Identification of the damping coefficient of a NES in both linear and non-linear domains

International audienceIn order to have the targeted energy transfer in the acoustic domain, R. Bellet proposed a non-linear vibro-acoustic absorber constituted by a thin viscoelastic circular membrane coupled to the first resonance mode of an open tube through a coupling box and excited by an acoustic field provided by a loudspeaker. The membrane damping in the Bellet?s model is described in term of linear and quadratic viscous-like damping. The damping coefficient were obtained using identification in the linear case. The comparison between experiments and computation revealed that this description was not sufficient to capture all the feature of the very rich dynamics of this nonlinear system. We concluded a single value of the damping coefficient independent of the amplitude of the excitation, was the origin of this discrepancy. We decided to estimate the damping coefficient using the Bellet?s model in both linear and non-linear domains. For the estimation of this coefficient, a series of experimental tests was realized, in which the amplitude of the sinusoidal voltage applied at the terminal of the loudspeaker changed and the frequency is varied for each input level. This experiment lets the measure of the pressure in the middle of the tube by a microphone and the displacement of the membrane in its center by a displacement sensor. Moreover, following these tests we have developed a MATHEMATICA code that allows the nonlinear identification of the damping coefficient of the NES using the harmonic balance method. We present the estimated variation of the damping coefficient as a function of the excitation amplitude, wherein a sudden increase of the dissipation during the energy pumping is clearly observed. This clearly indicates that some dissipative phenomenon neglected in our model must be accounted for a better description of energy pumping over its completely functioning range