Flexible multibody dynamics based on a non-linear Euler-Bernoulli kinematics

This paper presents a new dynamic model of a multi-beam system in the oating-frame approach. The proposed solution can be used to model light exible manipulators in fast dynamic conditions or large space structures undergoing moderate but nite deformations. The model is based on the non-linear Euler–Bernoulli kinematics proposed in J. Mech. Mach. Theory 1999; 34:205. From this ‘exact’ kinematics we develop two approximate models. The rst one is a linear model with respect to the deformation parameters, the second is a quadratic one. These two models capture the dynamic sti ening, and are consistent in the sense that they contain all the terms up to their maximal order with respect to the energy conservation. These two models are tested by simulation and compared with the standard oating frame model based on linear elastic kinematics and with the nite element codes of Reference [23] (Module d’analyse de m ecanismes exibles MECANO: Manuel d’utilisation. LTAS report, University of Liege, Belgium, 1988).