Size Effect of a Piezoelectric Patch on a Rectangular Plate with the Neural Network Model
Abstract
:1. Introduction
2. Physical Model
2.1. Dynamic Equation of the Thin Plate
2.2. Neural Network Modeling
3. Case Study
3.1. CASE 1: Input Side Length and Thickness
3.2. CASE 2: Input Area and Thickness
3.3. CASE 3: Input Volume
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Length , mm | 100 |
Width , mm | 100 |
Thickness , mm | 1.0 |
Density , | 2700 |
Modulus of elasticity , Pa | 70 × |
Poisson ratio | 0.33 |
Parameter | Value |
---|---|
Length , mm | 1.0~100 |
Width , mm | 1.0~100 |
Thickness , mm | 1.0~2.0 |
Density , | 2500 |
Modulus of elasticity , Pa | 56 × |
Poisson ratio | 0.36 |
Length | Thickness/mm | First-Order Natural Frequency/Hz | Error/% | Displacement Amplitude/mm | Error/% | ||
---|---|---|---|---|---|---|---|
COMSOL | ANN | COMSOL | ANN | ||||
10.0 | 1.0 | 856.87 | 856.87 | 0.00 | 0.69 × | 0.72 × | 4.35 |
15.0 | 1.1 | 816.18 | 816.18 | 0.00 | 1.38 × | 1.32 × | −4.35 |
20.0 | 1.2 | 778.09 | 778.10 | 0.00 | 2.11 × | 2.09 × | −0.95 |
22.5 | 1.3 | 757.29 | 757.29 | 0.00 | 2.33 × | 2.35 × | 0.86 |
27.5 | 1.4 | 733.13 | 733.13 | 0.00 | 2.91 × | 2.90 × | −0.34 |
35.0 | 1.5 | 722.68 | 722.68 | 0.00 | 3.82 × | 3.83 × | 0.26 |
40.0 | 1.6 | 725.77 | 725.77 | 0.00 | 4.20 × | 4.21 × | 0.24 |
57.5 | 1.7 | 841.62 | 841.62 | 0.00 | 7.18 × | 7.13 × | −0.70 |
65.0 | 1.8 | 930.04 | 930.04 | 0.00 | 8.63 × | 8.61 × | −0.23 |
82.5 | 1.9 | 1202.42 | 1202.42 | 0.00 | 17.46 × | 17.45 × | −0.06 |
97.5 | 2.0 | 1355.75 | 1356.81 | 0.08 | 15.87 × | 15.69 × | −1.13 |
Area | Thickness/mm | First-Order Natural Frequency/Hz | Error/% | Displacement Amplitude/mm | Error/% | ||
---|---|---|---|---|---|---|---|
COMSOL | ANN | COMSOL | ANN | ||||
100 | 1.0 | 856.87 | 856.87 | 0.00 | 0.69 × | 0.83 × | 20.23 |
400 | 1.1 | 787.51 | 787.51 | 0.00 | 2.38 × | 2.29 × | −3.74 |
900 | 1.2 | 750.04 | 750.05 | 0.00 | 4.27 × | 4.28 × | 0.13 |
1600 | 1.3 | 751.44 | 751.44 | 0.00 | 6.07 × | 6.10 × | 0.47 |
2500 | 1.4 | 791.77 | 791.77 | 0.00 | 7.94 × | 7.91 × | −0.39 |
3600 | 1.5 | 867.70 | 867.70 | 0.00 | 10.29 × | 10.29 × | −0.05 |
4900 | 1.6 | 982.22 | 982.22 | 0.00 | 13.87 × | 13.74 × | −0.93 |
6400 | 1.7 | 1117.52 | 1117.52 | 0.00 | 18.99 × | 18.98 × | −0.07 |
8100 | 1.8 | 1238.61 | 1238.61 | 0.00 | 23.26 × | 23.22 × | −0.16 |
Area | Thickness/mm | First-Order Natural Frequency/Hz | Error/% | Displacement Amplitude/mm | Error/% | ||
---|---|---|---|---|---|---|---|
COMSOL | ANN | COMSOL | ANN | ||||
