Investigation of viscous damping in perforated MEMS devices

Perforated structures are widely employed in MEMS devices for dissipation control, energy absorption, and performance optimization. Among these, the damping weakening effect is particularly intriguing, attracting considerable attention and widespread application. Evaluating the impact of perforations on damping is crucial for enhancing the performance of MEMS devices. This paper investigates the damping tuning mechanisms of perforations and presents two theoretical models for accurately predicting viscous damping. The two models exhibit unique advantages under high and low perforation ratios, respectively. Both models account for complex boundary conditions and various hole geometries, including cylindrical, conical, prismatic, and trapezoidal holes. Modeling and simulations demonstrate the complementarity of the two models, enabling accurate viscous damping predictions across nearly all perforation ratios. Subsequently, the theoretical models are validated through a series of vibration tests on perforated oscillators, with errors consistently controlled within 10%. Experimental results demonstrate that perforations can easily achieve a damping reduction of more than one order of magnitude. Moreover, compared to normal cylindrical holes, trapezoidal holes are found to achieve superior damping reduction with a smaller sacrifice in surface area, which holds great potential for capacitive, acoustic, and optical MEMS devices. This work lays the foundation for viscous damping design and optimization of MEMS device dynamics, creating new applications.