Abstract
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.
Highlights
The wide scale application of electro-statically driven MEMS sensors, using parallel plate capacitors have led to increasing interest in the study of energy dissipation due to the thin film of air trapped in such devices
If the lateral dimensions of the plate happen to be much larger than the height of the air gap, the trapped air behaves both like a spring and a viscous damper, a phenomenon known as squeeze film effect
Modeling a Cantilever In order to compare our results with experimental data we have modeled a cantilever beam as per dimensions mentioned in the work of Pandey et al [8]
Summary
The wide scale application of electro-statically driven MEMS sensors, using parallel plate capacitors have led to increasing interest in the study of energy dissipation due to the thin film of air trapped in such devices. Hung et al [5] presented a reduced order macro model based on basis functions generated from finite difference simulations They applied this technique to model a pressure sensor as a clamped-clamped microbeam to study the pull-in dynamics of the system using a 1D Euler beam Equation and the non-linear Reynolds Equation. Younis et al [7] studied the effect of squeeze film damping for an electrically actuated micro-plate, using the compressible Reynolds Equation They used perturbation methods to derive analytical expressions for pressure distributions in terms of the structural mode shape. Pandey et al [8] studied the effect of flexural mode shapes on the squeeze film offered stiffness and damping for a cantilever resonator, they used Green’s function to solve the linearized compressible Reynold’s Equation and used the modal projection method available in ANSYS to solve the coupled fluid structure problem for several flexural modes of vibration. The numerical results show good agreement with published experimental data and existing analytical solutions
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