Conclusions

Chapter 2 Single-Degree-of-Freedom Systems

2.6 Conclusions

period. Table 2.5.5 gives the general qualitative performance assessments of the compen- sation effectiveness of the predictive scheme on the AIC algorithms in the presence of time delays.

Table 2.5.4: Longest time delays (in seconds) compensated by the predictive scheme in the OCS, AID, and AVS algorithms

Algorithm

ocs

^{AID AVS}

ELC 0.04 0.04 >0.08 RRS 0.04 0.04 >0.08

Table 2.5.5: Qualitative assessments of the compensation effectiveness of the predictive scheme on the OCS, AID, and A VS algorithms

Algorithm

ocs

^AID AVS

ELC Good Good Excellent RRS Good Good Excellent

general is more effective in controlling the response of the PS. However, in the AID algorithm, drifting occurs in the response of the PS when the stiffness of the AS is more than twice that of the PS (see Figures 2.3.11 and 2.3.12).

4. An elasto-plastic AS can provide approximately the same control efficiency as a purely elastic AS does as long as the yielded AS can still provide sufficient control force on the PS. This feature greatly relaxes the requirement on the stiffness of AS and enhances the applicability of AIC system in practice.

5. In an AIC system, the proper length of the sampling interval depends on the frequency of the AS. In the OCS algorithm, a finer sampling interval is generally needed when the period of the AS is shorter and the motion of the AS becomes more rapid. How- ever, the AID and A VS algorithms are much less sensitive to the sampling interval because the dynamics of the AS are neglected. The impact velocity between the PS and AS is proportional to the length of the sampling interval and the square of the fre- quency of the PS.

6. Deteriorated but stable response of the PS is generally observed as the time delay gets longer in the OCS algorithm. The AID algorithm is robust with respect to the time delay. Instability often occurs in the A VS algorithm.

7. The predictive time delay compensation scheme presented is effective for compen- sating short time delays in the OCS algorithm, and very effective in compensating for long time delays in the A VS algorithm. It is, however, not effective in compensating the time delay in the AID algorithm but there is no need for compensation in this case.

L L

m1 mz

.. '; ' ' i ' ; .. "

..

^{.. . ... ...}

^.~ ~ ^t' I ,·· ··· .. ·· .. ··,·•··· ,, .... · .. · .. · .. · .. ,,,

PS

IE

AS

kl/2

-

^{kd2 kz/2 ~}

CJ cz

•...

^{·, ... < .. . . { : . . . . •'}

...

•• ^{.··•···} .. ^\ ;

.

•. ·>

L

^a(t)

Figure 2.1.1: Schematic representation of a SDOF AIC system

3

kz/2

.·

,.. .

^{.·. · / .. ·} _{.. ' I}

.p..

Ul

/ /

/ / /

A

^B,Cdetach

:_---~

/ · · · .1. · · · O;E attach

/ . .

/ . I

H ~

I .... F,,.

·-:..· ;_: ·_,:_,·

._

^{- -} · · :_..: · ~· i:_ · · · -' · ^{I detach}

... · ·j · · :-: · ~ .. ::-· :-: · -:-.. ~ · :-: · ..,... "'\: ^attach

I '

J't ' ....

f(t)J J

/ I

:,

("' ^{I ~.v} /

. / I

/ / / /

~

' . .

G" ·-·4x«•i-·-·-GH·-·-.

F

Figure 2.2.1: First full cycle motion of the PS and AS and control force- displacement curve in a forced vibration with fixed displace- ment limits (the proposed algorithm)

Figure 2.2.2:

-xO

attach

detach attach

x1 (t)

First full cycle motion of the PS and control force- displacement curve in a forced vibration with fixed dis- placement limits (the AID algorithm)

xO

~- x1 (t)

detach

~ ... : ... attach

detach

~ . ·t· . . . .

f(t) 1 · · · ' · · · · attach

x1 (t)

Figure 2.2.3: First full cycle motion of the PS and control force- displacement curve in a forced vibration with fixed dis- placement limits (the A VS algorithm)

..p..

0\

0.8 0.6 0.4 1: ~ 0.2

16 (]) 0

~

^-0.2

-0.4 -0.6 -0.8

-1 ..

I

l

: / " ·.

:I

/

I

\

... AVS ---AID

ocs

1:

I : I .

\

\

·.'-

I :

/ ...

0 0.2 0.4 0.6 0.8 1.2 1.4 1.6

Time (second)

Figure 2.2.4: Response of the PS in a free vibration (OCS)

.-....

1.8 2

0.4 ,----,---.----,r---.---.----,--.,----.---.---.

