The intensity of natural disasters has increased recently, causing buildings’ damages which need to be reinforced to prevent their destruction. To improve the seismic proofing capability of Accumulated Semiactive Hydraulic Damper, it is converted to an Active Interaction Control device and synchronous control and predictive control methods are proposed. The full-scale shaking table test is used to test and verify the seismic proofing capability of the proposed AIC with these control methods. This study examines the shock absorption of test structure under excitation by external forces, influences of prediction time, stiffness of the auxiliary structure, synchronous switching, and asynchronous switching on the control effects, and the influence of control locations of test structure on the control effects of the proposed AIC. Test results show that, for the proposed AIC with synchronous control and predictive control of 0.10~0.13 seconds, the displacement reduction ratios are greater than 71%, the average acceleration reduction ratios are, respectively, 36.2% and 36.9%, at the 1st and 2nd floors, and the average base shear reduction ratio is 29.6%. The proposed AIC with suitable stiffeners for the auxiliary structure at each floor with synchronous control and predictive control provide high reliability and practicability for seismic proofing of buildings.
Recently, strong earthquakes have caused great damage and loss of life. The Indian Ocean earthquake of 2004 caused widespread damage. In Sumatra Indonesia, the earthquake had a magnitude of 9.0 on the Richter scale (M 9.0), and the resulting South Asian tsunami killed more than 200,000 people. In 2008, the Wenchuan earthquake (M 8.0) struck along the Longmenshan Fault, a thrust structure along the border of the Indo-Australian Plate and Eurasian Plate. In 2011, an earthquake of the shore of Japan (M 9.0) caused a 10-meter-high tsunami that carried water into coastal areas, washing away buildings and leaving more than twenty thousand people dead or missing. In 2013, a strong earthquake in Pakistan (M 7.7) left 825 people dead and more than 700 injured. In 2015, an earthquake in Nepal (M 7.8) killed more than 7,600 people. An aftershock in May 2015 (M 7.3) caused numerous casualties. In January 2016, an earthquake with a Richter magnitude of 6.8 caused widespread damage in India and surrounding countries.
Taiwan, which is located on the Ring of Fire at the junction of the Eurasian Plate and the Philippine Sea Plate, has numerous earthquakes every year. In 1999, an earthquake with a Richter magnitude of 7.3 occurred in the vicinity of the Chelungpu Fault, which stretches for hundreds of kilometers under buildings and bridges. In February 2016, the Meinong earthquake (M 6.5) collapsed multiple buildings in southern Taiwan. In 2015, the “Seismic Hazard Potential Map of the Taiwan Area” was released by the Ministry of Science and Technology (MOST), Taiwan. According to the MOST, the probability of a strong earthquake of magnitude 6.5 occurring in southern Taiwan within the next thirty years is 64%, and the probability of a strong earthquake of magnitude 7.0 occurring in Eastern Taiwan is 20%. In Taiwan, the threat of earthquakes is not negligible.
The present structural design concept is based on economic considerations. The premise is not life-threatening as long as the structural design meets the principle of suffering no damage in a small earthquake, being repairable after a moderate earthquake, and not collapsing in a large earthquake. Some damage to buildings is inevitable. However, damaged buildings need to be reinforced as quickly as possible, for aftershocks can cause further damage or total collapse before the designated life span of the buildings. To mend this kind of building, many researchers have developed active [
In addition, Iwan [
The Accumulated Semiactive Hydraulic Damper (ASHD) is converted to an Active Interaction Control device in this study. An ASHD is a kind of controllable energy-dissipating element of a passive control system, and it is also treated as a semiactive control device. The main design concept is based on the energy-dissipating component; the damping force can be generated by the flow of fluid through the orifice so as to conduct control. An ASHD is composed of a hydraulic jack, a directional valve, a check valve, a relief valve, and an accumulator, as shown in Figure
Framework of Accumulated Semiactive Hydraulic Device [
