Reference Conditions and Substructuring Techniques in Flexible Multibody System Dynamics

The floating frame of reference (FFR) formulation is widely used in multibody system (MBS) simulations for the deformation analysis. Nonetheless, the use of elastic degrees-of-freedom (DOF) in the deformation analysis can increase significantly the problem dimension. For this reason, modal reduction techniques have been proposed in order to define a proper set of assumed body deformation modes. Crucial to the proper definition of these modes when the finite element (FE) FFR formulation is used is the concept of the reference conditions, which define the nature of the deformable body coordinate system. Substructuring techniques, such as the Craig-Bampton (CB) method, on the other hand, have been proposed for developing efficient models using an assembly of their lower order substructure models. In this study, the appropriateness and generality of using the CB method in MBS algorithms are discussed. It is shown that, when a set of reference conditions are not applied, the CB transformation leads to the free-free deformation modes. Because a square CB transformation is equivalent to a similarity transformation that does not alter the problem to be solved, the motivation of using the CB method in MBS codes to improve the solution is examined. This paper demonstrates that free-free deformation modes cannot be used in all applications, shedding light on the importance of the concept of the FE/FFR reference conditions. It is demonstrated numerically that a unique model resonance frequency is achieved using different modes associated with different reference conditions if the shapes are similar.