On selecting assumed modes in a controlled articulated flexible multibody dynamics system

The modeling and simulation of controlled-articulation flexible multibody dynamic systems often involves the use of approximating functions, or assumed modes, to represent the structural characteristics of the constituent component bodies. However, clear and complete guidance on appropriate component body modeling techniques is lacking. As a result, researchers and applications engineers encounter severe and unexplained numerical problems when simulating such systems. Earlier studies demonstrated these problems, explained their causes, and developed modeling guidelines from the perspective of accuracy, robustness, and simulation efficiency. In this study, the guidelines are tested and confirmed for a controlled-articulation flexible multibody dynamic system. In support of this effort, exact closed-form and numerical solutions are developed for the small elastic motions of a planar, flexible, two-link system in which each link is represented by an Euler-Bernoulli bar in transverse vibration. The inboard link is pinned to the ground, and the outboard link is pinned to the outboard end of the first link in an arbitrary configuration. Articulation is controlled by proportional and proportional/derivative feedback control laws. The exact solutions are "truth models" for the linear characteristics of an analogous non-linear large articulation model in which link deformations are represented by assumed modes. Using a linearized version of the non-linear large-articulation model as an assumed modes testbed, the modeling guidelines are tested against the exact solutions. The numerical results conform with expectation, and the efficacy of the guidelines is successfully confirmed.