Asymmetric post-flutter oscillations of a cantilever due to a dynamic follower force

Flutter instability of a cantilever beam subjected to a follower force of constant magnitude is well understood: the beam oscillates with increasing amplitude when the force is larger than the critical load. Post-flutter analysis, similar to previous efforts, shows that the addition of damping results in steady-state oscillations. These oscillations are symmetric, but addition of a slope-dependent term to the magnitude of the follower force results in asymmetry. These asymmetric oscillations are investigated in this paper: the Ritz–Galerkin method is used to obtain a finite degree-of-freedom model of the cantilever and the method of multiple scales is used to analytically predict the amplitude and asymmetry of the oscillations. Numerical simulation results indicate a close match with analytically predicted results.