Identification of the parameters of a simplified 2 degree of freedom model of a nonlinear vibroacoustic absorber coupled to an acoustic system in linear and nonlinear forced regimes

This article presents a method for identifying the parameters of a simplified 2 degree of freedom model representative of a linear primary system coupled to a non-linear absorber in a forced harmonic regime over a wide range of amplitudes and forcing frequencies covering different dynamical regimes. This is a priori a difficult operation because it is necessary to combine two apparently contradictory steps. The first step consists in establishing models representing the physics of the system which are analytically soluble, which imposes severe approximations. The second step consists in adjusting the parameters of the models to experimental data, which reveal some phenomena ignored by the models. To do so, two approximate analytic methods, Harmonic Balance and Complexification Averaging under 1:1 resonance, are used to describe the dynamics of the nonlinear system for its different operating regimes: linear behavior, nonlinear behavior without energy pumping, energy pumping, and saturation regime. Then, using a non-linear regression, the parameters of the simplified model are identified from experiments. The values obtained correspond to the expected physical quantities.