Attenuation of noise and vibration at low frequencies using a nonlinear microstructured material

Because of their large wavelength, the acoustic waves and mechanical vibrations at low frequencies cannot easily be reduced in the structures by using dissipative porous materials (like fiberglass) contrarily to the waves at middle and high frequencies. We propose to reduce the noise and the vibrations on a broad low-frequency band through a microstructured material by inclusions that are randomly arranged in the material matrix (which is also structural). The inclusions will have a dynamical behaviour which will be imposed in the nonlinear domain in such a way that the energy be efficiently pumped over a broad frequency band around the resonance frequency. Indeed, the nonlinearity leads to a pumping of the energy over a broader frequency band than the linearity. The first step of this work is to design and to analyze the efficiency of an inclusion, which is made up of a hollow frame including a point mass centered on a beam. This inclusion is designed in order to exhibit nonlinear geometric effects in the low-frequency band that is observed. For this first step, the objective is to develop the simplest mechanical model that has the capability to nearly predict the experimental results that are measured. The second step, which is not presented in the paper, will consist in developing a more sophisticated nonlinear dynamical model of the inclusion. In this paper, devoted to the first step, it is proved that the nonlinearity induces an attenuation on a broad frequency band around the resonance, contrarily to its linear behavior for which the attenuation is only active in a narrow frequency band around the resonance. We will present the design in terms of geometry, dimension and materials for the inclusion, the experimental manufacturing of this system realized with a 3D printing system, and the experimental measures that have been performed. We compare the prevision given by the stochastic numerical model with the measurements. The results obtained exhibit the physical attenuation over a broad low-frequency band, as intended.