الفهرس 
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Abstract
Micro-beams and micro-plates fabricated by deposition suffer from
stiffening and curling, resulting from residual stresses initiated during
fabrication. Stiffening and curling affect the performance of these microstructures
in
MEMS
applications.
Reducing
response
time
is
also
favourable
in
MEMS applications such as RF MEMS switches. Previous literature
shows that it is challenging to reduce both phenomena simultaneously. This
thesis proposes a new design concept aiming at reducing both stiffening and
curling. In addition, reducing switching time is also taken into consideration.
First, simplified model for a fixed-fixed beam is studied to examine
the factors affecting stiffening, and curling. The analytical solution of the
beam model depicts that stiffening can be decreased by increasing the ratio
between the second moment of area of the beam cross-section and its crosssectional
area.
In
addition,
increasing
this
ratio
increases
the
critical
buckling
temperature.
Thus, extending the operational temperature range of the
MEMS device. This simple beam model cannot capture the plate effects.
Thus, a Finite Element model is developed. The Finite Element model is
verified with previous results in the literature.
A preliminary parametric size optimization is done on three well known
configurations of flat micro-plates with fixed-fixed supports. The
objective is to study the effect of in-plane (2D) structure enhancement in
reducing stiffening, curling, and increasing the natural frequency. The higher
is the natural frequency, the lower the switching time. For comparison
purposes, same volume is set as a constraint for all three designs. Compared
to conventional rectangular micro-plate, a reduction of 34% in stiffening for
configuration 2, and 44% in curling for configuration 3 are achieved.
configuration 1 showed the maximum fundamental natural frequency. Thus,
it is predicted to have the lowest switching time. Moreover, configuration 2
ix
showed the maximum critical buckling temperature. The effect of changing
micro-plate material is also studied.
The next step after these preliminary simulations is to test the
outputs of the analytical model i.e. using designs of micro-plates with high
ratio of second moment of area to the cross-sectional area. In structural
design, many cross-sections are known to have a high previously mentioned
ratio. This thesis focuses on ribbed and corrugated sections, as they can be
easily manufactured in MEMS fabrication technology.
Results of the Finite Element simulations for ribbed switch show
that specific designs of ribbed micro-plates are superior to conventional flat
ones in many aspects. Stiffening and curling are both reduced by about 50%
and 64%, respectively. Critical buckling temperature is increased. The
sensitivity of stiffness to temperature variations is reduced by 50%. The
fundamental natural frequency is increased by 34%. For the same bending
stiffness, the mass of the ribbed micro-plate is reduced and hence a faster
response can be achieved.
The second design proposal is to use corrugated micro-plate as a
remedy to residual stress problems. The micro-plate is double corrugated in
both longitudinal and transverse directions. A parametric study is
implemented to study the effect of number of corrugations in both
directions and corrugation height on the micro-plate performance as
compared to a flat one with the same stiffness. Proposed corrugations result
in reducing stiffening, and curling, by 85%, and 73%, respectively. A selected
corrugated micro-plate achieved a reduction of 39% in switching time.
Three dimensional designs used in this thesis (ribbed and corrugated
micro-plates) show better results than two dimensional designs in reduci ng
the problems arising from residual stresses.
The three-dimensional design concept can be applied on any micro-
x
plate device such as resonators, pressure sensors, and micromirrors in order
to improve the reliability of these devices. Thus, corrugation concept is
applied as a case study on a previously designed radiofrequency switch in
literature. Significant reduction in stiffening and curling is achieved that can
reach 90% and 95% in stiffening and curling, respectively.