On a model reduction method for computing forced response using non-linear normal modes

This paper presents a method for constructing reduced order models using non-linear normal modes (NNM) in the context of non-linear vibrations. Starting from a discretised version of the non-linear problem, the non-linear normal modes (NNM) of the structure are computed using the Harmonic Balance Method (HBM). A two parameters (amplitude and phase) parametrization of the NNM is introduces and they are then used for the forced response construction, assuming that the solution involves only a single (non-linear) resonant mode. The solution is then eventually corrected by linear terms which helps decreasing the error outside resonance , in particular around anti-resonances. The procedure results in two algebraic equations containing only two variables, one controlling the amplitude of vibration and the other controlling the phase, thus leading to a drastic reduction in the number of degrees of freedom. The procedure is illustrated on a simple, but representative, example. It is shown that a single mode approximation is sufficient for computing a good approximation of the forced response around a particular mode