Axial Force Stabilization of Transverse Vibration in Pinned and Clamped Beams

An axial force stabilizes the transverse vibration of a beam with pinned and/or clamped boundary conditions. The nonlinearly coupled, longitudinal and transverse equations of motion of the beam with axial force control are simplified using a quasistatic assumption for longitudinal motion. It is shown that axial damping can ensure weak asymptotic stability of transverse vibration.