Hierarchical finite element simulation of perforated plates with arbitrary hole geometries
Peter Råback, Antti Pursula, and Timo Veijola
CSC - Scientific Computing, FI
Keywords: Squeezed-film-damping, perforated, finite element method
The squeezed-film-damping of micro-electro-mechanical devices may be
reduced by creating a number of small holes into the structure.
Unfortunately, in the simulation of the devices it is possible to
consider only a few holes in detail. A more feasible approach is to
homogenize the contribution of the holes over the whole domain.
In this paper we follow a hierarchical two-level simulation strategy.
We take a unit cell including one hole and compute the flow resistance
and the electrical capacitance correction as a function of the
aperture. By this homogenization, a full coupled analysis including
fluidic, elastic and electrostatic forces is performed. The solution
is obtained from a loosely coupled iteration scheme involving a
nonlinear Reynolds equation, a nonlinear plate equation, and a reduced
order equation for the electric field.
We apply the described methodology to a simple micro-mechanical
microphone with a perforated backplate. We perform harmonic and
transient analysis using ELMER finite element solver. In particular,
dynamical pull-in phenomena is modeled with different hole
The selected approach is not restricted to any given geometry and it
may therefore be applied to holes of any shape. This is important
since the manufacturing technology does not always allow idealized
shapes. Additionally, the model does not assume small displacements
and it may therefore be applied to study various nonlinearities of the
NSTI Nanotech 2003 Conference Technical Program Abstract