Reduced dynamics of a nonlinear exact rod is derived by restricting the coupled nonlinear equations of motion onto Proper Orthogonal Modes (POD) identified by a Proper Orthogonal Decomposition of the finite element approximation to the dynamics. For the case of a dominant POD mode, the reduced dynamical system is a geometrically exact nonlinear oscillator. Numerical integration reveals that the phase portrait of the reduced system, for the case of zero dissipation, has Hamiltonian structure. For harmonic forcing at low frequencies, the reduced system predicts exceptionally well the dynamics of the nonlinear rod over a wide range of forcing amplitude. For forcing frequencies in the order of the fundamental frequency for linear bending motions, the reduced model predicts very well the qualitative changes of the dynamics but it underestimates the critical parameters at which the qualitative changes occur at high levels of forcing amplitudes. It is conjectured that the reduced model stemming from the restriction of the full order system onto a single dominant POD describes the dynamics of a nonlinear normal mode of vibration. The POD method can be used to identify the normal modes of vibration of coupled systems with complicated nonlinearities.

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