Nonlinear normal modes of nonuniform exible beams

Flexible beams contain geometric nonlinearities emanated from the large displacements and large rotations of the cross sections. When the geometry of the beam is nonuniform, the equation of motion becomes complicated to derive, but can be e(cid:30)ciently approximated using the co-rotational (cid:28)nite element method. This paper proposes a procedure to compute nonlinear normal modes (NNM) of nonuniform (cid:29)exible beams. The Rosenberg’s de(cid:28)nition of NNM is applied. The periodic solutions are computed using the Harmonic Balance Method (HBM) and the continuation of the modes properties with respect to the energy level is performed using the arc-length method. Examples of clamped-clamped beams with di(cid:27)erent cross sections variations are presented, illustrating the respective impacts in the NNMs.