Coupling of bending and damping with axial motion for beams modeled with arbitrary Lagrangian–Eulerian formulation

This work investigates the influence of terms representing the coupling of bending stiffness and dissipative effects with axial motion for highly flexible beams modeled with an arbitrary Lagrangian–Eulerian (ALE) formulation. In the current work, axially moving beams undergoing large deformations are numerically modeled using an absolute nodal coordinate formulation (ANCF) and an ALE framework. In the resulting beam element model, an ANCF beam is extended by an independent axial (Eulerian) coordinate which models the axial motion. The influence of terms dependent on the axial coordinate appearing in the equations of motion is the focus of the present investigation. It is shown that the role of these terms is crucial in modeling problems involving large bending of axially moving beams. The consistency of the investigated ALE modeling with a conventional Lagrangian modeling is verified by comparisons of results obtained by reproducing numerical examples with the two modeling approaches. An exclusion of the axial-coordinate-dependent terms from the model highlights their significance in ALE modeling of beams with large bending deformations. Finally, obtained results show agreement to an analytical solution and a semi-analytical solution derived for the quasi-static and dynamic numerical example, respectively.