Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System
Abstract
:1. Introduction
2. Sandwich-Type ATVA with ER Materials Embedded
2.1. Design of the Sandwich ATVA with ER Materials Embedded
2.2. Expermental Setup to Measure the Dynamic Response of the ERF Embedded Sandwich Beam
- (1)
- The left side of the sandwich beam is clamped on top of an electromagnetic vibration shaker (LDS V406) which provides the exciting force to the ERF embedded beam.
- (2)
- A laser displacement sensor (Keyence LC2440; Keyence Corporation, Osaka, Japan) and a non-contacting eddy-current displacement probe (Keyence AH-416; Keyence Corporation, Osaka, Japan) are used to measure the displacements of the input excitation (the clamped side on the shaker) and the free end of the ERF embedded beam.
- (3)
- A high-voltage power amplifier is used to provide the electric field to the ER fluid via the two electrodes of the aluminum plates, which is located on the left side of the ERF embedded beam.
- (4)
- When the different electric fields are applied to the ERF, a dynamic signal analyzer (HP 35665A, Agilent, Santa Clara, CA, USA) is used to analyze the dynamic characteristics of the ERF sandwich beam. The vibration signal is provided to the shaker at the frequency from 0 to 200 Hz to actuate the ERF embedded beam.
- (5)
- The time response signals are captured by the dynamic signal analyzer (HP 35665A). Then, the frequency response is obtained by using fast Fourier transform (FFT) in HP 35665A. The same experimental steps were repeated for the electric field varying from 0 to 2 () in 0.25 () increments.
- (6)
- Figure 2 is the scheme view and diagram to measure the transmissibility of the ERF embedded TVA with the corresponding electric field. Figure 3 shows the transmissibility of the TVA as the different electric field is applied to the ERF. For each electric field applied to the ERF, the damping ratios of ERF can be obtained using the half-power point bandwidth method as follows according to the 1st mode frequency.
- (7)
- According to the 1st mode frequency of the ERF embedded sandwich beam in Figure 3, the equivalent shear modulus of the ERF can be obtained by using the goal driven optimization method in ANSYS Workbench. In the simulation, the goal is to find the optimal shear modulus of ERF to make the simulated 1st mode frequency of the ERFATVA be consistent with the actual value obtained by the experiments. Therefore, the damping ratio and shear modulus of the ERF are used in the ANSYS model.
3. Design and Analysis of the ERF Embedded ATVA for a Plate Structure
3.1. Governing Equations of the ERF Embedded Beam
3.2. Simulation Study to Obtain a Suitable Width of the ERF Embedded ATVA for a Plate Using ANSYS
3.3. Experimental Validations
4. Semi-Active Vibration Control of the Thin Plate Using the ERF Embedded ATVA
4.1. Experimental Setup for the Thin Plate with Varying Harmonic Vibrations
4.2. Semi-Active Vibration Control Using the Interval Type-2 Fuzzy
Type-2 Fuzzy Controller Design for ATVA
4.3. Semi-Active Vibration Controller with a Switching-Mode Rule for ATVA
5. Experimental Results and Discussion
5.1. Case I: External Vibration at the Specified Frequency
5.2. Case II: External Vibration with the Varying Frequency
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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L | W | h1 | w1 | h2 |
---|---|---|---|---|
150 mm | 30 mm | 0.3 mm | 2.5 mm | 2 mm |
Adhesives | ERF% | Volume | Weight | Equivalent density |
Silicone Sealant | 45% | 7.25 mL | 28.6 g | 2118.52 kg/m3 |
E (kV/mm) | F (Hz) | Amplitude (dB) | Damping Ratio (ζ) |
