Dynamics of sliding geometrically-exact beams: Large angle maneuver and parametric resonance (Q1913207)

We present the dynamic formulations for sliding beams that are deployed or retrieved through prismatic points. The beams can undergo large deformation, large overall motion, with shear deformation accounted for. Until recently, the sliding beam problem has been tackled mostly under small deformation assumptions, or under quasi-static motion. Here we employ geometrically-exact beam theory. Two theoretically-equivalent formulations are proposed: A full Lagrangian version, and an Eulerian-Lagrangian version. A salient feature of the problem is that the equations of motion in both formulations are defined on time-varying spatial domain. A Galerkin projection is then applied to discretize the resulting governing partial differential equations.