Assuming that two auxiliary structures (AS) are installed in the two degrees of freedom of the primary structure (PS), the organizational structure of this control system with an added mechanical sensor-switching assembly device developed from an Accumulated Semiactive Hydraulic Damper (ASHD) is shown in Figure Unlocked status of interaction IE: the control force of IE is zero. Auxiliary structures may freely vibrate. In this study, the auxiliary structure is considered as an independent oscillator. The equation of motion of each auxiliary structure can be expressed as follows: where suffix Locked status of interaction IE: there is an interaction acting force. The relative displacement of mass between the primary and auxiliary structures is incapable of change. Therefore, the relative displacement before the unlocked status is equal to that of just the locked status. That is, where
The systematic organization of ASHD as AIC [
Thus, the interaction force of the
According to previous research [
The equation of the optimal displacement is shown as follows:
The velocity can be obtained by differentiating the displacement equation with respect to time as
Multiple degrees of freedom (MDOF) shaking table test is used to investigate the control performance of the proposed AIC with different control conditions: passive control, synchronous control with prediction time control, synchronous control, asynchronous control with prediction time control, and predictive control at different floors. The auxiliary structure (AS) with various stiffeners added at different floors is also tested. In this study, the El Centro (1940) and Kobe earthquake records are used as excitation inputs to the shaking table. All of the tests are full-scale shaking table tests, and all are used to test and verify the seismic proofing capability of the proposed AIC with various control conditions. The dimensions of the shaking table are 3.0 m × 3.0 m. The maximum acceleration of the shaking table is ±9.8 m/s2 (±1.0 g) with hydraulic actuator loads of up to 15 tons. A two-story single-bay steel frame is used as the test structure, as shown in Figure
Natural frequency, damping ratio, and mass of test structure.
Original/FL | Stiffness (N/m) | Mass (kg) |
---|---|---|
1st FL | 327680 | 4402 |
2nd FL | 327680 | 4329 |
|
||
Dynamic parameters | ||
Parameters | Mode 1 | Mode 2 |
|
||
Frequency | 0.85 Hz | 2.256 Hz |
Damping ratio | 0.0028 | 0.0033 |
|
||
Mode vector | 0.608 | −1.241 |
1.000 | 1 |
The shaking table test for ASHD as AIC with various control conditions.
Three accelerometers, two displacement gauges, and two load cells are installed in the test model to measure the absolute acceleration, story drift, and output force of the damper. Figure
The full-scale shaking test structure added with IE, stiffeners, and sensors.
The signal process flowchart of this full-scale shaking table test.
To compare the seismic proofing capability of the proposed AIC under various control conditions, a two-story single-bay steel frame without control is excited with various earthquake records to obtain the time history of the structural responses of story drift, absolute acceleration, and base shear and thereby to determine the maximum structural responses. This test structure is tested under multiple control conditions: (1) passive control (i) with 2 stiffeners added at the 1st and 2nd floors and (ii) with 4 stiffeners added at the 1st floor and 3 stiffeners at the 2nd floor and (2) Active Interaction Control with (i) 2 stiffeners at the 1st and 2nd floors combined with synchronous control and predictive control of 0.13, 0.10, and 0.07 seconds, (ii) synchronous control with no predictive control, and (iii) asynchronous control with predictive control of 0.10 seconds. Then, testing conditions for location of control are 2 stiffeners added at the 1st and 2nd floors and (i) control at the 1st floor with predictive control of 0.10 seconds and (ii) control at the 2nd floor with predictive control of 0.10 seconds. Finally, a test structure with 4 stiffeners at the 1st floor and 3 stiffeners at the 2nd floor is tested with synchronous predictive control of 0.10 seconds. All test structures with various control conditions and added various stiffeners are under excitation with the El Centro and Kobe earthquake records, with various peak ground acceleration rates. All test results are analyzed to determine the maximum responses and ratios of the maximum shock absorption; those results are listed in Tables
The maximum structural response of test structure under excitation of El Centro earthquake record with various control conditions and different peak ground acceleration.
