An Analytical Solution for Free Vibration of Elastically ...
Solution Tutorial 3 Vibration SRajendran
description
Transcript of Solution Tutorial 3 Vibration SRajendran
![Page 1: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/1.jpg)
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 /
![Page 2: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/2.jpg)
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
![Page 3: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/3.jpg)
![Page 4: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/4.jpg)
![Page 5: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/5.jpg)
![Page 6: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/6.jpg)
![Page 7: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/7.jpg)
![Page 8: Solution Tutorial 3 Vibration SRajendran](https://reader033.fdocuments.us/reader033/viewer/2022061614/563db7ab550346aa9a8cdffd/html5/thumbnails/8.jpg)