Abstract
At low frequencies, for which the wavelengths are wide, the acoustic waves and the mechanical vibrations cannot easily be reduced in the structures at macroscale by using dissipative materials, contrarily to the middle- and high-frequency ranges. The final objective of this work is to reduce the vibrations and the induced noise on a broad low-frequency band by using a microstructured material by inclusions that are randomly arranged in the material matrix. The dynamical regimes of the inclusions will be imposed in the nonlinear domain in order that the energy be effectively pumped over a broad frequency band around the resonance frequency, due to the nonlinearity. 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 roughly 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 computational model with the measurements. The results obtained exhibit the physical attenuation over a broad low-frequency band, which were expected.
Highlights
Among the first papers devoted to the energy pumping by simple oscillators, the works by Frahm [1] and by Roberson [2] can be cited
The final objective of this work is to reduce vibrations and induced noise on a broad low-frequency band by using a microstructured material by inclusions that are randomly arranged in the material matrix
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 behaves as a nonlinear oscillator that is designed in order that the energy pumping be efficient on a broad frequency band around its resonance instead of a narrow frequency band as for a linear oscillator
Summary
Among the first papers devoted to the energy pumping by simple oscillators, the works by Frahm [1] and by Roberson [2] can be cited. 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 behaves as a nonlinear oscillator that is designed in order that the energy pumping be efficient on a broad frequency band around its resonance instead of a narrow frequency band as for a linear oscillator. The experiments yield for the Young modulus, 2.2 × 109 P a and for the Poisson coefficient 0.35 This inclusion has been designed in order that the first eigenfrequency of the frame be around 1, 200 Hz and the first eigenfrequency of the inclusion (point mass and beam) be around 167 Hz. We are interested in analyzing the stationary random response of the inclusion in the frequency band of analysis Ba = [−fmax, fmax] with fmax = 1, 024 Hz, induced by the stationary random excitation generated by an imposed acceleration of the two ends supports of the beam.
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