Vibration of microperforated plate with spatial distribution of multiple-sized perforations

Recent works by the authors on homogeneous MPPs have highlighted the structural damping capabilities of MPPs in the low frequency range. The developed theoretical approach was based on the analogy between an MPP and a porous plate. The added damping is due to visco-thermic effects coupled to fluid-structure interactions. The added damping maxes out at a characteristic frequency depending on perforation diameter. In order to reduce plate vibrations, it was advised to match the characteristic frequency to a plate mode. It is proposed here to maximize the added damping effect on several vibration modes by focusing on MPPs with multiple-sized perforations and with spatial distribution of perforations. As an extension of the previous analytical model, an approach based on the electro-acoustic analogy is established to capture the effect of multiple-sized perforations. Moreover, a perforation ratio gradient is included in the approach to model an MPP with inhomogeneous spatial distribution of perforations. Experimental measurements on MPPs validate the proposed analytical model. Results show that: (i) MPP with multiple-sized perforations increases the frequency band of the effective damping; (ii) the added damping increases when the perforations are distributed around the antinodes of the considered mode, (iii) the two effects can be combined.