Vibration et vibroacoustique de structures microperforées - Effet de l’amortissement visqueux ajouté sous faible et fort niveaux d’excitation

Abstract

Low-frequency (LF) vibrations and the resulting noise, are an environmental problem, particularly when mechanical excitations are of high amplitude. Current trends, particularly in the transport sector, are aimed at lightening and optimizing the overall dimensions of mechanical systems, with a view to reducing energy consumption. However, these objectives are not compatible with conventional methods of noise and vibration reduction (viscoelastic materials, dynamic dampers), which add significant mass to the structure and may, in some cases, be inefficient in terms of LF. The aim of this thesis is to address this issue by examining the vibratory and vibro-acoustic behavior of microperforated structures and the added damping effect induced by microperforations. In the first part, the added damping properties of finite-size microperforated plates (MPP) are studied for low-amplitude excitations. Based on a homogenized procedure derived from the field of porous plates and extended to MPP, an analytical vibration model is proposed. This model assumes that the fluid contained in the perforations acts as an equivalent fluid seen as a continuum defined on the domain of the non-perforated plate. The equations governing the dynamics are reduced to two coupled Partial Differential Equations (PDEs), written according to the bending displacement of the plate and that of the equivalent fluid. The proposed model is validated by measurements on microperforated beams. It is shown that microperforated plates can exhibit substantial added damping in BF resulting from fluid-structure interactions and viscothermal effects in the perforation boundary layers. Parametric studies show that i) this damping reaches a maximum for a characteristic frequency that depends on the perforation diameter, and ii) the lower this frequency, the greater the added damping. To reduce the contribution of a vibratory mode, it is therefore recommended to match the characteristic frequency to that of the mode by adjusting the diameter of the microperforations. In the second part, to improve the damping properties of MPP, it is proposed to study the vibratory behavior of MPP with inhomogeneous microperforations. Thus, the analytical model previously established has been adapted for i) MPP with multiple perforation diameters and for ii) MPP with different spatial perforation distributions. It is shown that i) MPP with multiple perforation sizes exhibit added damping over a wider frequency band, and ii) the added damping is increased when the perforations are distributed over the antinodes of the modes considered. Thus, by coupling the two effects, it is possible to obtain MPP that effectively reduce vibration responses over multiples modes. MPP are potentially used in extreme environments (aircraft engines, rocket nacelles). However, their vibratory behavior is sensitive to excitation amplitude. It is therefore proposed, in this third part, to extend the study to a non-linear framework. As the level of excitation amplitude increases, two non-linear regimes emerge : i) the first is related to the fluid and therefore essentially induced by fluid-structure coupling within the microperforations, ii) then, the second is related to the solid (large deformations) and the fluid. Only the first non-linearity is studied here. Thus, the nonlinear behavior of the fluid in the perforations is taken into account by introducing a Forchheimer correction into the previously developed model, leading to a nonlinear PDE system with an added damping term. After numerical resolution, it is shown that the damping maximum varies with the relative fluid-solid velocity and that, depending on the value of the linear resistance, this damping maximum can reach a maximum value for a critical value of relative fluid-solid velocity. Experimental measurements validate the model. Finally, it is proposed to use the homogenized model previously developed in a linear framework to analyze the influence of microperforations, including the effect of added damping, on the acoustic radiation of an MPP. An analytical radiation model is developed and compared with a numerical finite element approach.

Date	29 Jun 2024
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Thomas Dupont (Supervisor), Philippe Leclaire (Co-supervisor) & Mathias Legrand (Co-supervisor)