Inner workings of BeamDyn and the GEBT - Prescribing root motion

[KenoOhrmann]

Dear all,

I am currently working on a nonlinear beam model written in Modelica. It is based on the same GEBT formulation from O.A. Bauchau's "Flexible Multibody Dynamics" as BeamDyn.

The implementation works well for beams which are fixed to a stationary root. To obtain a solution, it is sufficient to carry out the calculations that take place in BeamDyn in BD_DynamicSolutionGA2. The explicit linearization and the N-R algorithm can be skipped here. Dymola is able to solve the nonlinear governing equation of motion on its own.

Now the prescribed motion at the root of the beam should also be taken into account in my implementation. I hope to gain some insight into how BeamDyn incorporates the root motion of the blade. For this I would like to ask some questions:

1. Are the accelerations resulting from BD_CalcForceAcc necessary for the incorporation of the root motion? How do they differ from those calculated in BD_DynamicSolutionGA2 as part of the N-R algorithm?

2. In my understanding the GEBT formulation is not using a floating frame of reference approach. In this case, the states are "global" and solved in an inertial reference system that is not rotating with the blade. In BeamDyn.f90 line 4488, BD_BoundaryGA2 sets displacement, velocity and acceleration of the first node to values that can be obtained from the prescribed root motion. In the following function call to BD_DynamicSolutionGA2 in line 4704, the displacement of the first node is overwritten and set to 0. This looks to me like a floating frame of reference approach, where the states are resolved in the root reference system of the blade. I think I need some clarification on the role of BD_BoundaryGA2 and the meaning that the prescribed values in the first node have for the N-R algorithm.

3. If my questions are too specific, maybe you can give me an explanation of the general idea behind the incorporation of the root motion into the GEBT formulation of BeamDyn?

Thank you in advance!