100 | 1.0 | 856.87 | 856.87 | 0.00 | 0.69 × | 0.83 × | 20.23 |
4 × 25 | 869.34 | −1.43 | 1.06 × | −21.39 | |||
2.5 × 40 | 878.65 | −2.48 | 1.34 × | −38.20 | |||
2 × 50 | 881.17 | −2.76 | 1.37 × | −39.56 | |||
400 | 1.1 | 787.51 | 787.51 | 0.00 | 2.38 × | 2.29 × | −3.74 |
16 × 25 | 790.67 | −0.40 | 2.46 × | −7.17 | |||
10 × 40 | 816.50 | −3.55 | 3.23 × | −29.18 | |||
5 × 80 | 851.29 | −7.49 | 3.52 × | −35.04 | |||
900 | 1.2 | 750.04 | 750.05 | 0.00 | 4.27 × | 4.28 × | 0.13 |
25 × 36 | 754.72 | −0.62 | 4.42 × | −3.27 | |||
18 × 50 | 783.56 | −4.28 | 5.52 × | −22.48 | |||
15 × 60 | 802.80 | −6.57 | 6.52 × | −34.40 | |||
10 × 90 | 831.08 | −9.75 | 5.50 × | −22.18 | |||
1600 | 1.3 | 751.44 | 751.44 | 0.00 | 6.07 × | 6.10 × | 0.47 |
32 × 50 | 763.72 | −1.61 | 6.62 × | −7.82 | |||
20 × 80 | 802.82 | −6.40 | 9.79 × | −37.65 | |||
2500 | 1.4 | 791.77 | 791.77 | 0.00 | 7.94 × | 7.91 × | −0.39 |
40 × 62.5 | 804.92 | −1.63 | 9.12 × | −13.30 |
Volume | First-Order Natural Frequency/Hz | Error/% | Displacement Amplitude/mm | Error/% | ||
---|---|---|---|---|---|---|
COMSOL | ANN | COMSOL | ANN | |||
405.00 | 764.52 | 764.52 | 0.00 | 0.70 × | 2.89 × | 310.74 |
506.25 | 786.92 | 786.92 | 0.00 | 3.33 × | 2.60 × | −22.14 |
2531.25 | 700.76 | 674.24 | −3.78 | 3.07 × | 10.73 × | 249.79 |
2890.00 | 736.39 | 736.39 | 0.00 | 4.63 × | 7.41 × | 59.82 |
3307.50 | 813.20 | 813.20 | 0.00 | 11.63 × | 14.74 × | 26.74 |
4000.00 | 780.70 | 780.70 | 0.00 | 6.13 × | 4.81 × | −21.48 |
7290.00 | 953.00 | 953.00 | 0.00 | 12.41 × | 12.42 × | 0.09 |
10,890.00 | 1120.99 | 1341.22 | 19.65 | 23.11 × | 27.42 × | 18.66 |
13,537.50 | 1161.84 | 1161.84 | 0.00 | 22.07 × | 23.27 × | 5.43 |
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Min, H.; Zhang, J.; Fan, M. Size Effect of a Piezoelectric Patch on a Rectangular Plate with the Neural Network Model. Materials 2021, 14, 3240. https://doi.org/10.3390/ma14123240
Min H, Zhang J, Fan M. Size Effect of a Piezoelectric Patch on a Rectangular Plate with the Neural Network Model. Materials. 2021; 14(12):3240. https://doi.org/10.3390/ma14123240
Chicago/Turabian StyleMin, Hequn, Jie Zhang, and Mu Fan. 2021. "Size Effect of a Piezoelectric Patch on a Rectangular Plate with the Neural Network Model" Materials 14, no. 12: 3240. https://doi.org/10.3390/ma14123240
APA StyleMin, H., Zhang, J., & Fan, M. (2021). Size Effect of a Piezoelectric Patch on a Rectangular Plate with the Neural Network Model. Materials, 14(12), 3240. https://doi.org/10.3390/ma14123240