Number of stiffeners at 1st floor | Number of stiffeners at 2nd floor | Control conditions | A0 |
D1 |
D2 |
A1 |
A2 |
Base shear |
---|---|---|---|---|---|---|---|---|
0 | 0 | NC | 0.445 | 25.8 | 16.8 | 1.057 | 1.353 | 8.2 |
2 | 2 | Passive | 0.423 | 17.5 | 9.9 | 1.393 | 1.701 | 12.4 |
2 | 2 | Passive | 0.908 | 33.4 | 18.1 | 3.149 | 3.121 | 25.4 |
4 | 3 | Passive | 0.439 | 14.0 | 10.7 | 1.616 | 2.408 | 15.8 |
4 | 3 | Passive | 0.795 | 25.7 | 18.8 | 3.000 | 4.178 | 29.7 |
2 | 2 | Synchronic and 0.13-second predictive control | 2.159 | 29.7 | 23.0 | 2.941 | 3.967 | 24.5 |
2 | 2 | Synchronic and 0.13-second predictive control | 1.758 | 23.7 | 17.7 | 2.632 | 3.349 | 24.1 |
2 | 2 | Synchronic and 0.13-second predictive control | 1.335 | 17.6 | 12.7 | 1.791 | 2.401 | 15.3 |
2 | 2 | Synchronic and 0.13-second predictive control | 0.957 | 12.0 | 8.1 | 1.807 | 1.708 | 13.6 |
2 | 2 | Synchronic and 0.13-second predictive control | 0.474 | 7.4 | 5.3 | 1.228 | 1.045 | 8.6 |
2 | 2 | Synchronic and 0.10-second predictive control | 2.189 | 31.0 | 24.1 | 3.095 | 4.413 | 25.7 |
2 | 2 | Synchronic and 0.10-second predictive control | 2.119 | 23.5 | 17.8 | 2.180 | 3.336 | 21.3 |
2 | 2 | Synchronic and 0.10-second predictive control | 1.503 | 17.3 | 12.7 | 1.669 | 2.512 | 14.5 |
2 | 2 | Synchronic and 0.10-second predictive control | 0.870 | 11.4 | 8.1 | 1.063 | 1.801 | 9.9 |
2 | 2 | Synchronic and 0.10-second predictive control | 0.476 | 7.5 | 5.2 | 0.806 | 1.098 | 8.3 |
2 | 2 | Synchronic and 0.07-second predictive control | 1.222 | 24.4 | 19.2 | 2.249 | 3.485 | 20.5 |
2 | 2 | Synchronic and 0.07-second predictive control | 0.881 | 18.1 | 14.0 | 1.515 | 2.364 | 14.3 |
2 | 2 | Synchronic and 0.07-second predictive control | 0.422 | 10.1 | 7.2 | 0.927 | 1.221 | 7.9 |
2 | 2 | Synchronic control | 1.406 | 25.9 | 20.5 | 2.301 | 3.677 | 21.0 |
2 | 2 | Synchronic control | 0.928 | 18.5 | 14.1 | 1.505 | 2.392 | 14.2 |
2 | 2 | Synchronic control | 0.423 | 11.0 | 7.3 | 0.903 | 1.267 | 8.1 |
2 | 2 | Asynchronic and 0.10-second predictive control | 1.646 | 31.4 | 26.7 | 6.112 | 4.653 | 28.7 |
2 | 2 | Asynchronic and 0.10-second predictive control | 1.473 | 21.4 | 19.6 | 4.199 | 3.445 | 19.1 |
2 | 2 | Asynchronic and 0.10-second predictive control | 0.855 | 17.8 | 14.2 | 2.749 | 2.629 | 11.5 |
2 | 2 | Asynchronic and 0.10-second predictive control | 0.456 | 9.0 | 8.3 | 1.663 | 1.443 | 7.0 |
2 | 2 | 0.10-second predictive control at 1st floor | 1.642 | 30.0 | 30.7 | 6.782 | 5.908 | 29.0 |
2 | 2 | 0.10-second predictive control at 1st floor | 1.259 | 22.1 | 22.8 | 4.928 | 4.238 | 20.9 |
2 | 2 | 0.10-second predictive control at 1st floor | 0.971 | 16.4 | 15.7 | 3.250 | 2.767 | 13.1 |
2 | 2 | 0.10-second predictive control at 1st floor | 0.437 | 8.8 | 8.4 | 1.774 | 1.547 | 7.7 |
2 | 2 | 0.10-second predictive control at 2nd floor | 0.851 | 24.2 | 20.9 | 3.727 | 3.798 | 20.9 |
2 | 2 | 0.10-second predictive control at 2nd floor | 0.465 | 12.8 | 11.2 | 1.759 | 1.902 | 11.1 |
4 | 3 | Synchronic and 0.10-second predictive control | 2.607 | 26.6 | 23.3 | 4.674 | 6.536 | 37.1 |
4 | 3 | Synchronic and 0.10-second predictive control | 2.374 | 21.9 | 20.3 | 4.116 | 5.336 | 35.3 |
4 | 3 | Synchronic and 0.10-second predictive control | 1.934 | 18.5 | 17.3 | 3.619 | 4.853 | 26.1 |
4 | 3 | Synchronic and 0.10-second predictive control | 1.295 | 14.8 | 13.5 | 2.913 | 3.406 | 22.3 |
4 | 3 | Synchronic and 0.10-second predictive control | 0.914 | 10.1 | 10.0 | 1.788 | 2.378 | 14.7 |
4 | 3 | Synchronic and 0.10-second predictive control | 0.435 | 6.5 | 4.1 | 0.883 | 1.379 | 9.4 |
The maximum structural response of test structure under excitation of Kobe earthquake record with various control conditions and different peak ground acceleration.
