Modelling out-of-plane and in-plane resonant modes of microplates in liquid media

Abstract

In this article, the quality factor and the resonant frequency of different vibrating modes of microplates immersed in liquid are simulated by means of a finite element method (FEM) and compared with experimental data. For the in-plane modes, we studied the first extensional mode of mid-point supported microplates, which may be efficiently actuated by a thin piezoelectric film on top of the structure. A comparison of different approaches to account for the viscous loading in computationally efficient 2D finite element models is presented. As an alternative to the harmonic response, a novel multitone excitation in the fluid–structure interaction model allows for the calculation of the frequency response of the structure. For the out-of-plane modes, different modes were simulated and compared to analytical models to validate our approach. Our 2D FEM model yields more accurate estimations of the experimental resonance frequency and quality factors than the available analytical models. With the help of these tools, the applicability of the micro-resonators as viscosity and density sensors is discussed.