77 = 5.111
If in mm
Rotation at A05 = (3.947-2.876)/304.8mm = 3.51E-3 *1454 = 5.111
So the factor for ft is 4.77 and for mm is 1454
The development team could not confirm if this would apply to every model, but that it might help. Remember, mode shapes are mass normalized. After increasing the length from 1 ft to 2 ft; the relation still holds.
"Mode Shape" sub report
Bentley AutoPIPE