0.3 0.2

~ 0.1

e

~ o

1: 0

(.) -0.1 -0.2 -0.3

- - - t -

-0.4 L__...J.._ _ __,_ _ ___,_ _ _ L-_...l... _ _J_ _ ____L _ ___J:...__.J______i

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Displacement of the PS

Figure 2.2.5: Control force-displacement curve in a free vibration (OCS)

0.3 0.2

~ 0.1

~

~ ⁰

0

(.) -0.1 -0.2 -0.3

-0.4 L__...J.._ _ __,_ _ _ _ _ , _ _ - - ' L - - . . . l . . . - - l - - - - ' - - - - ' - - - ' - - - l

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Displacement of the PS

Figure 2.2.6: Control force-displacement curve in a free vibration (AID)

0.4.----,---.--.---.---.----,r----r---.----,r----.

0.3 0.2

~ 0.1

~

e

1: 0

(.) -0.1 -0.2 -0.3

-0.4 t___...J.._ _ __._ _ _ t _ _ _ . . . J . . _ _ - l . . _ - - ' ' - - - . . . . 1 - - - l . . - - ' - - - . J

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Displacement of the PS

Figure 2.2.7: Control force-displacement curve in a free vibration (AVS)

:£:i

,£.

'E I I ^{( \}

Q)

E

Q) 0

0 ctl \J

"C..

.!!l -10

0 J

-20

0 2 4 6 8 10

200

--- Uncontrolled (Max= 118 cm/s) _ OCS (Max= -36 cm/s)

..!!! 100 ,£. E

~ 0 '"'

"(3

0 \..~

Cii > -100

-200

0 2 4 6 8 10

~ 1000

..!!! E --- Uncontrolled (Max= 677 em/sis)

,£. ^_ OCS (Max= 501 em/sis)

c: 500

~ 0

~ 0 Cii 0

<( 0

~ ^-500

0 en

~ -1000

0 2 4 6 8 10

Time {second)

Figure 2.3.1: Displacement, velocity, and acceleration time history re- sponses of the PS controlled by the OCS algorithm and ex- cited by the ELC ground motion

,£.

'E Q)

E _Q) 0

0 ctl Q. en -50 i:S

-100 0 400

~ 200 ,£. E

~ 0

"(3

Cii 0

> -200 -400 0

~ ..!!! 4000 ,£. E

c: 2000

~ 0

Q) 0

Cii 0

<( 0

~ -2000

::I

0 en

~ -4000 0

I I /' " "\ " '"'

...L.I \ I\~ I \ I \ / \

I \ I \ \ I \ I \ I \.

\ I I '- J ...1 '"'

v " v

2 4 6 8 10

" --- Uncontrolled (Max= -334 cm/s) OCS (Max= -54 cm/s)

" I 1\

I 1 I I . I 1\ I \ I I

v--,"vl-1'""'1(

7r,--, ⁿ

I I I I I '; I I \1 , ,

v I \ \

I I

2 4 6 8 10

2

--- Uncontrolled (Max= -2069 em/sis) _ OCS (Max= 1089 em/sis)

1\

4 6 8 10

Time {second)

Figure 2.3.2: Displacement, velocity, and acceleration time history re- sponses of the PS controlled by the OCS algorithm and ex- cited by the RRS ground motion

..p:..

00

E' _{I I} _AID (Max= -3 em)

~ 10

E ^{I I}

Ql

E Ql 0

al _\I I I I

a. \I

.!!l -10 I I

0 ^J

\I

-20 0 2 4 6 8 10

200

--- Uncontrolled (Max= 118 cm/s) _AID (Max= -30 cm/s)

~ 100

~ E

~ 0

·c::s

0 \.-

Ci5 > -100 -200

0 2 4 6 8 10

~ E ¹⁰⁰⁰ --- Uncontrolled (Max= 677 cm/s/s)

0 _AID (Max= 517 cm/s/s)

~ _c: 500

0

~ Ql 0 Ci5 0

<( 0

.l!l -500

:I

0 "'

~ -1000

0 2 4 6 8 10

Time (second)

Figure 2.3.3: Displacement, velocity, and acceleration time history re- sponses of the PS controlled by the AID algorithm and ex- cited by the ELC ground motion

E' ~ 50 E Ql

E 0

Ql 0

ttl \ I

a.

"'

^-50

i5

v

-100

0 2

400

~ 200

~ E

~ 0

·c::s

0

Ci5 > -200 "

-400

0 2

~ ..!!! 4000 E 0

~ 2000

0 ,.

~ ~ 0 Ci5 0

<( 0

.l!l -2000

:I

0

"'

~ -4000

0 2

r

\

I

'"'

I I I

1 4

"

4

_AID (Max= -13 em)

1"\

r\

v

6 8

--- Uncontrolled (Max= -334 cm/s) AID (Max= -81 cm/s)

I \

I I _I I I \ I I

r

6 8

\.

