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

Anish Roychowdhury, Arup Nandy, C. S. Jog, Rudra Pratap

1Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India 2Center for Nano Science and Engineering, Indian Institute of Science, Bangalore, India.
Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India.

DOI: 10.4236/jamp.2013.16005                

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.

Keywords

Squeeze Film Damping; Coupled Problem; 27-Node Brick; Micro-Plate

Conflicts of Interest

The authors declare no conflicts of interest.

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