Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks
Abstract
:1. Introduction
2. Effective Material Properties of GPLRC
3. Finite Element Implementation
4. Results and Discussion
4.1. Verification
4.2. Free Vibration Analysis
4.3. Buckling Analysis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Comparison Results | L1/L = 0.2 | L1/L = 0.4 | L1/L = 0.6 | Intact Beam |
---|---|---|---|---|
Present | 1019.9 | 1029.9 | 1035.2 | 1036.9 |
Ke et al. [38] | 1020.98 | 1029.853 | 1034.932 | 1037.0106 |
Comparison Results | Pcr | w1 |
---|---|---|
Present | 0.0090 | 0.3359 |
Wu et al. [49] | 0.0089 | 0.3350 |
Distribution Patterns | WGPL | L1/L | ||
---|---|---|---|---|
0.2 | 0.5 | 0.8 | ||
U-GPLRC | 0.1% | 1.1567 | 1.1328 | 1.1567 |
0.3% | 1.4200 | 1.3906 | 1.4200 | |
0.5% | 1.6417 | 1.6074 | 1.6417 | |
X-GPLRC | 0.1% | 1.2229 | 1.1929 | 1.2229 |
0.3% | 1.5762 | 1.5310 | 1.5762 | |
0.5% | 1.8628 | 1.8047 | 1.8627 | |
O-GPLRC | 0.1% | 1.0856 | 1.0666 | 1.0856 |
0.3% | 1.2393 | 1.2212 | 1.2393 | |
0.5% | 1.3758 | 1.3574 | 1.3758 | |
A-GPLRC | 0.1% | 1.1447 | 1.1189 | 1.1447 |
0.3% | 1.3604 | 1.3277 | 1.3604 | |
0.5% | 1.5332 | 1.4946 | 1.5332 | |
Pure epoxy | 0.0% | 0.9994 | 0.9785 | 0.9994 |
CDR | L1/L | ||||
---|---|---|---|---|---|
0.02 | 0.2 | 0.5 | 0.8 | 0.98 | |
0.0 | 1.8643 | 1.8643 | 1.8643 | 1.8643 | 1.8643 |
0.1 | 1.8513 | 1.8642 | 1.8584 | 1.8642 | 1.8513 |
0.2 | 1.8127 | 1.8637 | 1.8392 | 1.8637 | 1.8127 |
0.3 | 1.7513 | 1.8628 | 1.8047 | 1.8627 | 1.7518 |
WGPL | L1/L | ||||
---|---|---|---|---|---|
0.02 | 0.2 | 0.5 | 0.8 | 0.98 | |
0.0% | 0.9425 | 0.9941 | 0.9394 | 0.9941 | 0.9429 |
0.1% | 1.3980 | 1.4885 | 1.3917 | 1.4885 | 1.3988 |
0.3% | 2.2980 | 2.4727 | 2.2820 | 2.4728 | 2.2980 |
0.5% | 3.1880 | 3.4529 | 3.1618 | 3.4530 | 3.1880 |
CDR | L/h | ||
---|---|---|---|
20 | 30 | 40 | |
0.0 | 7.6778 | 3.4855 | 1.9753 |
0.1 | 7.5725 | 3.4537 | 1.9615 |
0.2 | 7.2426 | 3.3531 | 1.9172 |
0.3 | 6.6581 | 3.1618 | 1.8336 |
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Tam, M.; Yang, Z.; Zhao, S.; Yang, J. Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks. Materials 2019, 12, 1412. https://doi.org/10.3390/ma12091412
Tam M, Yang Z, Zhao S, Yang J. Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks. Materials. 2019; 12(9):1412. https://doi.org/10.3390/ma12091412
Chicago/Turabian StyleTam, Meifung, Zhicheng Yang, Shaoyu Zhao, and Jie Yang. 2019. "Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks" Materials 12, no. 9: 1412. https://doi.org/10.3390/ma12091412