Flexural–torsional bifurcations of a cantilever beam under potential and circulatory forces II. Post-critical analysis

Abstract

The post-critical behavior of a cantilever beam with rectangular cross-section, under simultaneous action of conservative and non-conservative loads, is analyzed. An internally constrained Cosserat rod model is adopted to describe the dynamics of the beam in finite displacement regime. The bifurcation equations for simple buckling (divergence), simple flutter (Hopf) and double-zero (Takens–Bogdanova–Arnold) bifurcations are derived by means of the multiple time scales method. Due to the nilpotent eigenvalue at the double-zero critical point, the evaluation of the generalized Keldysh's eigenfunctions is required. Finally, some numerical results are shown and the bifurcation scenario of the beam is discussed.