A fully symbolic generation of the equations of motion of multibody systems containing flexible beams

The modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multibody dynamics and the area of structural mechanics and vibration theory. A multibody approach using a recursive formalism in relative coordinates is adopted here. While leading to a highly non-linear system with a dense mass matrix, relative coordinates allow the setting up of the minimal set of equations of motion for open-loop systems. As for the recursive technique, the latter was proved to be a very good candidate for an optimized symbolic generation in the case of rigid multibody systems. These two assertions have led us to generalize such a formalism for a general multibody system containing flexible beams, in order to make its fully symbolic generation possible within the stand-alone program ROBOTRAN [1]. Several validation examples are presented to illustrate the method and to highlight the efficiency and the user-friendliness of this fully symbolic model, even when dealing with beams undergoing large motions.