Finite element dynamic modeling of elastic beam with prismatic joint

A finite element dynamic model of a translating beam through a prismatic joint is presented. The method adopts a fixed number of elements. The element length, on the contrary to the previously reported models, is constant. The time dependent nature of the boundary conditions is utilized to impose the prismatic joint constraints by varying the stiffness of the transition element. This method preserves all the dynamic coupling terms between the axial rigid body motion and the elastic deformations. The end mass dynamics is conveniently considered in the formulation. Furthermore, the introduced dynamic model offers a convenient formulation that can be incorporated into a general flexible multibody dynamics code and lends itself for control applications. The developed model is evaluated through comparisons with previously reported results of other models.