4th International Conference on Earthquake Engineering Taipei, Taiwan

October 12-13, 2006

Paper No. 199

NUMERICAL SIMULATION OF 3-STORY STRUCTURE WITH VIBRATION CONTROL DEVICE

Taichi Matsuoka1, Kazuhiko Hiramoto1, Katsuaki Sunakoda1, Takafumi Ohtake1 and Paul N. Roschke2

ABSTRACT

In a previous paper, the authors proposed a vibration control device using an inertia mass and a generator that is suitable for structural damping. Linear motion of the structure due to seismic vibration is converted into rotary motion by the ball screw, and electric power is converted by a generator through a gear. From the theory, the device has the resisting force characteristics of the sum of the damping force created by the resistance of the controller, and the inertial force from the disk that acts as a flywheel. In this paper, numerical simulations of a 3-story structure with the vibration control device attached to the first floor are carried out. Both frequency response and response to seismic excitation are calculated. With regard to seismic response, the Imperial Valley (1940) El Centro NS component is normalized to a maximum acceleration of 0.5 m/s2 and applied horizontally to the base floor; the displacement and acceleration responses of each story are evaluated. The vibration tests of the 3-story structure with the damper installed are carried out at the National Center for Research on Earthquake Engineering (NCREE) in Taiwan. Keywords: Vibration Control Device, Damping, Inertial Force, Power Generator, 3-Story Structure

INTRODUCTION Recent research concerning a novel damping device named “Mechatro Damper” that incorporates an electrical generating system has been reported by Sunakoda, et al., 1992/1995; Iwata, et al., 1994/1997; and Iiyama, et al., 1998. Not only does the damper have a controllable damping force that effectively controls structural vibration as a semi-active damper, but it also generates electric power.

In a previous paper the authors proposed a small-scale vibration control device using a power generator that has a large damping effect through a controllable damping coefficient that operates in low frequency ranges. The vibration control device (hereafter called V.C.D.) is suitable for vibration control of a flexible structure that has a long period of vibration. Dynamic properties were investigated experimentally and theoretically under sinusoidal excitation motion. Seismic responses of one degree of freedom vibration model attached the V.C.D. were calculated. It was clear from the numerical results that the V.C.D. was effective for reducing random vibration that are earthquake induced (Sunakoda, et al., 2005/2006).

In this paper in order to investigate the effects of vibration suppression for a large structure, performance tests of the V.C.D., as well as experimental vibration tests and numerical simulations of a 3-story benchmark structure are carried out at the National Center for Research on Earthquake

1 Research Assistant, Department of Mechanical Engineering, Akita University, 1-1 Tegata Gakuen-machi, Akita-shi, Akita 010-8502, Japan, matsuoka@ipc.akita-u.ac.jp 2 Professor, Zachry Department of Civil Engineering, Texas A&M University, College Station, Texas 77843-3136, USA, p-roschke@tamu.edu

Engineering (NCREE) in Taiwan. The V.C.D. consists of a ball screw, inertia disk and a power generator. It has dynamic characteristics of the sum of the controllable damping and the inertia mass in other words its operation is a function of the sum of the rotating moment of inertia of the inertial disk and variable damping provided by the power generator. A prototype large-scale V.C.D. is manufactured, and the resisting force characteristics of the device are measured in performance tests. Frequency responses and seismic responses of a 3-story benchmark structure with the V.C.D installed at the 1st and 2nd floor levels are calculated by using Matlab software. Experimental results are compared with the calculated results and as shown in what follows, they generally agree with each other. The validity of vibration suppression of the V.C.D for a large structure is confirmed.

CONSTRUCTION OF THE VIBRATION CONTROL DEVICE Construction of the V.C.D. using a power generator is shown in Fig. 1. The V.C.D. consists of a ball screw, a piston, an inertial disk, a gear, an electric power generator, and rod ends. Linear motion is converted into rotary motion by the ball screw and ball nut mechanism. The rotating speed of the ball screw shaft is magnified by using the gear. The inertial disk, which is a flywheel, is connected to the end of the ball screw shaft, and is able to provide inertia force by moment of inertia. The electrical power generator is connected to a variable current controller that has a function of an equivalent electrical resistance. The damping force is created by consuming the generated electric power, and it depends on amount of electrical current of the terminal. Damping Force According to the proposed theory (Sunakoda, et al., 2005/2006), when the relative displacement u between both of the rod ends is excited, the damping force FD can be given by the following expression.

