A comparison of reference conditions in floating frame formulations that use absolute interface coordinates

This study identifies and compares various reference conditions used to define floating frame of reference formulations in terms of absolute interface coordinates. Transforming from the generalized coordinates of the floating frame and the local elastic coordinates describing the mode shapes to absolute interface coordinates eliminates the need for Lagrange multipliers to incorporate kinematic constraints. If the reduction basis can describe rigid body motion (e.g. Craig-Bampton modes), inclusion of reference conditions which eliminate the rigid body motion from the elastic deformation is required to obtain a unique coordinate transformation. Three well-established reference conditions define the floating frame as: (1) attached to the node at the center of mass of the undeformed body, (2) attached to an interface node and (3) a weighted average of the variations of the absolute interface coordinates. The choice of reference conditions impacts the accuracy and computational cost of the resulting formulation. However, the selection is complicated by the independent derivations of the formulations and the absence of comparisons between them. In this work, the result of the derivation of the equations of motion in terms of absolute interface points are shown for each reference condition such that the formulations differ only in the implemented transformation matrices. As such, the relation between the reference conditions is illuminated. The accuracy and computational efficiency of the formulations are compared using a variation of a three-dimensional slider crank benchmark problem, providing an insight into their relative merits.