Number of stiffeners at 1st floor | Number of stiffeners at 2nd floor | Control conditions | A0 |
D1 |
D2 |
A1 |
A2 |
Base shear |
---|---|---|---|---|---|---|---|---|
0 | 0 | NC | 0.693 | 28.8 | 21.7 | 1.637 | 1.751 | 9.0 |
2 | 2 | Passive | 0.940 | 33.2 | 20.5 | 3.217 | 3.549 | 26.0 |
4 | 3 | Passive | 0.534 | 16.1 | 12.8 | 1.863 | 2.854 | 18.4 |
4 | 3 | Passive | 0.938 | 30.0 | 22.2 | 3.618 | 4.982 | 34.9 |
2 | 2 | Synchronic and 0.13-second predictive control | 2.053 | 32.0 | 25.4 | 3.292 | 4.657 | 29.5 |
2 | 2 | Synchronic and 0.13-second predictive control | 1.396 | 24.8 | 18.5 | 2.056 | 3.546 | 22.4 |
2 | 2 | Synchronic and 0.13-second predictive control | 1.082 | 16.9 | 11.6 | 1.380 | 2.247 | 15.6 |
2 | 2 | Synchronic and 0.13-second predictive control | 0.458 | 8.9 | 5.5 | 0.809 | 1.051 | 7.5 |
2 | 2 | Synchronic and 0.10-second predictive control | 1.973 | 32.2 | 25.4 | 3.310 | 5.298 | 31.7 |
2 | 2 | Synchronic and 0.10-second predictive control | 1.378 | 23.9 | 17.8 | 2.233 | 3.548 | 23.3 |
2 | 2 | Synchronic and 0.10-second predictive control | 0.946 | 16.3 | 11.0 | 1.362 | 2.441 | 14.5 |
2 | 2 | Synchronic and 0.10-second predictive control | 0.503 | 8.7 | 5.5 | 0.817 | 1.282 | 7.9 |
2 | 2 | Synchronic and 0.07-second predictive control | 0.919 | 26.1 | 15.9 | 2.160 | 3.081 | 21.8 |
2 | 2 | Synchronic and 0.07-second predictive control | 0.485 | 14.6 | 9.1 | 1.032 | 1.560 | 11.1 |
2 | 2 | Synchronic control | 0.862 | 26.6 | 15.9 | 2.164 | 3.041 | 21.6 |
2 | 2 | Synchronic control | 0.436 | 14.7 | 9.1 | 1.026 | 1.598 | 11.3 |
2 | 2 | Asynchronic and 0.10-second predictive control | 1.099 | 26.5 | 15.7 | 3.141 | 3.173 | 19.7 |
2 | 2 | Asynchronic and 0.10-second predictive control | 0.477 | 9.0 | 8.6 | 1.505 | 1.428 | 8.2 |
2 | 2 | 0.10-second predictive control at 1st floor | 1.337 | 29.9 | 26.9 | 4.914 | 4.652 | 25.6 |
2 | 2 | 0.10-second predictive control at 1st floor | 1.160 | 18.4 | 17.8 | 3.067 | 3.254 | 16.6 |
2 | 2 | 0.10-second predictive control at 1st floor | 0.482 | 8.8 | 8.3 | 1.561 | 1.509 | 8.0 |
2 | 2 | 0.10-second predictive control at 2nd floor | 0.917 | 29.1 | 20.8 | 4.347 | 3.920 | 26.3 |
2 | 2 | 0.10-second predictive control at 2nd floor | 0.489 | 15.0 | 11.0 | 2.051 | 2.155 | 12.2 |
4 | 3 | Synchronic and 0.10-second predictive control | 2.375 | 26.3 | 19.3 | 3.167 | 4.549 | 31.6 |
4 | 3 | Synchronic and 0.10-second predictive control | 1.752 | 20.8 | 15.5 | 2.443 | 3.691 | 26.2 |
4 | 3 | Synchronic and 0.10-second predictive control | 1.355 | 15.3 | 12.3 | 1.771 | 2.851 | 19.9 |
4 | 3 | Synchronic and 0.10-second predictive control | 0.925 | 9.1 | 8.0 | 1.236 | 1.823 | 12.2 |
4 | 3 | Synchronic and 0.10-second predictive control | 0.515 | 5.6 | 4.4 | 0.710 | 1.577 | 5.8 |
The ratios of maximum shock absorption of test structure under excitation of El Centro earthquake record with various control conditions and different peak ground acceleration.
