Download 2003 ME Graduate Student Conference

2013 ME Graduate Student Conference
April 27, 2013
THERMO-STRUCTURAL SIMULATION OF THERMALLY ACTUATED NANO- AND
MICRO-STRUCTURES
Elham Maghsoudi
Ph.D. Candidate
Faculty Advisor: Dr. Michael James Martin
ABSTRACT
The role of simulation as it is predictive in nature,
and provides information that is required in planning future
design and experiments, becomes more significant in the
areas where measurements are difficult. This work provides
a thermo-structural simulation for nano-scale and microscale structures which are thermally actuated. We consider
four applications: thermal positioning of wave guides [1-2],
thermal actuation of micro-scale switches [3], a novel
thermally actuated mechanical memory system [4], and
thermal actuation of micro-scale resonators [5].
Because these devices are thermally actuated, the heat
conduction equation in the system is a controlling
parameter. The dimensionless Knudsen number determines
which convective heat transfer coefficient must be used in
the simulation. The ambient pressure will change the
Knudsen number and as a result, the flow regime. Several
researchers have studied gas pressure effects on heat
transfer from the mico- and nano-structures to the
surrounding gas [6-10]. The results show that gas phase heat
transfer is an important parameter for devices of this size at
ambient pressure. As the pressure decreases below 5 Torr,
the effects of convection become minimal [9]. Since the
displacement is the response of the system in these devices,
several studies have been performed on conductive heat
transfer effects on the mechanical response of the system
[11-13].
In this work, the study began with simulating a doubly
clamped beam in micro-scale and nano-scale. Thermal
positioning, which is adding a constant, time-independent
heat flux to deflect the system is investigated in micro- and
nano-scale. The thermal positioning response is the
thermally steady state center displacement of the bridge.
The steady state thermo-structural equation is solved
numerically using an implicit Finite Difference method to
obtain the thermally steady state center displacement. The
results are non-dimensionalized to provide insight into
thermal positioning across a range of structure length scales
and material properties. The Displacement Ratio which is
the representative of the thermal noise is defined as the
center displacement, created by thermal stresses, divided by
thermal displacement. Thermal noise analysis and the
displacement variations by pressure suggest silicon carbide
as the most appropriate material to fabricate nano-devices
where positioning accuracy is a design requirement. It
shows the displacements of the order of angstrom for an
average heat load and thermal noises of tens of the order of
the magnitude for nano-scale structures [14].
The thermal positioning simulation is used to improve
the thermal efficiency of a thermal micro-switch [3] by
introducing various heating configurations: a distributed
heat configuration, a center-heating configuration and a
side-heating configuration. The results show that for a
specific steady state center displacement for distributedheating configuration and center-heating configuration, a
closed switch requires less heat at the top than an open
switch. Heat addition to the center of the top surface of the
bridge is the most efficient way to obtain a larger center
displacement per unit heat addition. It is more thermally
efficient than adding concentrated heat to the sides of the
top surface by a factor of 8.8 in the open position and 17 in
the closed position [15].
The thermal positioning simulation is also used to
simulate a novel thermal buckling storage nano-memory for
space exploration computer systems. The two technologies
of buckling beam [16] and thermal positioning are used to
design this storage nano-memory. Current space missions
use radiation locker for all the electronics. The current Juno
mission has a 200 kg “radiation vault” and still expected to
succumb to radiation after 6 months [17]. The high energy
particles collision simulation is performed for this memory
design. The results show that this memory is radiation
protected which makes it a unique design for space
exploration computer systems in harsh environments such
as Europa orbit of Jupiter. Using an unsteady simulation, the
power requirements for thermal actuations, optimal
geometry, and write time of the device for various materials
are investigated. The results show this memory has
reasonable power consumption and an acceptable data
storage density in comparison with the current memory
devices [4].
The study continued with the simulation of thermal
actuation in a nano-structure bridge. Thermal actuation
applies sinusoidal heating (time-dependent heat load)
leading to vibration in the bridge. The heat addition is
harmonic and time-dependent. The structural equation is rederived to take into account the acceleration and inertial
effects to study the dynamic behavior of the system. The
heat conduction equation includes thermo-elastic terms
[18]. The same implicit Finite Difference scheme is used to
solve the coupled thermo-structural equation at each time
step. The thermal actuation simulation analyzes the phase
delay between the excitation and the response, the steady
state amplitude, and the vibration amplitude for a range of
frequencies. The simulations also show the effect of
changing the power supplied and the ambient pressure on
the vibration amplitude and the steady state amplitude [5].
The results are applicable in simulating the dynamic
behavior of nano-scale devices used for switching, nanomanufacturing, and measurement.
Constant thermal properties assumption is acceptable
for very low heat flux added to the system. However,
temperature increase up to 300 K due to higher heat flux
added to the system creates substantial variations in some
thermal properties such as thermal conductivity and thermal
expansion coefficient [19]. Thermal conductivity changes
up to 59%, specific heat changes up to 19% and thermal
expansion coefficient increases up to 15% by 300 K
increase in the temperature. The transient thermo-structural
simulations were repeated for temperature dependent
thermal properties. The results show that the steady state
and vibration displacement variation by the total heat added
to the system corresponds to a nonlinear system while the
results using constant thermal properties show a linear
system. For high heat addition rates, temperature dependent
thermal conductivity changes the temperature distribution
significantly leading to a significant change in center
displacement. Although temperature dependent thermal
expansion coefficient does not affect the temperature
distribution it significantly increases the displacement due
to an increase in the thermal stress.
Future work will focus on applying this information to
the control of thermally actuated micro- and nano-systems
by determining Bode and Nyquist diagrams.
ACKNOWLEDGMENTS
I would acknowledge support provided by NASA and
the Louisiana Space Grant Consortium through LEQSF
(2010)-DART-42, “Robust Nano-Mechanical Memory for
Space Exploration.”
I would thank Professor Michael Murphy (Louisiana
State University) and Dr. Harish Manohara (NASA Jet
Propulsion Laboratory (JPL), California Institute of
Technology) for useful suggestions on thermal memory
design and simulation. I would also like to thank Professor
Guoqiang Li and Professor Harris Wong (Louisiana State
University) for their helpful comments on steady response
to steady (constant heat load) actuation. I would also like to
thank Professor Hosam Fathy (Pennsylvania State
University) for sharing files on structural vibration section
in transient response to harmonic actuation and Profrssor
Marcio DeQueiroz (Louisiana State University) for
technical communication on vibration part and providing
technical resources.
The computational simulations were performed on
LONI (The Louisiana Optical Network Initiative) clusters.
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