10

10

--- Uncontrolled (Max= -2069 cm/s/s) _AID (Max= 1457 cm/s/s)

r

4 6 8 10

Time (second)

Figure 2.3.4: Displacement, velocity, and acceleration time history re- sponses of the PS controlled by the AID algorithm and ex- cited by the RRS ground motion

~

K

¹⁰

'E (])

Eo~ ~

.!!l a. -10

Cl

"

^{I \I}

-20L---L---~---~---L ______ ^{_ _ J}

0 2 4 6 8 10

200~---~---.---,---r---~

~ 100

~ £.

~ 0 r---:-'

"(3 0 Ql > -100

"\

--- Uncontrolled (Max= 118 cm/s) _ AVS (Max= -58 cm/s)

t

-200L---~---~~---~---~---~

0 2 4 6 8 10

~ 1ooor---.---.---.---.---,

~ E

£.

--- Uncontrolled (Max= 677 em/sis)

I

_ AVS (Max= 656 em/sis) c:: 500

~

_(])

1

_{~ -500}

~

<( -1000 0,---;---~~---~---~~---

2 4 6 8 10

Time (second)

Figure 2.3.5: Displacement, velocity, and acceleration time history re- sponses of the PS controlled by the A VS algorithm and ex- cited by the ELC ground motion

£. 50 ... _c::

(])

E 0

(]) 0 Ill

a. til -50 i:5

v

-100

0 2

400

~ 200

~ £.

~ 0

"(3 0 Ql > -200

I _I

v,

"

I ^{I I} -400

0 2

~ ⁴⁰⁰⁰

£. E c:: 2000

~ 0

(]) 0

Ql 0

~ .l!l -2000

::::J

0 til

~ -4000

0 2

4

{\

V' I - ^I I

I I \ J

\

4

4

1"\

v

6 8

--- Uncontrolled (Max= -334 cm/s) AVS (Max= 117 cm/s)

I \

I I I \ 1\

\ I I I I

-

6 8

\.

10

I 10

--- Uncontrolled (Max= -2069 cm/s/s) _AVS (Max= 1904 em/sis)

6 8 10

Time (second)

Figure 2.3.6: Displacement, velocity, and acceleration time history re- sponses of the PS controlled by the A VS algorithm and ex- cited by the RRS ground motion

U\ 0

(/) ()

0

Cl

<(

(/)

~

0 0

11r---

0 0

11----

0 0

0.5

,..--, ....---

L- L-

0.5

.---.~

__J L - L.-.J

0.5

L...J - ^L...l L...JL...JL..JUL-

1.5 2 2.5 3 3.5 4

,---, r--1 r l r---1 ,..--, .-

LJ L-.J L-....J L...J I L-.J L...J !...__

1.5 2 2.5 3 ^3.5 4

,...-, r--1 r- r - r- r -

'---l L-..J 1..---' UL...JL...J L-...1

1.5 2 2.5 3 3.5 4

Time (second}

Figure 2.3.7: Attachment time histories controlled by the OCS, AID and AVS algorithms and excited by the ELC ground motion (1 - attachment and 0 - detachment)

(/) ()

0

Cl

<(

(/)

~

0

0

0 0

0

0

L-

0.5

..., n r -

L...ll '---

0.5

,..., .---- r -

L...J ' - - -

0.5

LJ u L...J L...J u L...JU u y

1.5 2 2.5 3 3.5 4

, . , r---1 ,....,....- .---1

.._ _'---- L . _ _ !...__

1.5 2 2.5 3 3.5 4

r- ^{r---1 . - - r -} ....--

'--- ^{L-.J L-...-.1 '---1 1..--}

1.5 2 2.5 3 3.5 4

Time (second)

Figure 2.3.8: Attachment time histories controlled by the OCS, AID and A VS algorithms and excited by the RRS ground motion (1 - attachment and 0- detachment)

Ut ,_.

.£. 'E

"E

~ 0

c. g

i5

^-5

-10k---~---~---~---~---~

0 2 4 6 8 10

400r---~---,---~---.---~

Max = -226 cm/s

~ 200

~ .£.

~ 0~'11--'

'g

(j) > -200

-400k---~---~---~---~---~

0 2 4 6 8 10

20r---~---,---,---.---~

:§ Max=-10g

~ c: 10

Ql

(j) 8 0 ~ffilhllldiVJIIITWIIIWIIII1Rin-#l

<(

.s -8 ^-10

~

-20~---~---~---~---~---~

0 2 4 6 8 10

Time (second)

Figure 2.3.9: Displacement, velocity, and acceleration time history re- sponses of the AS controlled by the OCS algorithm and ex- cited by the ELC ground motion

~

₍₎ 'E .£.

"E

~ 0 c.. g

i5

^-10

-20k---~---~---~k---L---~

0 2 4 6 8 10

1000r---r---~r---,---,---.

