Nonlinear bending vibrations of a rotating rod

The vibrations of a rod with a circular cross section revolving around its axis with immovable supports in the longitudinal direction are examined. A harmonic load orthogonal to the longitudinal axis and located in a plane rotating jointly with it acts on the rod. The geometrical nonlinearity caused by medial line length variation is taken into account. For free oscillations, three solutions are found for amplitude-frequency dependences and the corresponding modes. In the neighborhood of the principal resonance, the dependences between oscillation amplitudes in orthogonal planes and the angular velocity of rotation under constant frequency of the load are constructed.