Abstract
The floating frame of reference formulation is an established method for the description of linear elastic bodies within multibody dynamics. An exact derivation leads to rather complex equations of motion. In order to reduce the computational burden, it is common to neglect certain terms. In the literature this is done by strict application of the small deformation assumption to the kinetic energy. This leads to a remarkably simplified set of equations. In this work, the significance of all terms is investigated at the level of the equations of motion. It is shown that for a large number of applications the previously mentioned set of simple equations is sufficient. Furthermore, scenarios are described in which this simple set is no longer accurate enough. Finally, guidelines are provided, so that engineers can decide which terms should be considered or not. The theoretical conclusions drawn in this work are underlined by qualitative numerical investigations.
Highlights
The floating frame of reference formulation (FFRF) is a widely used strategy for the inclusion of a flexible body into multibody system dynamics
The third benefit is that negligence of the terms including W 1, W 2 and W 3 leads to equations of motion where the mass matrix and the quadratic velocity vector are decoupled with respect to the translational, rotational and flexible degrees of freedom
In this work the significance of all inertia related terms of a flexible body in the FFRF were investigated at the level of the equations of motion
Summary
The floating frame of reference formulation (FFRF) is a widely used strategy for the inclusion of a flexible body into multibody system dynamics. All inertia related terms of a flexible body in the FFRF are investigated on the level of the equations of motion with respect to their relevance. It is shown why the simplest possible formulation, stemming from the strict application of the small deformation assumption at the level of the kinetic energy, is sufficient for many applications. A clear guidance will be given when, in addition, the deformation dependent inertia tensor, inertia coupling, or elastic deformation related parts of the centrifugal and Coriolis forces should be considered This will be summarized in a “set of guidelines”. The paper will be concluded by summarizing the benefits when certain terms of the equations of motion can be neglected
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