The Campbell Diagram calculates coupled mode shapes based on contributions from the uncoupled mode shapes.
How can the coupled mode shapes be plotted?
Versions of Bladed involved: 4.0 onwards. (From 4.8 onwards, this article applies only to tower modes).
Article last updated: 30 Mar 2023
This is not currently directly supported in Bladed, but can be achieved as follows:
Information about the coupled mode shapes are output in the *.$01 file from a Campbell diagram calculation. This file describes the contributions of each uncoupled mode to each coupled mode.
The coupled mode shapes are based on a contribution from each uncoupled mode. This is the information in the “MAG” (magnitude) values. So, you can re-create the coupled mode shapes by multiplying each magnitude by the corresponding uncoupled mode shape. You can find the mode shapes in the $PJ file for older versions (Bladed 4.7 and earlier); look in the RMODE module. In Bladed 4.8 and later this information is in the XML section under <TowerMode>.
You should also include the phase, which takes a value of 0 or +/-PI/2 without damping, but can take other values once damping is included. The way to do this is to take sin(phase) then for example 0 will give a weighting of 0 and PI/2 will give a weighting of 1. If desired, you could then increment the phase for all components and plot the coupled mode shapes at different points in the harmonic cycle. Eigen modes from other software (e.g. Sesam) are usually calculated without damping. So it may be convenient to set structrual damping to zero for the purpose of comparison.
This process is fairly straightforward if you want to look at the coupled tower modes. However, it gets more tricky if you want to include the rigid body blade motion that results from tower deflection. You’d need to calculate this coupling yourself as it’s not directly stored in the mode shape result (e.g. you need to take account of tilt, azimuth, blade root length etc). Also note that since the introduction of multi-part blade modelling in v4.8, you can no longer apply the methods in this article to blade / rotor modes, but only to tower modes.
* Note that in 4.8 and later, the uncoupled mode shapes are also given in the $VE file. However, the modes shapes in the $VE are scaled differently compared to the $PJ file mode shapes. It's important to use the values fom the $PJ file as these are consistent with the mode shapes that are used in the linearisation calculation.
There is now a downloadable package, available via the Knowledge Base article here, containing a worked example (simplified) that helps guide you through the process.