Beyond 2D Flow Approximations in Modelling MEMS in Viscous Fluids by Use of the 3D Unsteady Stokeslet

Accurately modeling viscous fluid-structure interaction in MEMS remains a significant challenge in fluidic sensing and BioMEMS. We present a numerical method that couples the Kirchhoff plate equation with an efficient numerical integration of the unsteady Stokeslet, enabling fast and accurate simulation of MEMS resonators immersed in viscous fluids. The framework supports both 2D and full 3D Stokes flow formulations, incorporating GPU and PETSc acceleration for large-scale problems. Experimental validation using piezoelectrically actuated resonators demonstrates excellent agreement with the 3D model at frequencies below 500 kHz, revealing the frequency- and mode-dependent limits of conventional viscous-flow approximations at higher frequencies.