(1) uRR

KKl

Fa

TE

BD &⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ παη

=2

21

where lB is a lead of the ball screw, α is gear ratio, η is rotary conversion efficiency of the ball screw, K

B

E and KT denotes the coefficient of induced electromotive force and the generated torque, and R and Ra denotes the resistance of the terminal of the power generator and motor, respectively.

Therefore, the damping force of the V.C.D. varies as a function of the terminal resistance. The maximum damping force is generated in case of the resistance R = 0 (short circuit), and the minimum damping force is nearly equal to zero in the case of R = ∞ (open circuit). Inertial Force The inertial force of the device, FI , is proportional to the relative acceleration between both of the rod ends, and can be written by the following expression. Generator Inertial disk Ball nut Ball screw

Figure 1. Construction of the vibration control device.

Rod end Gear Ball bearing Coupling

Rubber

Terminal

( )uII

lF

BI &&21

22

21+α⎟⎟

⎠

⎞⎜⎜⎝

⎛ πη

= (2)

where, I1 and I2 are the rotating moment of inertia of the power generator and inertial disk, respectively.

From Eqs.(1) and (2) the total force of the V.C.D. is given by

⎟⎟⎠

⎞⎜⎜⎝

⎛α

+++α⎟⎟

⎠

⎞⎜⎜⎝

⎛ πη

= uRR

KKuII

lF

a

TE

B

&&& 221

22

)(21(3)

It is obvious from the above expression that the total force is proportional to the relative velocity

and the acceleration.

RESISTING FORCE CHARACTERISTICS

In order to investigate dynamic properties of the V.C.D., a series of performance tests are carried out by using a dynamic actuator. Components for two configurations of the trial V.C.D. were designed

Table 1. Design parameters of the V.C.D.

V.C.D. Length 687 mm Weight 15 kg Max. driving force 15 kN Stroke 50 mm Ball screw Lead LBB 5 mm Diameter 14 mm Rotary efficiency η 0.94 Inertial disk Equivalent mass me 6000 kg Moment of inertia I2 24.9×10-4 kgm2

Gear Gear ratio α 5 Power generator Type SS40E4-L1-5 Damping coefficient c 191×102 Ns/m Permitted watt 40 W Torque constant KT 0.074 Nm/A Electromotive force KE 0.074 Vs/rad Motor resistance Ra 1.7 Ω Moment of inertia I1 0.53×10-4 kgm2

-10 0 10-3

0

3Exp. Cal.

0.3 Hz -10 0 10

-3

0

3Exp. Cal.

0.5 Hz -10 0 10

-3

0

3Exp. Cal.

0.7 Hz

Forc

e [k

N]

Displacement [mm] Displacement [mm] Displacement [mm]

Figure 2. Resisting force characteristics of the V.C.D.

and manufactured in Japan and shipped to NCREE in Taiwan. The V.C.D. is inserted between the vibration actuator and a rigid wall. The design parameters of the trial V.C.D. are shown in Table 1. The force-displacement curve under exciting sinusoidal waves that have an amplitude of 10 mm and frequencies 0.3, 0.5, and 0.7 Hz are measured.

Figure 2 shows the experimental results together with the theoretical results. It can be seen from Fig. 2 that the V.C.D. has resisting force characteristics of the sum of the damping force created by the resistance of the terminal, and inertial force from the disk that acts as a flywheel. The curve becomes inclined toward the second and forth quadrants in all cases. In should also be noted that curves of the experimental results are influenced by an accidental gap of the ball screw in the test.

VIBRATION TESTS AND SIMULATIONS After performance tests had been completed on the V.C.D., vibration tests on 3-story benchmark structure that is modified to contain the damper are conducted by using a shake table at NCREE. The trial V.C.D. which has a damping ratio approximately ζ = 0.1 is attached between the base and 1st floor, and between the 1st and 2nd floors, respectively, as shown in Fig. 3. Table 2 lists the physical parameters of the 3-story benchmark structure. Both sinusoidal and random waves such as are caused by earthquakes are input horizontally by the shaking table. The equations of motion of the 3-degree-of-freedom system (Fig. 3(a)) are given by

Damper

1st

2nd

3rd

me, c

c1k1

k2

c3k3

m c2

m

m x3

x2

me, c

Damper

x1

x0

(a) Analytical model (b) Test setup (c) Photo

Figure 3. Test set up of 3-story benchmark structure.

