Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces I: Non-linear model and stability analysis

The stability of a cantilever elastic beam with rectangular cross-section under the action of a follower tangential force and a bending conservative couple at the free end is analyzed. The beam is herein modeled as a non-linear Cosserat rod model. Non-linear, partial integro-differential equations of motion are derived expanded up to cubic terms in the transversal displacement and torsional angle of the beam. The linear stability of the trivial equilibrium is studied, revealing the existence of buckling, flutter and double-zero critical points. Interaction between conservative and non-conservative loads with respect to the stability problem is discussed. The critical spectral properties are derived and the corresponding critical eigenspace is evaluated.