Full Beam Formulation for Coupled Elastic and Rigid Body Motion

The need for higher operating speeds has led to the study of flexibility in mechanisms. In most of the previous works, rotary inertia, normal, tangential and coriolis terms are neglected. These assumptions are valid at lower speeds and for slender links. In this paper, a procedure to include all inertia terms in a local moving coordinate system is introduced. It is shown that the inertia terms lead to the introduction of three element matrices in the finite element formulation. The proposed approach is used to model the rotating beam problem. The results of a numerical solution is reported and validated.