r - The Hong Kong Polytechnic University

Force (N)
600
500
400
300
200
100
Normal force
Theoretical
Experimental
total shear force (N)
300
200
100
0
-100
-200
Theoretical
Experimental
Total hysteresis loop
Friction Force (N)
200
150
100
50
0
-50
-100
-150
Damper hysteresis loop
Theoretical
Experimental
0
0 10 20 30 40 50 60
Time (s)
-300
-0.2 -0.1 0 0.1 0.2
TMD Stroke (m)
-200
-0.2 -0.1 0 0.1 0.2
TMD Stroke (m)
(d) Normal force (e) Total hysteresis loop (f) Damper hysteresis loop
Figure 7 Comparison of experimental and theoretical results due to El Centro earthquake (PGA=500gal,
N 0 =130 N).
Definition of performance indices
The comparison results were quantified by performance evaluations of the SAF-TMD system in terms of the
five performance indices (J 1 -J 5 ) in Table 2. The indices J 1 and J 3 in Table 2 represent the peak response ratios of
the structural displacement x p (t) and structural acceleration of the SAF-TMD system, respectively. The indices
J 2 and J 4 represent the root-mean-square (RMS) response ratios of x p (t) and & x p , a ( t)
, respectively. Performance
index J 5 represents the peak TMD stroke of the SAF-TMD. Notably, indices J 1 to J 4 were all divided by the
corresponding response values of the uncontrolled system (primary structure only), which are represented by
symbols with a top bar in Table 2. Therefore, for indices J 1 to J 4 , a value less than one implies that the
SAF-TMD system has a lower response than that of the uncontrolled system.
Table 2 Definition of performance indices
Response Peak structural displacement RMS structural displacement
max( x
p
( t))
w / TMD
RMS(
x
p
( t))
w / TMD
Index J1
=
J
2
=
max( x ( t))
RMS(
x ( t))
p
w / o TMD
p
w / o TMD
Response Peak structural acceleration RMS structural acceleration
Index
max( && x
p,
a
( t))
w / TMD
RMS(
&& x
p,
a
( t))
w / TMD
J
3
=
J
4
=
max( && x
p,
a
( t))
w / o TMD
RMS(
&& x
p,
a
( t))
w / o TMD
Stroke
Peak TMD stroke
Index J = max( v ( ))
5 s
t
Comparison of SAF-TMD and uncontrolled system responses
To demonstrate the control efficiency of the SAF-TMD, this subsection compares the experimental seismic
responses of the SAF-TMD system to the simulated responses of its uncontrolled counterpart system (primary
structure only). In the uncontrolled system, simulated responses were used instead of experimental ones for two
reasons: (1) the uncontrolled system easily exceeds the allowable displacement of 0.25m, which limits
comparison with earthquakes in which PGA is larger. (2) For comparison purposes, it would be very difficult for
the shaking table to generate two exactly same ground accelerations for the SAF-TMD and uncontrolled systems.
Therefore, simulations of the uncontrolled system for comparison purposes used the same ground acceleration
measured in the SAF-TMD test and the same system parametric values shown in Table 1.
Table 3 shows the performance indices of the SAF-TMD system when data for the selected earthquake was
applied. Table 3 shows that, although the SAF-TMD is less effective in reducing the peak response (J 1 and J 3 ) of
the system, it reduces the RMS structural displacement by 12-18% (see J 2 ) and the RMS structural acceleration
by 12-17% (see J 4 ), as compared to the RMS responses of the uncontrolled system.
Table 3 Performance indices of the SAF-TMD
Earthquake
PGA Disp. index Acc. index
(gal) J 1 J 2 J 3 J 4
300 0.98 0.88 1.03 0.88
El Centro 400 0.94 0.84 0.99 0.85
500 0.91 0.82 0.90 0.83
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