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ADVANCED DYNAMICS OF STRUCTURES
/
QUIZ
/
November 11, 2009
ADVANCED DYNAMICS OF STRUCTURES
/
QUIZ
/
November 11, 2009
1.
Write down the equation of motion of the rigidbody assemblage in terms of
)
(
t
θ
the
rotation angle of the support by using the principle of the virtual work. Obtain the free
vibration period
k
M
T
/
α
=
of the assemblage and determine
. Find
p
for the
resonance condition in terms of the parameters of the system
M
,
k
and
a
.
3a
3a
2a
2k
Total
mass 4M
q(t)=q
sin pt
o
5a
Q(t)=aq
sin pt
o
θ(
t
)
Hinge
k =ka
2
1
Total
mass M
3k
2.
Obtain the displacement function
)
(
t
v
of the undamped SDOF system subjected to the
external load
o
t
t
o
e
p
t
p
/
)
(
−
=
assuming that the system starts from the rest, i.e.,
0
)
0
(
)
0
(
=
=
=
=
t
v
t
v
.
m
and
k
denote the mass and the stiffness of the system,
respectively.
p
t
p(t)
o
t/t
p(t)=p
e
o
o
p(t)
m
v(
ı
)
k/2
k/2
0
3.
The frame shown can be assumed as a singledegreeoffreedom system and it is subjected
to a ground motion of impulse character
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This note was uploaded on 11/23/2010 for the course DEP 503E 10852 taught by Professor Prof.zekaicelep during the Fall '10 term at Istanbul Technical University.
 Fall '10
 Prof.ZekaiCELEP

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