solution tutorial 3 vibration srajendran
DESCRIPTION
Vibration, answers, questions, mechanical engineeringTRANSCRIPT
Review Basic Concepts, Tutorial 3 (Vibration)
Harmonic Forced Vibrations
Undamped Damped
EOM: tFkxxm o sin
Steady‐state response:
)sin( tX
EOM: tFkxxcxm o sin
Steady‐state response:
)sin( tX
20
mkF
X n
n
,0
222
0
cmk
FX tan 21
mkc
or or or or
20 /1
1/ nkFX
1/ 1/,0
n
n 22220 /2/1
1/
nnkF
X
21
/1/2tan
n
n
m
tFo sin
x
k
m
tFo sin
x
ck
0 1 2 3 40
1
2
3
kFX p
/0
n / / n 1 2 3 4
2/
0
n /
kFX/0
n /
Review Basic Concepts, Tutorial 3 (Vibration)
Harmonic Forced Vibrations (Caused by Rotating Unbalance)
EOM:
Steady‐state response:
)sin( tX
222
2
)()(
cMkmeX 2
1tan
Mkc
or or
222
2
)/2())/(1(
)/(
nn
n
meMX
2
1
)/(1/2tan
n
n
M
x
meω2
k/2 k/2
e ωtm
c
tex sin
0 1 2 3 4 50
1
2
3
ζ=1
0.5
0.30.15
ζ=0
MXme
n /
n /
2 sinMx cx kx me t
Static equilibrium position
