r - The Hong Kong Polytechnic University

Table 1 System parameters of the system
Component Item Value
Primary structure
SAF-TMD
Sliding
platform
PFD
Mass (m p)
Period (T p)
2100 kg
1.90 sec
Damping ratio (ζ s) 4.90 %
Maximum story drift (x p) ± 0. 25 m
Mass (m s)
Spring stiffness (k i)
Period (T i)
96 kg
1017 N/m
1.93 sec
Friction coefficient ( μ
i
) 0.009
Maximum stroke (x s) ± 0. 15 m
Friction coefficient of damper ( μ ) 0.20
Damper stiffness (k d)
Piezoelectric coefficient ( C )
Pre-compression force (N 0)
Range of driving voltage (V)
z
d
10 6 N/m
0.46 N/Volt
130 N
0-1000 Volt
N 0
Normal force (N)
Voltage & Normal force
800
y = 0.46*x + 1.3e+002
700
600
500
400
300
200
100
Experimental
Theoretical
0
0 200 400 600 800 1000
Control Voltage (V)
Figure 6 Force and voltage relationship of the PFD.
Test setup and input ground acceleration
Figure 4 depicts the test setup. One velocity sensor and one accelerometer are placed on the shaking table (the
ground), on the primary structure and on the SAF-TMD. Additionally, two LVDTs were used to measure the
relative-to-the-ground displacement of the primary structure and the TMD stroke. A load cell was embedded in
the PFD to measure normal force N(t) (Figure 2). The 1940 El Centro earthquake was applied in the shaking
table test as the ground acceleration.
TEST RESULTS AND DISCUSSION
Comparison of experimental and theoretical results
This section reports the experimental findings of the shaking table test. To ensure accurate experimental results,
the test data were first verified by the theoretical results simulated by SBM. Additionally, acceleration signals
measured by an accelerometer placed directly on the shaking table were used as input to simulate ground
excitations. Figure 7 compares the experimental and simulated responses of the SAF-TMD system subjected to
the El Centro earthquake (PGA=500gal). Note that each figure contains six sub-figures in the following
sequence: (a) time-history of the structural displacement x p (t), (b) time-history of the absolute acceleration of the
primary structure, (c) time-history of the TMD, (d) time-history of the normal force N(t), (e) total shear force of
the SAF-TMD S s (t) vs. TMD stroke v s (t), (f) damper force u d (t) of the PFD vs. TMD stroke v s (t). Sub-figures (e)
and (f) of Figure 7 also show the hysteretic behaviors of the SAF-TMD and PFD, respectively. In Figure 7, the
following observations can be made: (1) all measurement data are consistent with the predicted SAF-TMD
system behavior, i.e., the test data are reliable, and numerical method is effective for analyzing SAF-TMD
system dynamic response. (2) Figure 7(d) demonstrates that the normal force N(t) of the PFD damper has been
altered by the embedded piezoelectric actuator. This behavior differs from the constant normal force typically
observed in a PF-TMD. This also implies that the slip force of the PFD has been altered by the actuator. (3) Due
to the complicated friction behavior as well as measurement noise, the discrepancy in the experimental and
theoretical hysteresis loops of the PFD (Figure 7(f)) is relatively larger than that in other system responses.
Nevertheless, this discrepancy does not significantly affect the global responses of the SAF-TMD because for
both the displacement and acceleration responses, the experimental results are consistent with the theoretical
results (sub-Figs. (a) and (b) in Figure 7).
0.2
0.15
Structural displacement
Theoretical
Experimental
2
1.5
Structural acceleration
Theoretical
Experimental
0.2
0.15
TMD stroke
Theoretical
Experimental
Displacement (m)
0.1
0.05
0
-0.05
-0.1
Acceleration (m/s 2 )
1
0.5
0
-0.5
-1
Stroke (m)
0.1
0.05
0
-0.05
-0.1
-0.15
-1.5
-0.15
-0.2
0 10 20 30 40 50 60
Time (s)
-2
0 10 20 30 40 50 60
Time (s)
-0.2
0 10 20 30 40 50 60
Time (s)
(a) Structural displacement (b) Structural acceleration (c) TMD stroke
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