Gesing, A., Tran, T., Huber, D., Steinmüller-Nethl, D., Pfusterschmied, G., Schneider, M., Platz, D., & Schmid, U. (2023). The gas-liquid-Q-factor-inversion in MEMS plate resonators. Journal of Sound and Vibration, 559, Article 117777. https://doi.org/10.1016/j.jsv.2023.117777
We present a semi-numerical method for solving the dynamics of microplates in viscous fluids. The method is based on the Kirchhoff plate equation with a hydrodynamic force deduced from the Stokes equations. The equation of motion is solved with the Galerkin mode decomposition (GMD) using the vacuum vibrational modes of cantilevered microplates as the basis functions. We investigate the Q-factor of the vibrational modes of microplate-resonators in gases and liquids. In gases, the Euler–Bernoulli (EB) modes (modes with nodal lines only along the plate's width) exhibit the lowest Q-factors, while non-EB modes exhibit the highest Q-factors. In liquids, the opposite is found. EB modes exhibit the highest Q-factors, and non-EB modes lower Q-factors. We name this opposite Q-factor pattern in gases and liquids the gas-liquid-Q-inversion (GL-Q-inversion). Experiments in water and air showed a Q-factor agreement with the GL-Q-inversion, and differences in Q-factor between simulation and experiments were below 25%. Further numerical analysis reveals the physical mechanism underlying the GL-Q-inversion in terms of the system's stored and dissipated energy. The results and methods shown here will pave the way to efficiently exploit the two-dimensional vibrational modes of microplate-resonators to improve their performance in gaseous and liquid environments.
