Hydrodynamic loading and viscous damping of patterned perforations on microfabricated resonant structures

We examined the hydrodynamic loading of vertically resonating microfabricated plates immersed in liquids with different viscosities. The planar structures were patterned with focused ion beam, perforating various shapes with identical area but varying perimeters. The hydrodynamic loading of various geometries was characterized from resonant frequency and quality factor. In water, the damping increased linearly with the perimeter at 45.4 × 10 ^-3 Ns/m ², until the perforation's radius was 123% ± 13% of the depth of penetration of fluid's oscillation. The added mass effect decreased with perforations and recovered to the level of un-perforated structures when the perforation's radius became smaller than the depth of penetration.