TITLE:
A Monolithic, FEM-Based Approach for the Coupled Squeeze Film Problem of an Oscillating Elastic Micro-Plate Using 3D 27-Node Elements
AUTHORS:
Anish Roychowdhury, Arup Nandy, C. S. Jog, Rudra Pratap
KEYWORDS:
Squeeze Film Damping; Coupled Problem; 27-Node Brick; Micro-Plate
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.1 No.6,
November
28,
2013
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.