Deformation and flexibility equations for idealized ARIS umbilicals, under planar end-loading conditions

The International Space Station (ISS) relies on the Active Rack Isolation System (ARIS) as the central component of an integrated, station-wide strategy to isolate microgravity space-science experiments. ARIS uses electromechanical actuators to isolate an International Standard Payload Rack (ISPR) from disturbances due to the motion of the ISS. Disturbances to microgravity experiments on ARIS-isolated racks are primarily transmitted via the ARTS power and vacuum umbilicals. Recent experimental tests indicate that these umbilicals resonate at frequencies outside the ARIS controller's bandwidth, at levels of potential concern for certain microgravity experiments. Reduction in the umbilical resonant frequencies could help to address this issue. This report develops equations for the in-plane deflections and flexibilities of an idealized umbilical (thin, flexible, cantilever beam) under end-point, in-plane loading (inclined-force and moment). The effect of gravity is neglected due to the on-orbit application. The analysis assumes an initially straight, cantilevered umbilical with uniform cross-section, which undergoes large deflections with no plastic deformation, such that the umbilical terminus remains in a single quadrant and the umbilical slope changes monotonically. The analysis is applicable to the ARIS power and vacuum umbilicals, under the indicated assumptions.