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Pré-Publication, Document De Travail Année : 2019

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

Résumé

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.
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Dates et versions

hal-02305325 , version 1 (04-10-2019)

Identifiants

  • HAL Id : hal-02305325 , version 1

Citer

Aurelien Grolet. On a model reduction method for computing forced response using non-linear normal modes. 2019. ⟨hal-02305325⟩
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