Max = 534 cm/s

500

; 0~

'g

(j)

> -500

-1000~---~---~---k---~---~

0 2 4 6 8 10

40r---,---r---,r---~---~

:§

~ c: 20

Ql

~O~II'It.lltJ

<(

~ .s -20

..0

<(

Max=25g

-40~---~---~---~k---~---~

0 2 4 6 8 10

Time (second)

Figure 2.3.10: Displacement, velocity, and acceleration time history re- sponses of the AS controlled by the OCS algorithm and ex- cited by the RRS ground motion

VI t--J

E _{I I} _AID (Max= -9 em)

~ 10

... _c I I

CD

E CD 0

0 co

c. .!!l -10

Cl J

-20 0 2 4 6 8 10

200

--- Uncontrolled (Max= 118 cm/s) _AID (Max= -39 cm/s)

~ 100

~ E

~ 0

·c::;

0 \

CD "'

> -100 -200

0 2 4 6 8 10

~ ¹⁰⁰⁰ --- Uncontrolled (Max = 677 cm/s/s)

~ E _AID (Max= 603 cm/s/s)

c 500

~ 0

CD 0

CD 0

<( 0 CD -500

"5 0 _<I)

~ -1000

0 2 4 6 8 10

Time (second)

Figure 2.3.11: Displacement, velocity, and acceleration time history re- sponses of the PS controlled by the AID algorithm and ex- cited by the ELC ground motion (y= 4)

E ~ 50 'E CD

E 0

CD 0

c. co _<I) i5 -50

v

-100

0 2

400

~ 200

~ ~

:5

₀ ⁰

CD > -200 J

-400

0 2

~ .!!?. 4000 E 0

~ 2000

0

~ CD 0 CD 0

0

<(

.l!! -2000

::3

0 _<I)

~ -4000

0 2

4

(\

I , I I J

I I

\ 'J

4

_AID (Max=-19cm)

,...

v

6 8

--- Uncontrolled (Max= -334 cm/s) AID (Max= -79 cm/s)

1': _1\

^1\

t

^~I

\ I ^{I I} \ I

6 8

10

10

--- Uncontrolled (Max= -2069 cm/s/s) _AID (Max= 1332 em/sis) ('

M.f:AA!V\M

^...,

4 6 8 10

Time (second)

Figure 2.3.12: Displacement, velocity, and acceleration time history re- sponses of the AS controlled by the AID algorithm and ex- cited by the RRS ground motion (y= 4)

Ul VJ

ocs 1

.-.-AID

---AVS

.

. 10'1

'0 '

g

c.

'

<( E 10²

(

/ / /

10'L_

10-¹ 10° 10¹

Frequency (Hz)

(b) 10⁵

... Uncontrolled

ocs 1

.-.-AID

10⁴

---AVS

, ·-

CD

' ·""'

^·~

'0

' /

'

i

::l ¹⁰³

<( E

' ... ·/ ^v

10²1- ..

/ / \ I

/ \ I

/

\I 10¹

10-¹ 10° 10¹

Frequency (Hz)

Figure 2.3.13: Fourier Amplitude Spectra of the responses of the PS ex- cited by the (a) ELC and (b) RRS ground motions

0.8

0.6

0.4

..

... Uncontrolled ocs

0.2 ~ /I _.-.-AID

---AVS

ol

^{_ / ' I I I}

0 2 4 6 8 10

Time (second)

(b)

0.8

0.6

0.4 '·-·

... Uncontrolled

0.2~ ocs

I

^{.-.-AID ---AVS}

0

0 2 4 6 8 10

Time (second)

Figure 2.3.14: Energy flow diagrams of the AIC system excited by the (a) ELC and (b) RRS ground motions

Ul ~

_[3

€ 0

l52

c:-

E ::J

-~ E 1

::::2:

/

/ / '

' ...

... Uncontrolled Controlled .-.-AID ---AVS

... / ...

' ^{... /}

-

~oy- 1 ~--~--~--~~~~~;---~--~~~~=::j

_10°

Period (second)

10¹

12

'E 10

~

€ ⁸

0 c:-

.9 6

en E ::J

E 4

·x a!

::::2:

2 0 10-¹

,... .

/

~

(b)

A - -. . ' . .

/1 ' "

... Uncontrolled Controlled .-.-AID ---AVS

/ . '

/f~

10°

Period (second}

10¹

Figure 2.4.1: SDS ofthe PS under the (a) ELC and (b) RRS excitations

'E ~

€ 0

l5

c:-

E ::J

~ E ^0.5

10-¹ 10°

Period (second}

(b)

10¹

6.---~--~~~~~~.---~--~~~

'E 5

~

:1§4

0 c:-

en .93 E ::J

E 2

·~

::::2:

1

OL---~--~~~~~~~---~--~~~~~~

10-¹ 10° 10¹

Period (second}

Figure 2.4.2: SDS of the AS under the (a) ELC and (b) RRS excitations

Ul.

Ul.

