DYNAMICS OF SLIDING GEOMETRICALLY-EXACT BEAMS - LARGE-ANGLE MANEUVER AND PARAMETRIC RESONANCE

We present the dynamic formulations for sliding beams that are deploye d or retrieved through prismatic joints. The beams can undergo large d eformation, large overall motion, with shear deformation accounted for . Until recently, the sliding beam problem has been tackled mostly und er small deformation assumptions, or under quasi-static motion. Here w e 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 equa tions of motion in both formulations are defined on time-varying spati al domain. This feature raises some complications in the computational formulation and computer implementation. We discuss in detail the tra nsformation of the equations in the full Lagrangian formulation from a time-varying spatial domain to a constant spatial domain via the intr oduction of a stretched coordinate. A Galerkin projection is then appl ied to discretize the resulting governing partial differential equatio ns. Even though the system does not have any rotating motion as in gyr oscopic systems, the inertia operator has a weak form that can be deco mposed exactly into a symmetric part and an anti-symmetric part. The d istinction between the full Lagrangian formulation and the Eulerian-La grangian formulation from the computer implementation viewpoint is ind icated. Several numerical examples - 'spaghetti/reverse spaghetti prob lem,' beam under combined sliding motion and large angle maneuver, par ametric resonance - are given to illustrate the versatility of the pro posed approach. The results reveal a rich dynamical behavior to be exp lored further in the future.