Number of stiffeners at 1st floor | Number of stiffeners at 2nd floor | Control conditions | A0 | D1 | D2 | A1 | A2 | Base shear |
---|---|---|---|---|---|---|---|---|
0 | 0 | NC | 44.5 | 0% | 0% | 0% | 0% | 0% |
2 | 2 | Passive | 42.3 | 29% | 38% | −39% | −32% | −60% |
2 | 2 | Passive | 90.8 | 36% | 47% | −46% | −13% | −52% |
4 | 3 | Passive | 43.9 | 45% | 35% | −55% | −81% | −97% |
4 | 3 | Passive | 79.5 | 44% | 37% | −59% | −73% | −104% |
2 | 2 | Synchronic and 0.13-second predictive control | 215.9 | 76% | 72% | 43% | 40% | 38% |
2 | 2 | Synchronic and 0.13-second predictive control | 175.8 | 77% | 73% | 37% | 37% | 25% |
2 | 2 | Synchronic and 0.13-second predictive control | 133.5 | 77% | 75% | 43% | 41% | 38% |
2 | 2 | Synchronic and 0.13-second predictive control | 95.7 | 78% | 78% | 20% | 41% | 23% |
2 | 2 | Synchronic and 0.13-second predictive control | 47.4 | 73% | 71% | −9% | 27% | 1% |
2 | 2 | Synchronic and 0.10-second predictive control | 218.9 | 76% | 71% | 40% | 34% | 36% |
2 | 2 | Synchronic and 0.10-second predictive control | 211.9 | 81% | 78% | 57% | 48% | 45% |
2 | 2 | Synchronic and 0.10-second predictive control | 150.3 | 80% | 78% | 53% | 45% | 47% |
2 | 2 | Synchronic and 0.10-second predictive control | 87.0 | 77% | 75% | 49% | 32% | 38% |
2 | 2 | Synchronic and 0.10-second predictive control | 47.6 | 73% | 71% | 29% | 24% | 5% |
2 | 2 | Synchronic and 0.07-second predictive control | 122.2 | 65% | 58% | 22% | 6% | 9% |
2 | 2 | Synchronic and 0.07-second predictive control | 88.1 | 64% | 58% | 28% | 12% | 12% |
2 | 2 | Synchronic and 0.07-second predictive control | 42.2 | 59% | 55% | 7% | 5% | −3% |
2 | 2 | Synchronic control | 140.6 | 68% | 61% | 31% | 14% | 18% |
2 | 2 | Synchronic control | 92.8 | 66% | 60% | 32% | 15% | 17% |
2 | 2 | Synchronic control | 42.3 | 55% | 54% | 10% | 1% | −4% |
2 | 2 | Asynchronic and 0.10-second predictive control | 164.6 | 67% | 57% | −56% | 7% | 5% |
2 | 2 | Asynchronic and 0.10-second predictive control | 147.3 | 75% | 65% | −20% | 23% | 29% |
2 | 2 | Asynchronic and 0.10-second predictive control | 85.5 | 64% | 56% | −35% | −1% | 26% |
2 | 2 | Asynchronic and 0.10-second predictive control | 45.6 | 66% | 52% | −54% | −4% | 16% |
2 | 2 | 0.10-second predictive control at 1st floor | 164.2 | 68% | 50% | −74% | −18% | 3% |
2 | 2 | 0.10-second predictive control at 1st floor | 125.9 | 70% | 52% | −65% | −11% | 9% |
2 | 2 | 0.10-second predictive control at 1st floor | 97.1 | 71% | 57% | −41% | 6% | 26% |
2 | 2 | 0.10-second predictive control at 1st floor | 43.7 | 65% | 49% | −71% | −16% | 4% |
2 | 2 | 0.10-second predictive control at 2nd floor | 85.1 | 51% | 35% | −84% | −47% | −34% |
2 | 2 | 0.10-second predictive control at 2nd floor | 46.5 | 53% | 36% | −59% | −35% | −31% |
4 | 3 | Synchronic and 0.10-second predictive control | 260.7 | 82% | 76% | 25% | 17% | 22% |
4 | 3 | Synchronic and 0.10-second predictive control | 237.4 | 84% | 77% | 27% | 26% | 19% |
4 | 3 | Synchronic and 0.10-second predictive control | 193.4 | 83% | 76% | 21% | 17% | 26% |
4 | 3 | Synchronic and 0.10-second predictive control | 129.5 | 80% | 72% | 5% | 13% | 6% |
4 | 3 | Synchronic and 0.10-second predictive control | 91.4 | 81% | 71% | 18% | 14% | 12% |
4 | 3 | Synchronic and 0.10-second predictive control | 43.5 | 74% | 75% | 14% | −4% | −18% |
