Finite element dynamic modeling of a translating and rotating flexible link

A finite element dynamic model for a translating and rotating beam is formulated. The developed model adopts a finite element mesh with a fixed number of elements, where the element length is constant. The time-dependent boundary conditions manifested by the prismatic joint constraints are considered. A transition element with variable stiffness is introduced at the interface with the joint hub. In this finite element formulation, all the inertia coupling terms between the beam reference motions and the local elastic deformations are considered. In addition, the model accounts for the dynamics of the end mass as well as the associated coupling effects. Numerical simulations and comparisons with results obtained by other methods are presented to demonstrate the validity and accuracy of the developed model.