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

No damper

No damper

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

Mode shapes -TMD tuned to mode 1

Modal periods

Periodic forcing T = 1s

Periodic forcing T =1s

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

TMD tuned to mode 2

TMD tuned to mode 2

Periodic forcing T =.4stuned to mode 2

TMD tuned to mode 2periodic forcing T =.4s

TMD tuned to mode 2periodic forcing = .4s

TMD at node 2 Tuned to mode 1T =1s

TMD at node 2 Tuned to mode 1T=1s

Earthquake loading - No TMD

TMD tuned to mode 1

Earthquake loading -No TMD

TMD tuned to mode 1

Tforcing=1sTMD at node 2 Tuned to mode 2

T = .408s

Tforcing=1sTMD at node 2 Tuned to mode 2

T =.408s

Example 4.2

sec1

2

39438

1000

075.

135.

94.

05.

,

T

k

m

f

m

eqv

optd

opt

πω

ξ

ξ

Mode shapes

Inter-element profiles

Damping ratios

Modal response- T=1sec

Damper properties

Nodal and damper displacementsT=1sec