Physical Experiments and Computer Simulations of a Stepped Cantilever Beam with a Hybrid Coordinate Formulation

Abstract

The modal coordinate formulation (MCF) has been used to describe small deformations, and the absolute nodal coordinate Formulation (ANCF) has usually been employed to describe large deformations in flexible multibody dynamics. In this article, a hybrid coordinate formulation (HCF) was suggested to combine the modal coordinates for small deformations with the absolute nodal coordinates for large deformations. The kinematic constraint equations for a spherical joint and the equation for two perpendicular vectors were developed with both coordinates and applied to other types of kinematic joints including a fixed joint. A stepped cantilever beam was tested to show the validity of the suggested hybrid formulation. Physical experiments with a high-speed camera were carried out to capture the large deformation of the beam and to verify the results of computer simulations. The numerical results obtained from the hybrid coordinates were compared with the results from the simulation using the absolute nodal coordinates only and physical experiments.