![Page 1: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/1.jpg)
Example 4.4
sT
sT
kc
c
c
k
k
m
m
ii
408.
99.15
0.1
2
0064.
02.
505.
752.
96.78
44.118
0.1
0.1
2
2
1
1
1
2
1
2
1
2
1
ω
πω
α
α
ξ
5.
0.1
0.1
5.
2
1
25.1~
25.1~
2
1
m
m
![Page 2: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/2.jpg)
No damper
![Page 3: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/3.jpg)
No damper
![Page 4: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/4.jpg)
TMD at node 2 Tune to mode 1TMD at node 2 Tune to mode 1
modal mass =1.25
modal amplitude =1.0
Want equivalent modal damping = 0.1
Requires mbar =.065
The appropiate damper parameters are f=.91 =.145
mdamper=1.25mbar
=.081
dξ
134.
71.591.
64.2
1
d
d
d
c
k
ωω
![Page 5: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/5.jpg)
Mode shapes -TMD tuned to mode 1
![Page 6: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/6.jpg)
Modal periods
![Page 7: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/7.jpg)
Periodic forcing T = 1s
![Page 8: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/8.jpg)
Periodic forcing T =1s
![Page 9: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/9.jpg)
TMD at node 2 - Tuned to mode 2
48.c
36.31k
46.14
15.m
5.4u
u
11.
.94f
03.
049. and 15.For
2.~)(
5.
25.1~
d
d
d
d
d
d
2
22
222
22
2
ω
ξ
ξξ
φ
φ
m
mm
mm
m
eq
dd
![Page 10: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/10.jpg)
TMD tuned to mode 2
![Page 11: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/11.jpg)
TMD tuned to mode 2
![Page 12: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/12.jpg)
Periodic forcing T =.4stuned to mode 2
![Page 13: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/13.jpg)
TMD tuned to mode 2periodic forcing T =.4s
![Page 14: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/14.jpg)
TMD tuned to mode 2periodic forcing = .4s
![Page 15: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/15.jpg)
![Page 16: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/16.jpg)
TMD at node 2 Tuned to mode 1T =1s
![Page 17: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/17.jpg)
TMD at node 2 Tuned to mode 1T=1s
![Page 18: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/18.jpg)
Earthquake loading - No TMD
![Page 19: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/19.jpg)
TMD tuned to mode 1
![Page 20: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/20.jpg)
Earthquake loading -No TMD
![Page 21: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/21.jpg)
TMD tuned to mode 1
![Page 22: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/22.jpg)
![Page 23: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/23.jpg)
Tforcing=1sTMD at node 2 Tuned to mode 2
T = .408s
![Page 24: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/24.jpg)
Tforcing=1sTMD at node 2 Tuned to mode 2
T =.408s
![Page 25: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/25.jpg)
![Page 26: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/26.jpg)
Example 4.2
sec1
2
39438
1000
075.
135.
94.
05.
,
T
k
m
f
m
eqv
optd
opt
πω
ξ
ξ
![Page 27: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/27.jpg)
Mode shapes
![Page 28: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/28.jpg)
Inter-element profiles
![Page 29: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/29.jpg)
Damping ratios
![Page 30: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/30.jpg)
Modal response- T=1sec
![Page 31: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/31.jpg)
Damper properties
![Page 32: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/32.jpg)
Nodal and damper displacementsT=1sec
![Page 33: Example 4.4. No damper TMD at node 2 Tune to mode 1 modal mass =1.25 modal amplitude =1.0 Want equivalent modal damping = 0.1 Requires mbar =.065 The](https://reader036.vdocuments.us/reader036/viewer/2022081421/56649d385503460f94a11b3f/html5/thumbnails/33.jpg)