=

~ _~

s ~ ¹ 00 E

~ E

~ ~

.-.- Alpha= 0.02 ---Alpha = 0.04 _Alpha= 0.10

,...:

^-=~ ""laz:..· ..-. _ ... _ - ... ..,... / ..._, -...::

=---- .· .--:-.··-···.:--': ;,_;... . ... ~ ':"';': .--:-···--·"·"':"'-, ·. ':"-:~

0~----~--~--~~~~~---~--~~~~~~

1~ 1~ 1~

(b) Effect of damping ratio on PS (ELC)

~2r---~--~~~~~----~~~~~~~

1 €

0

~ ~ 1

E ~

~ E

... Beta= 1 .-.-Beta= 5 ---Beta= 10

\

' ,_~, I ... · · · · / \ \ . ~ ... -·'V'"· -

.

....:.·: ...

:.:·.,·'-

^{... . / ... ·-.} -:-.·.--:-. ,...,._ ...

:

~"""':.-:::: ^:-;.:..

~ ~o~-1~--~~~--~~~~~~----~--~~~~~~

10° 10¹

e

_~

=

~

(c) Effect of stiffness ratio on PS (ELC)

2r---~--~~~~~~---~~--~~~~~

... Gamma= 1 .-.- Gammaa = 2 ---Gamma=4

Gamma= 10

~ ~ 1

§

~

^{. . .}

~

·~ ^E

I

: :...:;~~

.·· ---·-."·

-:.:-

-

^{..- _.---:-. -> -· ~ ~ ~---}...-·.-,... ... ^-

^::

^:__~:_

~ ₀

-

I

1~ 1~ 1~

Period (second)

Figure 2.4.3: SDS of the PS excited by the ELC ground motion (effects of the mass, damping, and stiffness of the AS)

~ I

~

.-.-Alpha= 0.02 --- Alpha = 0.04 _Aipha=0.10

04

s ~ 00

§2 E

...

~ -0~----~--~~~~~~~----~--~~~~~~

1~ 10° 10¹

(b) Effect of damping ratio on PS (RRS)

E

6

l ...

^{Beta= 1 1 1\}

^j

~ .-.- Beta= 5 ~

€ ---Beta=10 / \\

0 4 Beta=20

~ ~

§ ²

-~ E

-:-/.::: . .--_.;-:c..,~~·§.-.!. ... -

~oL---~~-~~~~~-~~~--~~~~

10-¹ 10° 10¹

(c) Effect of stiffness ratio on PS (RRS)

~6r---~--~~~~~----~~~~~~~

5

~

... Gamma= 1 .-.- Gamma = 2 ---Gamma=4

04

~ ~

§2

~ E

Gamma=10

---

^{. ...:..·}

~ ~o~-1~--~~~--~~~~~---~--~~~~~~

===--::---···..:.-·."= ·.::: :__ - - - ...

~

- ::::.·.:::;. ..

~

10°

Period (second)

10¹

Figure 2.4.4: SDS of the PS excited by the RRS ground motion (effects of the mass, damping, and stiffness of the AS)

Ul 0'1

~ E ... Alpha= 0.01 .-.- Alpha= 0.02 --Alpha = 0.04 _Aipha=0.10

=E Cl

a

~ ¹

E ::I -~ E

/ . .

...

,,.,..

_{_,. ..}

...

~ ~0~1~--~--~~~~~~--~~~~~~~~

10° 10¹

(b) Effect of damping ratio on AS (ELC)

~2~--~----~~~~----~~~~~~

~ ... Beta= 1

.-.-Beta= 5 ---Beta= 10

;!:::

5

~ ~ 1 E ::I

-~ E

Beta=20

.;.>-.?

/ ~-: :.-..:....

~ ~o~-1~--~--~~~~~~--~~~~~~~~

10° 10¹

(c) Effect of stiffness ratio on AS (ELC)

2~----~--~~~~~~~--~--~--~~~~~~

e

~

;!:::

5

a

~ ¹

E ::I

-~ E

... Gamma=1 .-.-Gamma= 2 ---Gamma=4 Gamma= 10

/

~ ~

/

_,..- ...

/ ...

---

/ /

o~----~--~~~~~~~----~--~~~~~~

10-1 10°

Period (second)

10¹

Figure 2.4.5: SDS ofthe AS excited by the ELC ground motion (effects of the mass, damping, and stiffness of the AS)

~ E

=E6

Cl

.94 ~

en E ::I

E 2

~

... Alpha= 0.01 .-.-Alpha= 0.02 --- Alpha = 0.04 _Aipha=0.10

o~----~--~~~~--~~----~--~~~~~~

10-1 10° 10¹

(b) Effect of damping ratio on AS (RRS)

~8~--~--~--~~~----~~--~~~,

~ E

€6

Cl

a4

~

E ~ ²

-~

... Beta= 1 .-.-Beta= 5 ---Beta= 10

Beta= 20

~OL_--~~~~~~~~~--~--~~~~~

10-¹ 10° 10¹

(c) Effect of stiffness ratio on AS (RRS)

~8~--~--~~~~~----~~~~~~~

~ E

Cl

€6

.94 ~

en E ::I

E 2

·x

... Gamma= 1 .-.- Gamma= 2 --Gamma=4 Gamma= 10

/

/ /

/

/

--

-·-

^.

