Nonlinear normal modes of nonuniform exible beams

Gustavo Wagner, Roberta Lima, Rubens Sampaio


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 eficiently approximated using the co-rotational nite element method. This paper proposes a procedure to compute nonlinear normal modes (NNM) of nonuniform exible beams. The Rosenberg's definition 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 dierent cross sections variations are presented, illustrating the respective impacts in the NNMs.


Nonuniform exible beams; Nonlinear normal modes; Co-rotational nite element; Harmonic Balance Method

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