The ratios of maximum shock absorption of test structure under excitation of Kobe earthquake record with various control conditions and different peak ground acceleration.
Number of stiffeners at 1st floor | Number of stiffeners at 2nd floor | Control conditions | A0 | D1 | D2 | A1 | A2 | Base shear |
---|---|---|---|---|---|---|---|---|
0 | 0 | NC | 69.3 | 0% | 0% | 0% | 0% | 0.0% |
2 | 2 | Passive | 94.0 | 15% | 30% | −45% | −49% | −112.0% |
4 | 3 | Passive | 53.4 | 27% | 23% | −48% | −112% | −164.0% |
4 | 3 | Passive | 93.8 | 23% | 24% | −63% | −110% | −185.5% |
2 | 2 | Synchronic and 0.13-second predictive control | 205.3 | 62% | 60% | 32% | 10% | −10.2% |
2 | 2 | Synchronic and 0.13-second predictive control | 139.6 | 57% | 57% | 38% | −1% | −23.1% |
2 | 2 | Synchronic and 0.13-second predictive control | 108.2 | 62% | 66% | 46% | 18% | −10.2% |
2 | 2 | Synchronic and 0.13-second predictive control | 45.8 | 54% | 62% | 25% | 9% | −24.7% |
2 | 2 | Synchronic and 0.10-second predictive control | 197.3 | 61% | 59% | 29% | −6% | −23.1% |
2 | 2 | Synchronic and 0.10-second predictive control | 137.8 | 58% | 59% | 31% | −2% | −29.3% |
2 | 2 | Synchronic and 0.10-second predictive control | 94.6 | 59% | 63% | 39% | −2% | −17.2% |
2 | 2 | Synchronic and 0.10-second predictive control | 50.3 | 58% | 65% | 31% | −1% | −19.9% |
2 | 2 | Synchronic and 0.07-second predictive control | 91.9 | 32% | 45% | 0% | −33% | −82.1% |
2 | 2 | Synchronic and 0.07-second predictive control | 48.5 | 28% | 40% | 10% | −28% | −76.1% |
2 | 2 | Synchronic control | 86.2 | 26% | 41% | −6% | −40% | −92.4% |
2 | 2 | Synchronic control | 43.6 | 19% | 33% | 0% | −45% | −98.7% |
2 | 2 | Asynchronic and 0.10-second predictive control | 109.9 | 42% | 54% | −21% | −14% | −37.4% |
2 | 2 | Asynchronic and 0.10-second predictive control | 47.7 | 55% | 43% | −34% | −19% | −31.7% |
2 | 2 | 0.10-second predictive control at 1st floor | 133.7 | 46% | 36% | −56% | −38% | −46.6% |
2 | 2 | 0.10-second predictive control at 1st floor | 116.0 | 62% | 51% | −12% | −11% | −10.0% |
2 | 2 | 0.10-second predictive control at 1st floor | 48.2 | 56% | 45% | −37% | −24% | −26.9% |
2 | 2 | 0.10-second predictive control at 2nd floor | 91.7 | 24% | 28% | −101% | −69% | −120.2% |
2 | 2 | 0.10-second predictive control at 2nd floor | 48.9 | 26% | 28% | −78% | −74% | −90.9% |
4 | 3 | Synchronic and 0.10-second predictive control | 237.5 | 73% | 74% | 44% | 24% | −2.1% |
4 | 3 | Synchronic and 0.10-second predictive control | 175.2 | 71% | 72% | 41% | 17% | −14.7% |
4 | 3 | Synchronic and 0.10-second predictive control | 135.5 | 73% | 71% | 45% | 17% | −12.5% |
4 | 3 | Synchronic and 0.10-second predictive control | 92.5 | 76% | 72% | 43% | 22% | −1.2% |
4 | 3 | Synchronic and 0.10-second predictive control | 51.5 | 74% | 73% | 42% | −21% | 14.2% |
Time history of story drift, absolute acceleration, and base shear responses of bare structure under excitation of Kobe earthquake record with PGA = 0.50 m/sec2 (50 gal).
Time history of story drift, absolute acceleration, and base shear responses of test structure added with two stiffeners and with synchronic and 0.13-second predictive control under excitation of Kobe earthquake record with PGA = 0.50 m/sec2 (50 gal).
