Non-linear hydrodynamic forces in opposite micro cantilever beams oscillating in viscous fluid

The present study investigates the nonlinear hydrodynamic forces in opposing microcantilever beams oscillating in a viscous fluid. Using FEM-based models solves complete Navier Stokes equations, we estimate the nonlinear damping and added mass forces at high oscillation frequencies due to convetive inertial forces and vortex formation at edges of the beams, considering both in-phase and out-of-phase conditions. Additionally, we calculate the inertial and drag forces using the semi-analytical boundary element method (BEM) by incorporating the unsteady Stokes equation. Our findings indicate a strong correlation between numerical and semi-analytical BEM results for small amplitude and up to 100kHz of frequency. This research is particularly significant for MEMS devices, where maintaining small gaps between opposing or substrate beams is crucial. We focus on key aspects such as added mass effects and damping effects (Quality factor), using both methods to compute the hydrodynamic coupling effects while ensuring no influence from surrounding walls. Our study reveals that the maximum effective gap for significant hydrodynamic coupling effects is 15 micrometers; beyond this gap, the coupling effects become negligible and sensitivity of the structre is invarient. Furthermore, we extend our analysis to non-uniform beams to explore nonlinear damping at small oscillation amplitudes, providing a comprehensive understanding of the dynamic behaviors in these systems.