Analytical modeling of a MEMS beam resonator with release-etch holes

Abstract

In this study, a simplified reduced-order modeling scheme is developed to determine the resonant frequency of a doubly clamped beam microelectromechanical system resonator with square release-etch holes. New formulations of the effective bending and shear stiffnesses are proposed and applied to the Timoshenko beam equations. The model is validated by comparison with finite element analysis results. The results show that the model can achieve a high accuracy for a wide range of dimensions. In conclusion, the developed model is expected to contribute to reduced-order modeling of microelectromechanical systems devices.

Dynamic response of the micro-perforated crab beam used in MEMS vibratory gyroscope device

“…To consider the influence level of the cutout holes in the whole structure, the fill factor is mentioned as the ratio of hole size (w or d) to meshed grid l [8], [11].…”

“…To find out the resonant frequencies of the single beams considered Timoshenko beams [10,11], their dynamic equations are written as follows [12]:…”

“…The single beam is considered and calculated by using Euler Bernoulli or Timoshenko beam theory based on assumptions that the total induced stress throughout the cross section is the same for both fully filled and the corresponding perforated one and the stress distribution throughout the filled segment in the perforated nanobeam is assumed to be linear and continuous [10][11][12]. Some different types of beams were also considered based on this approach to define their dynamic characteristics in the vibration problem.…”