All of the control methods provide shock absorption of displacement. However, the displacement shock absorption of the test structure is less under excitation of the Kobe earthquake record than under excitation of the El Centro earthquake record. Although the structural response of displacement can be reduced by a passive stiffened structure, the decrement rate is not proportional to the stiffness ratio. Notably, adding more stiffeners increases the structural responses to acceleration and base shear. Actually, dynamic responses are relative to structural frequencies. The test and analysis results of Tables
When the structural control capability is insufficient to control the dynamic response of the test structure, the following phenomena occurred.
From the above descriptions, it is clear that the displacement control, acceleration control, and base shear control of the three active control methods—
The predictive time control method is intended to predict a transient time for the time delay problem of the proposed AIC. If the device has no predictive reaction, the AIC device response for velocity is too slow to switch at the optimal time, and the control effect of this device will be degraded. In contrast, if the prediction time is too long, the device will become unstable. In order to investigate the influence of prediction time on the control effect of the proposed AIC, a series of AIC under passive control and active control without prediction time and with prediction times of 0.07, 0.10, and 0.13 seconds and an AIC device with synchronous switching are tested to determine the seismic proofing capability of the AIC device proposed in this study. The average shock absorption ratios of the test structure with various control conditions under excitation of the El Centro and Kobe earthquake records are shown in Figures
The average shock absorption ratios of the test structure with various control conditions under excitation of the El Centro earthquake.
The average shock absorption ratios of the test structure with various control conditions under excitation of the Kobe earthquake.
The test results for the influence of prediction time on the control effect of the proposed AIC are discussed as follows.
Hysteretic loop of interaction force of the test structure at the 1st floor under excitation of scaled-down Kobe earthquake with PGA = 0.862 m/sec2 (86.2 gal).
Hysteretic loop of interaction force of the test structure at the 1st floor with predictive control of 0.07 seconds under excitation of the Kobe earthquake with PGA = 0.912 m/sec2 (91.2 gal).
Hysteretic loop of interaction force of the test structure at the 1st floor with predictive control of 0.10 seconds under excitation of the Kobe earthquake with PGA = 0.946 m/sec2 (94.6 gal).
The control forces of the interaction system are induced earlier on the primary structure when stiffness of the auxiliary structure is greater to reduce the time delay problem. But greater stiffness increased the impact force, amplified acceleration responses, and increased the base shear forces of the structure. In order to investigate the influence of the stiffness of the auxiliary structure on the control effect, two sets of shaking table tests are conducted under synchronous control with a prediction time of 0.10-second condition to test and verify the control effects:
Comparison of the shock absorption ratios of the test structure under excitation of the El Centro earthquake with different control types.