Table 2. Physical parameters of the 3-story benchmark structure.

Total height 9 m Width 3 m Span 2 m Weight of each story m 6 t (18 t total) Stiffness k1 1.6609×106 N/m k2 1.9152×106 N/m k3 1.5694×106 N/m Damping coefficient c1 8.7314×102 Ns/m c2 3.6620×103 Ns/m c3 5.4533×103 Ns/m

(4) 0)()(0)()()())(()(

0)()())(())(()()(

2332333

323122323122122

21201121201121011

=−+−+=−+−+−+−++−+

=−+−+−++−++−+−+

xxkxxcxmxxkxxkxxcxxccxxmx

where, xi denotes the absolute displacement of base and each floor, respectively, and me is the equivalent inertia mass derived from Eq.(2). The above equations of motion can be expressed in matrix form as follows

(5)

where, [M], [K] and [C] are the mass, stiffness and damping matrix, respectively, and ui (= xi – x0) is the relative displacement between base and each floor. Numerical simulations of seismic response are carried out by using Matlab software. Frequency Response Figure 4 shows the calculated frequency responses at the 1st floor of the benchmark structure when it is subjected to sinusoidal excitation. It is apparent from Fig. 4 that the peak of the displacement ratio at the first resonant frequency decreases to about 1/6~1/8 of the case in which the V.C.D. is not present. It is clear from the frequency response that the resonant frequency of the structure can be shifted toward the low frequency range with the aid of the inertial device. Seismic Response The Imperial Valley earthquake (1940) El Centro North-South component normalized to be 0.5 m/s2 at maximum acceleration are input to the horizontal direction of the shake table, and the acceleration and displacement of each floor are measured by accelerometers and linear variable displacement transducers. In what follows the experimental results are compared with the calculated results.

Figure 4. Frequency responses of 3-story benchmark structure.

0.5 1 5 1010-2

10-1

100

101

102

Frequency [Hz]

Am

plitu

de ra

tio x

1/x0

Without the V.C.D. 1st floor only 1st and 2nd floor

mxxkxxkxxccxxccxxmxxmx

e

ee

&&&&

&&&&&&&&&&

&&&&&&&&&&&&&&m

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

−−−

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−+−

−+=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−++−−

−−++=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡+−

−+=

−=++

0

0

0

0

03

02

01

3

2

1

33

3322

221

33

3322

221

0

}{,}{,0

0][

0

02][,

00002

][

}{}]{[}]{[}]{[

xxx

xxxxxxx

uuu

ukkkkkk

kkkK

cccccccc

cccccC

mmmm

mmmM

xmuKuCuM

ee

ee

The maximum response acceleration of the 1st floor and relative displacement between the base and 1st floor are given in Table 3 and the response waves are shown in Fig. 5. It can be seen from Table 3 and Fig. 5 that the maximum acceleration and relative displacement decrease to approximately 1/2~1/4 and 2/3~1/3, respectively, of their counterpart values during experiments without the V.C.D. It is apparent from these figures that the experimental results substantially agree with the calculated results and the effects of vibration suppression are confirmed experimentally and theoretically.

CONCLUSIONS In this paper, a vibration control device using a generator is developed and tested. The resisting force characteristics are measured using by dynamic actuator. Dynamic responses of a full-scale 3-story benchmark structure attached the V.C.D. are measured and calculated. The conclusion may be summarized as the follows:

1. The experimental results of resisting force of the V.C.D. are in good agreement with theoretical results, and the damping force created by resistance is proportional to the velocity.

2. The V.C.D. has dynamic characteristics of the sum of the inertial force and the damping force. 3. The resonant frequency of the 3-story structure can be shifted toward the low frequency range

with the aid of the inertial device. 4. When the V.C.D. is attached to the 1st floor of the structure, the maximum displacement of

each story decreases to approximately 1/2~1/3 of the values that are obtained when the V.C.D. is not installed likewise the acceleration decreases to approximately 1/4~1/3 of their counterparts. Clearly, the V.C.D. has positive effects of vibration suppression for the structure.

5. The experimental results of seismic response agree reasonably well with the calculated results, and the propriety of the numerical simulations is confirmed.

