A Monolithic, FEM-Based Approach for the Coupled Squeeze Film Problem of an Oscillating Elastic Micro-Plate Using 3D 27-Node Elements

In this study we describe an FEM-based methodology to solve the coupled fluid-structure problem due to squeeze film effects present in vibratory MEMS devices, such as resonators, gyroscopes, and acoustic transducers. The aforementioned devices often consist of a plate-like structure that vibrates normal to a fixed substrate, and is generally not perfectly vacuum packed. This results in a thin film of air being sandwiched between the moving plate and the fixed substrate, which behaves like a squeeze film offering both stiffness and damping. Typically, such structures are actuated electro-statically, necessitating the thin air gap for improving the efficiency of actuation and the sensitivity of detection. To accurately model these devices the squeeze film effect must be incorporated. Extensive literature is present on mod- eling squeeze film effects for rigid motion for both perforated as well as non-perforated plates. Studies which model the plate elasticity often use approximate mode shapes as input to the 2D Reynolds Equation. Recent works which try to solve the coupled fluid elasticity problem, report iterative FEM-based solution strategies for the 2D Reynolds Equation coupled with the 3D elasticity Equation. In this work we present a FEM-based single step solution for the coupled problem at hand, using only one type of element (27 node 3D brick). The structure is modeled with 27 node brick elements of which the lowest layer of nodes is also treated as the fluid domain (2D) and the integrals over fluid domain are evaluated for these nodes only. We also apply an electrostatic loading to our model by considering an equivalent electro-static pressure load on the top surface of the structure. Thus we solve the coupled 2D-fluid-3D-structure problem in a single step, using only one element type. The FEM results show good agreement with both existing analytical solutions and published experimental data.

A tip-coupled, two-cantilever, non-resonant microsystem for direct measurement of liquid viscosity

We report a non-resonant piezoelectric microelectromechanical cantilever system for the measurement of liquid viscosity.The system consists of two PiezoMEMS cantilevers in-line,with their free ends facing each other.The system is immersed in the fluid under test for viscosity measurement.One of the cantilevers is actuated using the embedded piezoelectric thin film to oscillate at a pre-selected non-resonant frequency.The second cantilever,the passive one,starts to oscillate due to the fluid-mediated energy transfer.The relative response of the passive cantilever is used as the metric for the fluid's kinematic viscosity.The fabricated cantilevers are tested as viscosity sensors by carrying out experiments in fluids with different viscosities.The viscometer can measure viscosity at a single frequency of choice,and hence some important considerations for frequency selection are discussed.A discussion on the energy coupling between the active and the passive cantilevers is presented.The novel PiezoMEMS viscometer architecture proposed in this work will overcome several challenges faced by state-of-the-art resonance MEMS viscometers,by enabling faster and direct measurement,straightforward calibration,and the possibility of shear rate-dependent viscosity measurement.