An efficient formulation for flexible multibody dynamics using a condensation of deformation coordinates

Abstract

This paper introduces a more efficient formulation for flexible multibody dynamics based on the floating frame of reference formulation (FFRF). A two-step condensation method is proposed. The first condensation involves coordinate reduction using a modal transformation, from nodal coordinates to modal coordinates, in the context of model order reduction (MOR). The second condensation involves re-fabrication of the equations of motion using a dynamic condensation of the deformation modal coordinates obtained from the first condensation. In the first condensation, constraint modes are corrected by condensation of the truncated modes that represent the effects of residual flexibility. As a result, the first condensation offers a more accurate deformation field in the reduced order model, which consequently leads to a more accurate flexible multibody simulation. In the second condensation, the equations of motion of a flexible multibody are once more reduced to the equations of motion in terms of absolute coordinates for the body reference frames. In this way, the proposed method deals with smaller sized equations of motion than in the conventional FFRF, where they are represented in terms of both absolute coordinates and deformation modal coordinates. The effect of the first condensation was verified using a benchmark example of a slider–crank mechanism with a flexible connecting rod. The efficiency of the proposed condensation method was also investigated using a computational complexity analysis with an $n$ -flexible body pendulum.