Comparison of the Classical Formulation With the Reference Conditions Formulation for Dynamic Flexible Multibody Systems

Within the framework of the “floating frame of reference” formulation for dynamic flexible multibody systems, the separation of local and global motion is important. We compare the new approach with reference conditions as algebraic constraints with the classical one leading to a system of ordinary differential equations. The approach using reference conditions is motivated either from the need of keeping the error introduced when linearizing the elastic forces as small as possible (Buckens frame) or from minimizing the relative kinetic energy contained in the elastic deformations (Tisserand frame). The reference conditions impose algebraic constraints on the body level leading to a differential-algebraic equation (DAE) to be solved. The equivalence and the differences of the two approaches are shown. The index of the DAE system with reference conditions is shown to be either 2 or 1.