Comparison of shock absorption ratios of the test structure under excitation of the Kobe earthquake with different control types.
The switching of the connection status of the auxiliary structure for each floor is dependent on the story velocity. According to the contributions of multiple modal shapes, it is difficult to reach simultaneously the switching requirements of the connection status for each floor such that there is little difference in switching between each floor. If the upper floor reaches the switching requirement, the auxiliary structure will switch first to produce the extra control force to the lower level and cause greater acceleration responses. Figure
The reasons for inducing extra acceleration response of test structure with asynchronous switch.
Before switching
After switching at 2nd floor
After switching at 1st floor
If the upper level switches first, the acceleration responses of the lower level will increase suddenly, as shown in Figure
Comparison of shock absorption ratios of the test structure with synchronous and asynchronous control under excitation of the El Centro earthquake.
Comparison of shock absorption ratios of the test structure with synchronous and asynchronous control under excitation of the Kobe earthquake.
Figures
In order to find the optimal place and right quantity to install this kind of device, a series of tests are planned. In this study, the shock absorption ratios of passive control, full control, control at the 1st floor, and control at the 2nd floor are investigated with a structure having a stiffening ratio of 1.193, synchronous control, and predictive control of 0.10 seconds. The test results for the average shock absorption ratios of the test structure under various control conditions are shown in Figures
Comparison of shock absorption ratios of the test structure with different control types under excitation of the El Centro earthquake.
Comparison of shock absorption ratios of the test structure with different control types under excitation of the Kobe earthquake.
Figures
An Active Interaction Control (AIC) system was proposed by Iwan [ All of the control methods, applied in this research, provide shock absorption effects of displacement. The shock absorption effects of displacement for the test structure under the control of synchronous switching with predictive control greatly reduce the displacement of the structure. Nevertheless, the structural responses to acceleration and base shear are increased by this device under passive control. However, these structural responses are not increased by the proposed AIC device with synchronous control and a suitable prediction time. The control effects of the test structure with the proposed AIC under active control without prediction time are poor because the response to structural velocity does not provide sufficient time for the AIC device to switch at the optimal time. The area of the hysteretic loop increased when the AIC is under active control and had proper prediction time. Therefore, the seismic proofing capability of displacement and acceleration control of the test structure with this AIC under active control with proper prediction time could be increased. Test results show that, for the test structure under the control of the proposed AIC with synchronous control and predictive control of 0.10~0.13 seconds, the shock absorption ratios of displacement are greater than 71%, the average acceleration reduction ratios are 36.2% and 36.9% at the 1st and 2nd floors, respectively, and the average base shear reduction ratio is 29.6%. The time delay defects of the AIC control forces, induced from the interaction element to the primary structure, are reduced by the stiffness of the auxiliary structure. The test results show that adding more stiffeners to the auxiliary structure could provide the characteristics of a stabilized structure under excitation of a near fault earthquake with velocity impulse action. The connection statuses of the auxiliary structures for each floor with simultaneous switching are hard to attain because they are dependent on the velocity of each floor. To prevent these phenomena, a rule for the synchronous control method is proposed. The test results reveal that the structural responses of displacement and acceleration control are controlled well by this proposed control method, which does not amplify the structural responses to acceleration. The test results for the influence of the control positions of the AIC in the structure show that full control of the structure provides the best shock absorption effects, and control at the first floor is the second best option.
In this study, the ASHD is converted to AIC and predictive control methods with synchronous control are proposed to improve the seismic proofing capability of the proposed AIC. A full-scale two-story single-bay steel frame is tested on a shaking table to verify the energy-dissipating capability of this proposed device. All of the test results show that the proposed AIC with suitable stiffeners for the auxiliary structure at each floor and synchronous control and predictive control provide high reliability and practicability for improving the seismic proofing capability of a building under excitation by external forces.
If the function of displacement corresponding to time has
According to the least square regression, the optimal estimation of polynomial coefficient in (
The optimal displacements can be easily predicted using
And
See Tables
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to acknowledge the support of Taiwan Ministry of Science and Technology through Grant nos. MOST-103-2625-M-260-001 and MOST-103-2625-M-167-001.