---|---|---|---|
0 | 29.5 | 23.473 | 0.0363 |
0.25 | 29.75 | 21.777 | 0.0432 |
0.5 | 30.5 | 20.127 | 0.0573 |
0.75 | 32.75 | 19.658 | 0.0574 |
1 | 33 | 18.705 | 0.0587 |
1.25 | 34.5 | 17.700 | 0.0589 |
1.5 | 36 | 17.457 | 0.0593 |
1.75 | 37 | 17.961 | 0.0529 |
2 | 37.25 | 18.075 | 0.0560 |
2.25 | 38.25 | 18.774 | 0.0512 |
W (mm) | 1st Mode Variation (Hz) | 2nd Mode Variation (Hz) | 3rd Mode Variation (Hz) |
---|---|---|---|
20 | 1.362 | 1.811 | 10.069 |
22 | 1.331 | 1.724 | 10.756 |
24 | 1.406 | 1.939 | 14.912 |
26 | 1.378 | 1.862 | 16.391 |
28 | 1.392 | 1.825 | 17.613 |
30 | 1.374 | 1.86 | 18.352 |
32 | 1.357 | 1.963 | 18.790 |
34 | 1.399 | 1.941 | 18.980 |
36 | 1.361 | 2.001 | 19.157 |
E (kV/mm) | F (Hz) | Amplitude (dB) | Damping Ratio (ζ) |
---|---|---|---|
0 | 11.625 | 16.103 | 0.0218 |
0.5 | 11.875 | 10.142 | 0.0140 |
1 | 12 | 12.677 | 0.0205 |
1.5 | 12.375 | 15.809 | 0.0541 |
2 | 13.375 | 11.629 | 0.0329 |
E (kV/mm) | F (Hz) | Amplitude (dB) | Damping Ratio (ζ) |
---|---|---|---|
0 | 18.375 | 17.876 | 0.0156 |
0.5 | 18.125 | 14.201 | 0.0129 |
1 | 18.25 | 12.423 | 0.0212 |
1.5 | 18.5 | 14.365 | 0.0151 |
2 | 18.5 | 15.304 | 0.0119 |
E (kV/mm) | F (Hz) | Amplitude (dB) | Damping Ratio (ζ) |
---|---|---|---|
0 | 77 | 20.795 | 0.0083 |
0.5 | 77.625 | 19.547 | 0.0087 |
1 | 77.875 | 17.414 | 0.0108 |
1.5 | 78.125 | 18.382 | 0.0122 |
2 | 78.625 | 17.588 | 0.0119 |
Shaker Amplitude (mVpk) | 50 | 100 | 200 | 50 | 100 | 200 | |
---|---|---|---|---|---|---|---|
8 Hz Displacement (mVrms) | 10 Hz Displacement (mVrms) | ||||||
E (kV/mm) | 1 | 98 | 201 | 413 | 162 | 312 | 633 |
1.5 | 82 | 181 | 363 | 148 | 267 | 515 | |
2 | 86 | 162 | 338 | 129 | 218 | 403 | |
13 Hz Displacement (mVrms) | 17 Hz Displacement (mVrms) | ||||||
E (kV/mm) | 1 | 17 | 35 | 68 | 98 | 194 | 378 |
1.5 | 14 | 28 | 53 | 85 | 181 | 363 | |
2 | 8 | 13 | 27 | 72 | 155 | 352 | |
19 Hz Displacement (mVrms) | 21 Hz Displacement (mVrms) | ||||||
E (kV/mm) | 0 | 33 | 75 | 153 | 28 | 54 | 110 |
0.5 | 36 | 77 | 158 | 25 | 52 | 106 | |
1 | 37 | 78 | 159 | 26 | 53 | 108 | |
23 Hz Displacement (mVrms) | 25 Hz Displacement (mVrms) | ||||||
E (kV/mm) | 0 | 21 | 41 | 80 | 16 | 34 | 69 |
0.5 | 22 | 41 | 82 | 17 | 34 | 70 | |
1 | 22 | 41 | 81 | 16 | 34 | 71 |
Shaker Amplitude (mVpk) | 50 | 100 | 200 | 50 | 100 | 200 | |
---|---|---|---|---|---|---|---|
74 Hz Displacement (mVrms) | 76 Hz Displacement (mVrms) | ||||||
E (kV/mm) | 1 | 4 | 7 | 13 | 9 | 20 | 39 |
1.5 | 3 | 6 | 12 | 8 | 19 | 37 | |
2 | 5 | 8 | 14 | 10 | 20 | 37 | |
78 Hz Displacement (mVrms) | 80 Hz Displacement (mVrms) | ||||||
E (kV/mm) | 0 | 26 | 53 | 104 | 15 | 30 | 61 |
0.5 | 18 | 33 | 68 | 15 | 30 | 60 | |
1 | 16 | 29 | 58 | 20 | 41 | 78 | |
1.5 | 14 | 23 | 47 | 23 | 46 | 87 |
Drms | VS | S | M | |
---|---|---|---|---|
f | ||||
VS | B | VB | VB | |
S | VB | V | VB | |
M | M | VB | M |
Excitation Frequency (Hz) | Type-1 Fuzzy Controller (%) | Type-2 Fuzzy Controller (%) |
---|---|---|
8 | 81.4 | 81.5 |
10 | 19.9 | 36.1 |
18 | 38.3 | 40.9 |
20 | 24.8 | 40.3 |
77 | 88.6 | 89.7 |
79 | 37.3 | 54.2 |
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Lin, C.-J.; Lee, C.-Y.; Liu, Y. Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System. Appl. Sci. 2017, 7, 707. https://doi.org/10.3390/app7070707
Lin C-J, Lee C-Y, Liu Y. Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System. Applied Sciences. 2017; 7(7):707. https://doi.org/10.3390/app7070707
Chicago/Turabian StyleLin, Chih-Jer, Chun-Ying Lee, and Ying Liu. 2017. "Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System" Applied Sciences 7, no. 7: 707. https://doi.org/10.3390/app7070707