How are the tower attachment mode shapes calculated?
The Craig-Bampton method uses a mixture of “normal” and “boundary” mode shapes.
- Boundary mode shapes are calculated by applying loads or displacements to the tower top and calculating the resulting nodal displacements. The tower is constrained at the tower base for this calculation. Such modes are sometimes referred to as “static” modes as they represent static deflection as a result of an applied unit loads or displacements.
- Normal modes are calculated by constraining the nodes at the tower base and the tower top and then solving the eigenvector/value solution to find the “internal” vibration mode shapes.
There are two different type of modes that could be calculated for the boundary modes
- Attachment modes, which are calculated by applying unit forces and moments (6 in total) at the nacelle attachment node. These mode shapes tend to include a mixture of rotation and translation at the nacelle attachment node.
- Constraint modes, which are calculated by applying unit translations and rotations (6 in total) at the nacelle attachment node. In this case, when 1 DoF is activated, the other 5 are constrained to not move.
Bladed uses attachment modes rather than constraint modes. However, once the attachment modes are calculated, the shapes are transformed in order to achieve a diagonal stiffness matrix. For the rotational modes, this transformation results in mode shapes with very little translation at the nacelle attachment node, which look somewhat like constraint modes. This is a slightly confusing situation where some of the Bladed modes look like constraint modes, and some look like attachment modes.