mems - problems
TRANSCRIPT
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8/11/2019 MEMS - problems
1/8
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8/11/2019 MEMS - problems
2/8
L72
\ l
5 .
Modeli,ng
MEMS
and
NEMS
Again
consider
the
isothermal
thermopneumatic
actuator
from
p
4.
using
the
energy
from
Problem
4,
plot
the
potential
well
f
system.
Discuss
the
possible
motions
of
the
pendulum
in
terms
potential
well.
6. Again
consider
the
equation
of
motion
for
a
pendulum
from
prob
Rewrite
this
as
a
first-order
system.
Find
ail
critical
points
of this
in
the
phase
plane.
Linearize near each critical point and determ
local
behavior
of
solutions.
7.
Again
consider
the
equation
of
thermopneumatic
actuation
from
lem
4.
Rewrite
this
as a
first-order
system.
Find
all
critical po
this
system
in
the
phase
plane.
Linearize
near
each
critical
poi
determine
the local
behavior
of
solutions.
Plot
the
frequency-response
diagram
for
the
forced
mass-spring
for
various
values
of
?.
How
does
the
resonant
frequency
.ha.rg
f
How
does
the
magnitude
of
the
response
depend
on
1?
H;
the
width
of
the
peak
depend
on
7?
Discuss
your
answer
in
te
the
Q
for
the
system.
9 . Compute an effectivespring constant for an elastic microbeam of
1500pm,
width
5pm,
and
height
10prm.
you
may
assume
a
y
modulus
of
150GPa.
Compute
the
natural
frequency
of the
beam
system
from
problem
modeling
it
as
a mass-spring
and
using your
effective
spring
con
Assume
the
beam
has
density
2300kg/m3
using
the
effective
spring
constant
from
problem
9
and
assum
density
of
2300kg
l^t,
consider
a
mass-spring
system
where
the
is
a
ball
10pm
in
diameter.
If
the
e
is
250,,000,
what
is
the
constant
a?
IJsing
the
modified
nonlinear
version
of
Hooke,s
law,
write
dow
governing equation for an
undamped
mass-spring
oscillator.
scal
equation
and
interpret
the
dimensionless
constants
that
arise.
an
energy
and
sketch
the
potential
well
for
this
system.
Section
5. 4
13.
constd,u:,r,r"ud{-:pt"j."formations
of
an
erastic
string
with
load
p
(y
-
t1z1@
+
L/2).
Find
the
shape
of
the
deflecteJ
string
usin
Green's
function
representation
of the
solution.
''
14.
Consider
an
elastic
string
with
initial
deformation
sin(rr)
that
leased
from
rest.
solve
for
the
motion
of
the
string
at
all times
Plot
your
solution
for
various
times.
8 .
10.
1 1 .
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8/11/2019 MEMS - problems
3/8
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