/ ...

...

---

... .

-

^... _... ^-~

/

/ ~

ttl

I .

~ o ,:-·--

======= ^I

10-¹ 10° ^•

Period (second)

10¹

Figure 2.4.6: SDS of the AS excited by the RRS ground motion (effects of the mass, damping, and stiffness of the AS)

Ul -..l

3 2

E' ~

'E Q)

E 0 '-' al

~-1 0

-2 -3 -4

0 2 4 6

Time (second)

... Elastic

- - Elasto-Piastic (Case I) _ Elasto-Piastic (Case II)

8

(b) AS Response with an elasto-plastic AS (ELC)

10

6.---.---.---.---.---,

4

5

²

~

~

a.

5

^-2

-4

:::·: ^:

·.· · ..

... Elastic

- - Elasto-Piastic (Case I) _ Elasto-Piastic (Case II) -6L---L---~---~---~---~

0 2 4 6 8 10

Time (second)

Figure 2.4.7: Displacement time histories ofthe (a) PS and (b) AS with an elasto-plastic AS excited by the ELC ground motion

E' ~

'E Q)

E '-'

a. al _C/)

0

E' ~

'E Q)

E al a. .!!l 0

5

0

_J

-10 0

15 10 5 0 -5 -10 -15 0

\\\f

... Elastic

--- Elasto-Piastic (Case I) _ Elasto-Piastic (Case II)

v

2 4 6 8

Time (second)

(b) AS Response with an elasto-plastic AS (RRS)

...

~:

' :

2 4 6

Time (second)

--- Elasto-Piastic (Case I) _ Elasto-Piastic (Case II)

8

10

10

Figure 2.4.8: Displacement time histories of the (a) PS and (b) AS with an elasto-plastic AS excited by the RRS ground motion

U\

00

/ / /

Ci) ^/

E 100

~

... T1 =0.445 .-.-. T1 = 0.96 5 --- T1 =2.0 5

T1 = 4.6 ⁵ ... ^{/ /}

·;.·./

... .

·g

~

Qi > ^/

/ /

... , ...

...

...

~ _c. ^{50 _.:- ...}

E

~ E

~

(' ...

. ^;/

----

/

_- --

·- - -

OL----L----L----L----~--~----~----L----L--~

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 O.Q18 0.02 Sampling Period (second)

(b) Effect of Sampling Period on Impact Velocity (RRS)

2 5 0 . - - - - . - - - - . - - - - . - - - - . - - - - , - - - . - - - - . - - - - . - - - .

200

... T1 =0.445 .-.-. T1 = 0.96 5 - - T1 = 2.0 5

T1 = 4.65 ^...

-

~ 150 ...

·g

...

...

...

...

/.:; -~ . ..-.

~ u 100

.E ~ _{50 ~ . .} ... . - ,.,.. .... - .

---·-.,..,

-

OL---~--~~--~--~----~--~----~--~--~

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Sampling Period (second)

Figure 2.5.1: Effect of sampling interval on the impact velocity excited by the (a) ELC and (b) RRS ground motions

VI

\0

.!:..

€ 0

.e ~ (/)

§ ^0.5

I f.

I I"

. \

\

.-.- dt = 0.01 s - - dt = 0.005 s

dt = 0.0025 s

-~

:::!:

~o~-1~--~--~--~~~~~~----~--~~~~~~

10° ₁₀¹ 1.5

~ ~ 0

a

~

(b) Effect of Sampling Period- AID (ELC)

... dt = 0.02 s .-.- dt = 0.01 s --- dt = 0.005 s

dt= 0.0025 s

10°

§ 0.5 -~ E

:::!:

~o~-1----~--~--~~~~~~----~--~~~~~:J

10¹

E' 1.5 .!:..

€ 0

.e ~ (/)

(c) Effect of Sampling Period- AVS (ELC)

... dt=0.02s .-.- dt = 0.01 s --- dt = 0.005 s

dt = 0.00255

10°

Period (second)

§ 0.5 -~ E

:::!:

~o;,-1----~--~--~~~~~----~--~~~~~~

₁₀¹

Figure 2.5.2: Effect of sampling interval - SDS of the PS excited ^by the ELC ground motion

.-.- dt = 0.01 s --- dt = 0.005 s .:)::::

;§4

.e ~ (/)

§ ²

E

dt = 0.0025 s

~ ~oy-1~--~--~--~~~~~~----~--~~~--~~

_{10° 10}¹

{b) Effect of Sampling Period- AID (RRS)

