Stability analysis for nonplanar free vibrations of a cantilever beam by using nonlinear normal modes

Stability analysis of nonplanar free vibrations of a cantilever beam is made by using the nonlinear normal mode concept. Assuming nonplanar motion of the beam, we introduce a nonlinear two-degree-of-freedom model by using Galerkin’s method based on the first mode in each direction. The system turns out to have two normal modes. Using Synge’s stability concept, we examine the stability of each mode. In order to check the validity of the stability criterion obtained analytically, we plot a Poincaré map of the motions neighboring on each mode obtained numerically. It is found that the maps agree with the stability criterion obtained analytically.