Problems and Solutions Section 1.5 (1.66 through 1.74)
1.66
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 1.21, 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 1.21
!
n
=
k
m
=
EA
lm
(1)
and
n
=
500 Hz
2
"
rad
1 cycle
#
$
%
’
=
3142 rad/s
Solving (1) for
A
yields:
A
=
n
2
lm
E
=
3142
( )
2
.4
( )
100
( )
20
"
10
10
A
=
0.0019 m
2
=
19cm
2
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View Full Document1.67
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 1.24. 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 1.24,
!
n
2
=
3
EI
ml
3
and
n
=
3
Hz
2
"
rad
1 cycle
#
$
%
’
=
6
rad/s
Solving for
EI
EI
=
n
2
ml
3
3
=
6
( )
2
100
( )
1
( )
3
3
=
11843.5 Nm
2
1.68
Consider the spring system of Figure 1.29. 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
 J.G.Lee
 Suspension, Coil spring

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