Vibration Tests of a Three Story Benchmark Structure with Vibration Control Devices that Generate Po

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Vibration Tests of a Three Story Benchmark
Structure with Vibration Control Devices that
Generate Power
ASCE Structure Congress 2008 in Vancouver, Canada

• Taichi Matsuoka, Akita University, Japan
• Katsuaki Sunakoda, Akita University, Japan
• Hiramoto Kazuhiko, Akita University, Japan
• Paul Roschke, Texas AM University, TX, U.S.A.

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CONTENTS
1. Background 2. Construction 3. Performance
Tests 4. Experiments 5. Control Theory 6.
Seismic Tests 7. Conclusion
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BACKGROUND
Recently, structural problems in tall
buildings and power plants have become evident as
a result of long-period vibrations due to
earthquakes. In order to ameliorate these
problems a number of damping devices have been
developed by many researchers. One of the
authors also has developed the Mechatro damper
which has a damping force that is imposed on the
structure by a power generator. The force of the
damper is proportional to its velocity. On the
other hand, the mechanical snubber utilizes an
inertial force derived from a flywheel that is
proportional to acceleration. That is, the
device has a so-called series inertial mass. The
authors developed a vibration cut-off system
using water or a functional fluid that acts as a
series inertia mass, and the effects of vibration
cut-off have been confirmed. In a previous
paper the authors proposed a new vibration
control device (VCD) that also generates power.
The VCD has an inertial force created by an
inertial disk and damping force provided by
energy dissipation of the power generator. This
device acts as a semi-active damper, and
functions as a fail-safe mechanism under
controller malfunction.
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PURPOSE
A prototype model was fabricated and vibration
tests were carried out in a laboratory. The
focus of this paper is application of the
prototype large-scale VCD to a real structure.
Two new VCDs that have a force capacity in the
range of 15 kN
In order to investigate dynamic properties of
the VCD, performance tests are carried out and
the resisting force characteristics of the device
are measured.
Vibration tests by a shake table with the VCDs
National Center for Research on Earthquake
Engineering (NCREE) in Taiwan
Control law based on minimizing the Lyapunov
function
The effects of vibration suppression using the
VCD are confirmed.
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Schematic of the V.C.D.
Ball nut
Flywheel
Power generator
Ball screw
Rod end
Gear
Bearing
Coupling
140mm
700mm
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Design Parameters of the V.C.D.
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Generates Force
The relative displacement between both of the
rod ends is u, the angle of the ball screw shaft
(?1), and the power generator shaft (?2) are
given by the following equations, (1) where ?
denotes an increasing ratio of the gear, and L is
the lead of the ball screw. The resisting force
between both of the rod ends F is given
by (2) where ? is the rotary conversion
efficiency of the ball screw, T1 and T2 are
torques of the ball screw and power generator,
respectively. Rotary torques T1 and Ti act
at the shaft of the ball screw and at the power
generator, respectively, and they are given
by (3) where I1 is a rotating moment of inertia
of the inertial disk, the ball screw shaft and so
on, and I2 is a moment of inertia of the power
generators shaft. Braking torque Tb is expressed
by the following, (4)
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where KE and KT are factors of induced
electromotive force and generated torque, and Ra
and R are the internal and terminal resistance of
the power generator, respectively. The total
resisting force is given by a sum of the above
expressions. Substituting Eq. (2) into T2 Ti
Tb, from Eq. (1) (4) gives the
following, (5) Therefore, the VCD has a
maximum damping force. The case of terminal
resistance R 0 is termed a closed circuit,
while a minimum damping force R 8 is taken to
be an opened circuit. A factor of first term
which is proportional to acceleration (defined by
an equivalent mass me), and second term which is
proportional to velocity is defined by a damping
coefficient cd.
Inertial force
Variable damping force
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PERFORMANCE TESTS
In order to determine dynamic properties of the
VCD, a series of performance tests are carried
out using a dynamic actuator. The resisting
force and displacement are measured by a load
cell, and a displacement transducer,
respectively, for sinusoidal displacements that
have amplitudes of 5 and 10 mm and frequencies of
0.3, 0.5 and 0.7 Hz. In addition, three types of
terminal resistance are studied.
V.C.D.
Vibration actuator
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Force-Displacement Curve