~6,---~~~~--~~==~~~~~~~~~~~--~

~ I

€

··· dt= 0.02 s .-.- dt = 0.01 s --- dt = 0.005 s

04

a

~

§2 E

dt= 0.0025 s

1

:::!:

~o~-1----~--~--~~~~~~--~~~~~~~~~

_{10° 10}1

(c) Effect of Sampling Period- AVS (RRS)

Esr-~~~~~~~~~~~~­

.!:.. I

€

... dt= 0.02 s .-.- dt = 0.01 s --- dt = 0.005 s

04

a

~

E §2

dt= 0.0025 s

1

:::!:

~oy-1~--~--~--~~~~~~----~--~~~~~~

_10°

Period (second)

10¹

Figure 2.5.3: Effect of sampling interval - SDS of the PS excited ^by the RRS ground motion

0\ 0

_ TD=Os _ TD=Os

E' --- TD = 0.02 s E" --- TD = 0.02 s

-2. 10 .-.- TD = 0.04 s -2. 20 .-.- TD = 0.04 s

... ... TD =0.08 s

E ... TD = 0.08 s

c ..

I]) .. ^I])

E 0 .. _{E 0}

I]) I])

CJ g _'

i5.. Ill i5..

.!!l -10 .!!l -20

0 0

-20 -40

0 2 4 6 8 10 0 2 4 6 8 10

(b) Effect ofTime Delay- AID (ELC) (b) Effect of Time Delay- AID (RRS)

20 40 ^{I I I I}

_ TD=Os

! 20~

^{_ TD=Os}

E' --- TD = 0.02 s --- TD = 0.02 s

10 .-.- TD = 0.04 s .-.- TD = 0.04 s

-2. ... TD = 0.08 s ... TD = 0.08 s

E c

I]) I])

E 0 E 0

I]) I])

g ^CJ Ill

~ ^{-10 15. .!!l -20} _0\

0 0

...

-20 -40

0 2 4 6 8 10 0 2 4 6 8 10

(c) Effect of Time Delay- AVS (ELC) (c) Effect of Time Delay- AVS (RRS)

20 40- ^I I I I

TD=Os

~ 20~

^_TD=Os

E' --- TD = 0.02 s --TD=0.02s

10 .-.- TD = 0.04 s .-.- TD = 0.04 s

-2. :. ..

... TD"' o.o8.s :it;-.. :··· TD= O.(l8 s

E

..

.. _c

Cll Cll

E 0 E 0

I]) Cll

CJ .. _g

Ill

i5.. i5..

.!!l -10 .. .!!l -20

0 0

-20 -40

0 2 4 6 8 10 0 2 4 6 8 10

Time (second) Time (second)

Figure 2.5.4: Effect of time delay - displacement time histories of the PS Figure 2.5.5: Effect of time delay - displacement time histories of the PS

excited by the ELC ground motion excited by the RRS ground motion

.-.- TD = 0.02 s --TD=0.04s

~

~ ~

~ ~ 1

E ~

~ E

TD = 0.08 s

~ ~0~,~--~--~~~~~~----~~~~~~_j

10' 10'

(b) Effect ofTime Delay- AID (ELC)

2.---~--~--~~~~~---~--~~~~~~

~ E

~ ~

£ ~ 1

w E

~ E

~ ~

... TD=Os .-.- TD = 0.02 s --- TD = 0.04 s TD = 0.08 s

·"'·

'

OL---~--~--~~~~~---~--~~~~~~

1~ 10' 10'

(c) Effect of Time Delay- AVS (ELC)

E2r---~--,-~~~~~~~~~~~~~

... TD=Osl .-.- TD = 0.02 s --- TD = 0.0~ s

~

~ 5

~ ~ 1

~ E

~ E

~

~-.,''

'

I /.-- . <:-..' I/.;' . : "'~ .

. ·. ·~

_.:.;

I . ,... :·

...

TD = o.of s

~o~-,~--~--~~~~~~----~~~~~~~

10'

Period (second)

10'

Figure 2.5.6: Effect of time delay - SDS of the PS excited by the ELC ground motion

~

5

£ ~ 5

w E _~ E

.-.- TD = 0.02 s --- TD = 0.04 s TD= 0.08 s

I

t~.

I \ ' '

I \

~ ~

10¹

~o~-,--~--~~~~~---~~~==j

_10'

E ~

~

10~--~--~~~~~--~~~~~~~~ (b) Effect of Time Delay- AID (RRS) ... TD=Os

.-.- TD = 0.02 s --- TD = 0.04 s

~

£ ~ 5 w

E ~

E

TD= 0.08 s

-~

~ 0

10~-,--~~~~~~~==~

_{10' 10'}

E ~

~

10.---~-c~~~r-~.---~~--~~~~ (c) Effect of Time Delay- AVS (RRS) ... TD=Osl

.-.- TD = 0.02 s --TD=O.O~s

~

£ ~ 5 w

E ~

TD= o.of s

-~ E

~

~0~_,----~~~~~~--~~---~~=======

^10'

Period (second)

10'

Figure 2.5.7: Effect of time delay - SDS of the PS excited by the RRS ground motion

Ri

E"

⁴

~

"E

(])

E ~

g.