ACKNOWLEDGMENTS The authors would like to acknowledge Dr. Chin-Hsiung Loh of National Taiwan University and Dr. Pei-Yang Lin of National Center for Research on Earthquake Engineering for assistance in carrying out the experiments.

REFERENCES Iwata, Y., Suzuki, K., Iiyama, F. and Sunakoda, K., (1994), “Semiactive Control of Seismic Isolation System

Using Mechatro Damper”, Proc. ASME PVP, 275-2, 129-135.

Table 3. Maxima of the seismic response of 3-story benchmark structure.

Acceleration [m/s2] Displacement [mm] Story Exp. Cal. Exp. Cal. Without the V.C.D. 1st

2nd 3rd

1.24 1.04 1.26

0.54 0.77 1.10

10.8 9.65 6.33

8.15 5.82 4.29

With the V.C.D. at 1st floor only 1st 2nd 3rd

0.39 0.49 0.60

0.29 0.43 0.55

6.14 5.37 3.16

5.70 3.12 2.15

With the V.C.D. at 1st and 2nd floor 1st 2nd 3rd

0.25 0.35 0.41

0.25 0.32 0.32

4.34 3.90 2.12

3.97 2.45 1.23

[m/s2]

0 10 20 30 40-0.5

0

0.5

x 0..

Time [s]

(a) Input acceleration (El Centro NS 0.5 m/s2) [m/s2] [mm]

-100

10

-100

10

0 10 20 30 40-10

010

0 10 20 30 40

Cal. Exp.

Cal. Exp.

Cal. Exp.

-101

-101

0 10 20 30 40-101

0 10 20 30 40

Cal. Exp.

Cal. Exp.

Cal. Exp. x 1.. u 1

u 2-u

1

x 2..

u 3

-u2

x 3..

(b) Without the V.C.D. [m/s2] [mm]

-100

10

-100

10

0 10 20 30 40-10

010

0 10 20 30 40

u 3-u

2u 2

-u1

Cal. Exp.

Cal. Exp.

Cal.

u 1

Exp. -101

-101

0 10 20 30 40-101

0 10 20 30 40

Cal. Exp.

Cal. Exp.

Cal. Exp.

x 1..

x 2..

x 3..

(c) With the V.C.D. at 1st floor only (ζ = 0.1) [m/s2] [mm]

-100

10

-100

10

0 10 20 30 40-10

010

0 10 20 30 40

u 3-u

2u 2

-u1

Cal. Exp.

Cal. Exp.

Cal.

u 1

Exp.

-101

-101

0 10 20 30 40-101

0 10 20 30 40

Cal. Exp.

Cal. Exp.

Cal. Exp. x 1..

x 2..

x 3..

Time [s] Time [s] Time [s] Time [s]

(d) With the V.C.D. at 1st and 2nd floor (ζ = 0.1 each)

Figure 5. Seismic response waves of 3-story benchmark structure. Iwata, Y., Sunakoda, K. Iiyama, F. and Suzuki, K., (1997), “Hybrid Control of Seismic Isolation System Using

Mechatro Damper” (in Japanese), Trans. JSME, Series C, 63 (613), 2991-2995.

Iiyama, F., Sunakoda, K. and Suzuki, K., (1998), “Hybrid Control of Seismic Isolation System Using Mechatro Damper”, Proc. ASME PVP, 379, 157-161.

Ohtake, T., Sunakoda, K. and Matsuoka, T., (2005), “Study on a Vibration Control Device Using Power Generator” (in Japanese), Proc. JSME Dynamics and Design Conference 2005, No.307, CD-ROM, 5p.

Ohtake, T., Sunakoda, K. and Matsuoka, T., (2006), “Study on Vibration Control Device Using Power Generator”, Proc. ASME PVP2006-ICPT-11, Seismic Engineering, No.93534, CD-ROM, 5p.

Sunakoda, K., Iiyama, F. and Ikahata, N., (1992), “Study of a High Damping Device based on Electricity Generating System”, Proc. ASME PVP, 229, 133-136.

Sunakoda, K. Iwata, Y., Iiyama, F. and Suzuki, K., (1995), “Semiactive Control of Seismic Isolation System Using Mechatro Damper” (in Japanese), Trans. JSME, Series C, 61 (584), 1308-1312.