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/m2, 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. We acknowledge the support of National Science Foundation (NSF) Grant No. EEC-0425626 (NSF Nanoscale Science and Engineering Center at Ohio State University to R.B.), NSF Grant No. CBET-0939511 (R.B.), and funding support from UIUC. E.A.C. was funded at UIUC from NSF Grant No. 0965918 IGERT: training the next generation of researchers in Cellular and Molecular Mechanics and BioNanotechnology. We thank Dr. Larry J. Millet at University of Illinois at Urbana-Champaign for his valuable suggestions.