Flexible body dynamics in a local frame with explicitly predicted motion : FLEXIBLE BODY DYNAMICS

This paper deals with formulation of dynamics of a moving flexible body in a local frame of reference. In a conventional approach the local frame is normally fixed to the corresponding body and always represents the positions and angles of the body: the positions and angles are represented by Cartesian coordinates and Euler angles or Euler parameters, respectively.

The elastic degrees of freedom are expressed by, e.g. nodal coordinates in a finite element analysis, modal coordinates, etc. However, the choice of these variables as the generalized coordinates makes the resulting equations of motion extremely complicated. This is because the representation of the rotation of a body is highly non-linear and this non-linearity makes the coefficient matrices dependent on the coordinates themselves.

In this paper, we propose an alternative way of treating the issue by explicitly predicting the body motions and regularly updating the local frame. First, the motion of the local frame is assumed to explicitly follow the associated moving body. Then, the equations of motion are derived in a set of generalized coordinates that express both rigid-body and elastic degrees of freedom in the local frame.

These equations are solved by a time integration with a given time interval. The motion of the local frame in the interval is estimated from a prediction of the rigid-body motions. Then, the gap between the predicted and the actual motions is evaluated. Finally, the predictions are iteratively corrected by the obtained responses in the rigid-body motions so that the gap should remain within an imposed tolerance.