Vibration and damping analysis of a thin finite-size microperforated plate

Abstract

Microperforated plates (MPP) are commonly used to absorb acoustic waves in sound control technologies. However, less is known concerning the added damping exhibited by thin finite-size MPPs. This added damping effect is known to be induced by viscous and thermal exchanges in the boundary layers near the fluid–solid interface of the perforations, which results in energy dissipation. The present work actually shows that MPPs can feature a significant added viscous damping, especially at low frequencies of vibration. An analytical approach based on an alternative form of the Biot theory for finite-size porous plates is developed. Parametric studies highlight the existence of a characteristic damping frequency at which the added damping of the perforations reaches a maximum. For specified boundary conditions, the damping level can be maximized by adjusting the geometrical parameters of the perforations (diameter, perforation ratio) so that the resonance frequency of the plate coincides with the characteristic damping frequency. The damping reaches a maximum at a particular frequency, and is also effective over a non-negligible bandwidth. Formulations on the mass density and Young’s modulus as a function of the perforation ratio are provided to address the sensitivity of mass and stiffness to the microperforations. The structural damping capabilities of MPPs are validated by measurements on finite-size MPPs which confirm the significant damping increase in the low-frequency range.