Dynamic analysis of a multibody system including a very flexible beam element

Abstract

In this paper, the dynamic behavior of a multibody system including very flexible beam elements is presented. The very deformable motion of a beam is demonstrated using absolute nodal coordinate formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between flexible beams and a rigid multibody system, a combined system equation of motion is derived using an absolute nodal coordinate and a rigid body coordinate. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example in this study. To do this, formulations for the sliding joint between a very flexible beam and a rigid body were derived using a non-generalized coordinate, which has no inertia or forces associated with it. This sliding joint is very important to many mechanical applications such as cable cars, pulley systems, and pantograph-catenary system for high-speed trains. In addition, a computation method for the dynamic stress in flexible multibody simulation using an absolute nodal coordinate is presented based on EulerBernoulli beam theory, and its reliability was verified by commercial program NASTRAN. Numerical examples are shown using the developed analysis program for flexible multibody systems that include a large deformable beam.