^-4

i5

TD=OS --- TD = 0.02 s .-.- TD = 0.04 s ... TD = 0.08 s

-s~---~---~---~---L---~

0 2 4 6 s 10

{b) Time Delay Compensation- AID (ELC)

Sr---.---.---,---.---.

E"

4

~

"E

E

^o

(])

g.

1il ^-4 i5

TD=Os --- TD = 0.02 s .-.- TD = 0.04 s ... TD =.0.08 s

-s~---~---~---~~---L---~

0 2 4 6 s 10

(c) Time Delay Compensation- AVS (ELC)

Sr---.---.r---,---.---,

E"

~

"E

E

^o

g.

~ ^-4

i5

-s~---~---~---~---~---~

0 2 4 6 8 10

Time (second)

Figure 2.5.8: Time delay compensation - displacement time histories of the PS excited by the ELC ground motion

I

¹⁵

"E

(]) '

E 0 1-1---

(])

~ 1il ^-15

Cl

TD=Os --- TD = 0.02 s .-.- TD = 0.04 s ... TD = 0.08 s

-30~---~---~---~---~---~

0 2 4 6 s 10

(b) Time Delay Compensation- AID (RRS)

30r---.---.---,---.---.

"[ 15

"E _(])

_ TD=Os --- TD = 0.02 s .-.- TD = 0.04 s ...•. TIF= O.<lf\s /"

~0~ . /\_/ \.· \_1 ^{. I}

.. '"

0.. 1il

.!!! -15

Cl

-30~---~---~---~~---L---~

0 2 4 6 s 10

(c) Time Delay Compensation- AVS (RRS)

30r---.---.---.---.---,

1

¹⁵

"E

(])

_ TD=Os --- TD = 0.02 s .-.- TD = 0.04 s ... TD= 0.08 s

~0~

c.. 1il

.!!! -15

Cl

-30~---~---~---~---~---~

0 2 4 6 s 10

Time (second)

Figure 2.5.9: Time delay compensation - displacement time histories of the PS excited by the RRS ground motion

(.;,) 0'1

-3.

€ 0

;::..

.9 (/)

§ 0.5

-~ E

::2

~oy-·~--~--~--~~~~~~----~--~~~~~~

10° 10'

E' 1.5 -3.

<!=

25 ;::..

~

(b) Time Delay Compensation- AID (ELC)

... TD=OS .-.- TD = 0.02 s --- TD = 0.04 s TD=0.08 s

I

\

\

"'

I .\'\ ...

.·\\ _\.· -·:...:;:; ^.;"' ...

~.·.-.-.

^...

:..;.-_:-_-::-.~ ...

§ 0.5

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ctS

::2

~oy-·~----~--~~~~~~~----~--~--~~~~~

_{10° 10'}

E' 1.5 -3.

0 €

;::..

~

(c) Time Delay Compensation- AVS (ELC)

... TD=Os .-.- TD = 0.02 s --- TD = 0.04 s TD = 0.08 s

-.I'

§ 0.5

-~ E ::2

-.,...'-".~··

.

^{~;. ..}

~or.-,----~--~--~~~~~;---~--~~~~~~

_10°

Period (second)

10'

Figure 2.5.10: Time delay compensation - SDS of the PS excited by the ELC ground motion

<!=

.-.- TD = 0.02 s --- TD = 0.04 s

254

;::..

(/) .9

TD = 0.08 s

§2 E

::2 ~

~oY'~----~--~~~~~~~----~--~--~~~~~ ^~_...,-

• ...-:"'·..:::: .. -:.-' ·'""-" --'"-'."'"c' ; · / " . - · ·

10° 10'

(b) Time Delay Compensation- AID (RRS)

~6~~~~~~~~~~~~

E I ^{... TD=O~} "

.-.- TD = ^{O.Q2 s}

--- m = o.d4 ^s

_ TD=O.Ofls

I \

1.'\ \

,, ·,

^\

-3.

<!=

254 ;::..

.9 (/)

§ 2 E

/.·

II /.

·~

::2

~o~-,--~--~~~~~--~--~~~~J

_{10° 10'}

(c) Time Delay Compensation- AVS (RRS)

E'6r-~~~~~~~~~~~~~

-3. I ... TD=Os .-.- TD = 0.02 s --TD=0.04s

<!=

254

;::..

~

§2 E

~ ::2

TD = 0.08 s

===--"""7.··-· ~

~o~-,--~--~~~~~----~~--~~

10°

Period (second)

10'

Figure 2.5.11: Time delay compensation - SDS of the PS excited by the RRS ground motion

~