MENG 475 Final
December 24, 2002
ID:
Note: 10 points will be deducted from your grade if this sheet is not returned
b
1) (15) In your own words define the
following terms:
a) Modal analysis
b) Mode shape
c) Forced vibration
d) Free vibration
e) Proportional damping
a
partial
credit
1
2) A sign is being held up by two strings
from the ceiling with l1=l2=2m, w=1m,
m=12kg. K=100N/m. Irod=ml2/12
a) (10) What is the natural frequency of
the system for twisting vibrations?
b) (15) What are the equations of motion
for the system for the swinging of the
sign using the variables indicated?
c) (10) What are the natural frequencies
for the system for swinging vibrations?
d) (10) What is the amplitude of the first
mode shape (q1), given that 1(0)=0
rad and 2(0)=0.1 rad? (assume a
mode shape of [12.34, 27.32]T if you
cannot solve (c).
l1
l1
l1
1
m1
zz
k
l1
l2
2
2
l2
l2
w
Full credit
m1
zz
3) For the beam shown on the right:
l
l
l
a) (10) Determine the flexibility matrix (l=1, EI=1)
m1
m2
b) (10) What would you enter into MATLAB to
calculate the steady state vibration amplitude of
the two masses if m1 also had an effective rotating
imbalance of 0.01m at 50HZ. (m1=10, m2=5)
c) (10) Assuming that m2 and the damping are negligible, what should EI be for the beam so that the
steady state total force transmitted to the walls ground is 25% of the effective force of the
imbalance? (For partial credit, just give k)
4) (15) The misalignment between the two machines of the figure is measured by face-rim
technique on the machine to be shimmed. The measurement planes are located both 5" from the
coupling. The results indicate a reading of -20 thousandths (bottom at zero) at the rim
measurement plane, and a reading of 35 thousandths at the face plane (bottom at zero).
Determine the size of the shims that need to be placed under (or removed from) each support to
align the shafts of the two machines. (You do not need to derive the equations.)
coupling
Machine to
be Shimmed
Fixed Machine
20”
11”
12”
15”
MENG 475 Final
December 24, 2002
ID:
Note: 10 points will be deducted from your grade if this sheet is not returned
b
1) (15) In your own words define the
following terms:
a) Mode shape
b) Modal analysis
c) Free vibration
d) Forced vibration
e) Proportional damping
a
partial
credit
1
2) A sign is being held up by two strings
from the ceiling with l1=l2=1m, w=2m,
m=12kg. K=100N/m. Irod=ml2/12
a) (10) What is the natural frequency of
the system for twisting vibrations?
b) (15) What are the equations of motion
for the system for the swinging of the
sign using the variables indicated?
c) (10) What are the natural frequencies
for the system for swinging vibrations?
d) (10) What is the amplitude of the first
mode shape (q1), given that 1(0)=0.1
rad and 2(0)=0 rad? (assume a mode
shape of [12.34, 27.32]T if you cannot
solve (c).
l1
l1
l1
1
m1
zz
k
l1
l2
2
2
l2
l2
w
Full credit
m1
zz
3) For the beam shown on the right:
l
l
l
a) (10) Determine the flexibility matrix (l=2, EI=1)
m1
m2
b) (10) What would you enter into MATLAB to
calculate the steady state vibration amplitude of
the two masses if m1 also had an effective rotating
imbalance of 0.01m at 50HZ. (m1=5, m2=10)
c) (10) Assuming that m2 and the damping are negligible, what should EI be for the beam so that the
steady state total force transmitted to the ground is 25% of the effective force of the imbalance?
(For partial credit, just give k)
4) (15) The misalignment between the two machines of the figure is measured by face-rim
technique on the machine to be shimmed. The measurement planes are located both 5" from the
coupling. The results indicate a reading of 15 thousandths (bottom at zero) at the rim
measurement plane, and a reading of -20 thousandths at the face plane (bottom at zero).
Determine the size of the shims that need to be placed under (or removed from) each support to
align the shafts of the two machines. (You do not need to derive the equations.)
coupling
Machine to
be Shimmed
Fixed Machine
20”
11”
12”
15”