Problems and Solutions Section 1.5 (1.57 through 1.65)
1.57
A helicopter landing gear consists of a metal framework rather than the coil
spring based suspension system used in a fixedwing aircraft.
The vibration of the
frame in the vertical direction can be modeled by a spring made of a slender bar
as illustrated in Figure 1.20, where the helicopter is modeled as ground.
Here
l
=
0.4 m,
E
= 20
×
10
10
N/m
2
, and
m
= 100 kg.
Calculate the crosssectional area that
should be used if the natural frequency is to be
f
n
= 500 Hz.
Solution:
From Figure 1.20
ω
n
k
m
EA
lm
=
=
and
ω
π
n
=
=
500
3142
Hz
2
rad
1 cycle
rad/s
Solving for
A
yields:
A
lm
E
A
n
=
=
(
) (
)(
)
×
=
=
ω
2
2
10
3142
4 100
20
10
0 0019
19
.
.
m
cm
2
2
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1.58
The frequency of oscillation of a person on a diving board can be modeled as the
transverse vibration of a beam as indicated in Figure 1.23.
Let
m
be the mass of
the diver (
m
= 100 kg) and
l
= 1 m.
If the diver wishes to oscillate at 3 Hz, what
value of
EI
should the diving board material have?
Solution:
From Figure 1.23,
ω
n
EI
ml
2
3
3
=
and
ω
π
π
n
Hz
=
=
3
2
6
rad
1 cycle
rad/s
Solving for
EI
EI
ml
n
=
=
(
) (
)( )
=
ω
π
2
3
2
3
6
100 1
3
11843 5
.
Nm
2
1.59
Consider the spring system of Figure 1.28.
Let
k
1
=
k
5
=
k
2
=100 N/m,
k
3
= 50
N/m, and
k
4
= 1 N/m.
What is the equivalent stiffness?
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 Spring '09
 abduljaba
 Natural Frequency, Suspension, Coil spring

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