Added Viscous Damping in Microperforated Plates Within a Nonlinear Acoustic Regime

Résumé

Microperforated plates (MPPs) are simple systems, classically used for their acoustic absorption capabilities. Recent works by the authors have shown that MPPs feature added viscous damping in the low-frequency range. Energy dissipation occurs through viscous friction mechanisms in the boundary layers of the microperforations coupled with fluid-solid interactions, which results into added viscous damping in a solid dynamics context. The vibratory response of such systems is well captured through an ad-hoc homogenization procedure, which yields two coupled partial differential equations (PDEs) governing the dynamics of a structural plate and a virtual plate of fluid. It was shown that the added damping reaches a maximum at a characteristic frequency, which only depends on the perforation diameter. However, these systems, likely to be used in hostile environments such as aircraft turbines, are known to be sensitive to mechanical and/or acoustic excitation levels. Two non-linear regimes of interest can be identified: (i) a non-linearity induced by high fluid flow, and (ii) a non-linearity induced by high fluid flow along with large structural displacement. In the present work, only the first configuration is considered. As the fluid velocity in the perforations increases, inertial phenomena occur in the perforations which affect the response of the structure. These effects can be captured analytically by introducing the Forchheimer correction, which depends on the relative fluid-solid velocity. This correction arises as an antisymmetric quadratic damping term in one of the above PDEs. The latter are solved numerically and quantitative studies are performed on the sensitivity of added damping to the excitation level. The proposed model is validated by experiments performed on a cantilevered MPP. Analytical and experimental results suggest that the added viscous damping depends on the relative fluid-solid velocity. The added damping effect can reach a maximum for a critical value, with all other independent parameters fixed.