Experiment Calculation
0.3 Hz
0.5 Hz
0.7 Hz
Force kN
(a) me 6000 kg, R 8 W, cd 0 Ns/m
0.3 Hz
0.5 Hz
0.7 Hz
Force kN
Displacement mm
(d) me 6000 kg, R24 W, cd 9000 Ns/m
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Force-Displacement Curve
Experiment Calculation
0.3 Hz
0.5 Hz
0.7 Hz
Force kN
(c) me 6000 kg, R15.2 W, cd 13600 Ns/m
0.3 Hz
0.5 Hz
0.7 Hz
Force kN
Displacement mm
(d) me 6000 kg, R10.8 W, cd 18400 Ns/m
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Force-Displacement Curve
Experiment Calculation
0.3 Hz
0.5 Hz
0.7 Hz
Force kN
Displacement mm
Displacement mm
Displacement mm
me 12000 kg, R 8 W, cd 0 Ns/m
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EXPERIMENTS
x3
m3
3rd
Weight
k3
c3
x2
m2
2nd
V.C.D.
me, c2d
k2
c2
A/D
x1
m1
1st
PC
me, c1d
D/A
x0
k1
c1
Controller
Analytical model
Shaking table
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Parameters of 3-story structure
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Equation of Motion
The equation of motion of 3-story benchmark
structure in matrix form is given by (6) where
M, K and C denote a matrix of mass, stiffness and
damping, xi is absolute displacement at i-th
story, and given in (7) where mi, ki,
and ci are mass, stiffness, and internal damping
coefficient, cid is the damping coefficient of
V.C.D. located at i-th story, and the mass and
damping ratios of i-th story are ?i me/mi, and
?i (cicid)/2(miki)0.5, respectively.
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Control Theory
In order to dissipate the kinetic and potential
energy of the structure, a control law based on
the Lyapunov function is used. The Lyapunov
function is defined by (8) The factor ? in Eq.
(8) is a balance factor between kinetic and
potential energy. For example, in the case of ?
0.5, it is a sum of the normal kinetic and
potential energy. A measure of the speed of
energy dissipation is derived by differentiating
Eq. (8), as follows (9) For the purpose of
maximizing the speed of energy dissipation,
elements of Eq. (9) that depend on variable
damping are the 1st and 4th matrices. This leads
to the follows (10) which can be minimized using
Eqs. (7) and (10) to the following (11)
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Seismic Tests
(11) Terms in Eq. (11) that depend on the
variable damping, namely the first and third
terms, are to be minimized. The third term is
always negative under any condition, since it is
a square of relative velocities therefore Eq.
(11) is optimized for all c2d magnitudes. On
the other hand, the value of the first term is
influenced by a product of absolute velocity and
relative velocity and, therefore, Eq. (11) is
optimized for the c1d term by maximizing the
product term of the damping force generated and
setting it to zero under any other conditions.
That is, the control law can be represented by
bang-bang operation, and the variable damping
coefficient is changed as follows (12)
Always positive
Variable damping
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Experimental Apparatus
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Experimental Results
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Experimental Results (Acc.)
Exp.
Cal.
Time s
Exp.
Cal.
Exp.
Cal.
Time s
Time s
(b) Without the V.C.D.
Exp.
Cal.
Exp.
Cal.
Exp.
Cal.
Exp.
Cal.
Exp.
Cal.
Exp.
Cal.
Time s
Time s
(c) With the V.C.D. (z1control, z20.1, e1e21)
(d) With the V.C.D. (z1control, z20.1, e1e22)
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Experimental Results (Disp.)
Exp.
Cal.
u1 mm
Exp.
Cal.
u2 mm
Exp.
Cal.
u3 mm
Time s
Time s
(b) Without the V.C.D.
Exp.
Cal.
Exp.
Cal.
u1 mm
u1 mm
Exp.
Cal.
Exp.
Cal.
u2 mm
u2 mm
Exp.
Cal.
Exp.
Cal.
u3 mm
u3 mm
Time s
Time s
(c) With the V.C.D. (z1 control, z20.1, e1e21)
(d) With the V.C.D. (z1control, z20.1, e1e22)
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CONCLUSION
The V.C.D. has dynamic characteristics of the
sum of the inertial force proportional to
acceleration, damping force proportional to
velocity, and friction force. The experimental
results are in good agreement with the
theoretical results. When the V.C.D. is
attached to the 1st and 2nd floors of the
structure, the maximum relative displacement of
each story decreases to approximately 1/21/3 of
the values that are obtained when the V.C.D. is
not installed, likewise the acceleration
decreases to approximately 1/41/3 of their
counterparts. Clearly, the V.C.D. has positive
effects of vibration suppression for the large
structure. The experimental results of seismic
response agree reasonably well with the
calculated results, and the propriety of the
numerical simulations is confirmed.
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Acknowledgement
The authors would like to appreciate Prof. Dr.
Chin-Hsiung Loh of National Taiwan University,
and Dr. Pei-Yang Lin of National Center for
Research on Earthquake Engineering for help in
our experiments. This work was supported by
Grant-in-Aid for Scientific Research in JAPAN
(KAKENHI, No. 19560224). End. Thanks !