Dynamics of the Elastica With End Mass and Follower Loading

Orthotropic, polymeric tubes subjected to internal pressure may undergo large deformations while maintaining linear moment-curvature behavior. Such tubes are modeled herein as inertialess, elastic cantilever beams (the elastica) with a payload mass at the tip and with internal pressure as the eccentric tip follower loading that drives the configurations through large deformations. From the nonlinear equations of motion, dynamic beam trajectories are calculated over a range of system parameters for the special case of a point mass at the tip and a terminated ramp pressure loading. The dynamic responses, which are unique because the loading history and the range of motion are fully defined, are presented in nondimensional form and are compared to static responses presented in a companion study. These results are applicable to the dynamic design of high flexure, tube-type, robotic manipulator arms.