Free Vibration Analysis of Functionally Gradient Sandwich Composite Plate Embedded SMA Wires in Surface Layer
Abstract
:1. Introduction
2. Theoretical Formula
2.1. Geometry and Material Properties
2.2. Vibration Equation
- (1)
- Transverse strain of sandwich plate .
- (2)
- The straight line perpendicular to the neutral surface before deformation will no longer maintain a straight line after deformation.
3. Results and Discussion
3.1. Verification and Materials
3.2. Investigating the Influence of Gradient Parameter
3.3. Investigating the Influence of Graphite Volume Fraction
3.4. Investigating the Influence of SMA Volume Fraction
3.5. Investigating the Influence of SMA Pre-Strain
4. Conclusions
- (1)
- Free vibration of a sandwich composite plate which embeds SMA wires in the surface sheets and functionally gradient distribution in the core has been developed. The constitutive equation considered thermal effect and pre-strain, the Reddy shear deformation theory, and Hamilton principle were utilized to derive the governing equations and the frequency equation.
- (2)
- The gradient distribution and volume fraction of graphite in the core layer of the sandwich composite plate have a significant effect on natural frequencies. The natural frequency and the critical buckling temperature of a positive gradient distribution of graphite in the core of the sandwich composite plate are higher than those of non and negative gradient distribution. Moreover, the increase of graphite volume fraction increases the natural frequency but decreases the critical buckling temperature. Therefore, the graphite in the core layer can be designed by the form of distribution and volume fraction, thereby controlling the natural frequency of sandwich plate.
- (3)
- Temperature-rising SMA transforms from the martensitic phase to the austenitic phase, which results in an increase in modulus and recovery stress, thus increasing the influence of the volume fraction and pre-strain on the natural frequency. Both volume fraction increments and pre-strain increments of SMA embedded in the surface sheets of the sandwich plate can increase the natural frequency and critical buckling temperature.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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FGMs | Gradient Index (p) | ||||
---|---|---|---|---|---|
0 | 0.5 | 1 | 2 | ||
Al/Al2O3 | Benachour et al. | 5.7694 | 4.9000 | 4.4166 | 4.0057 |
Zhao et al. | 5.6763 | 4.8209 | 4.3474 | 3.9474 | |
Present | 5.7689 | 4.9123 | 4.4328 | 4.0176 | |
Al/ZrO2 | Benachour et al. | 5.7694 | 5.4380 | 5.3113 | 5.2923 |
Zhao et al. | 5.6763 | 5.1105 | 4.8713 | 4.6977 | |
Present | 5.7689 | 5.3511 | 5.2696 | 5.1254 |
Samadpour et al. | Present | |||||||
---|---|---|---|---|---|---|---|---|
Without SMA | 0.862 | 0.696 | 0.485 | 0.259 | 0.877 | 0.712 | 0.493 | 0.261 |
0.842 | 0.855 | 0.904 | 0.938 | 0.853 | 0.867 | 0.916 | 0.949 | |
0.813 | 0.960 | 1.126 | 1.224 | 0.832 | 0.972 | 1.133 | 1.237 | |
0.811 | 0.925 | 1.084 | 1.171 | 0.826 | 0.932 | 1.091 | 1.180 | |
0.803 | 0.888 | 1.005 | 0.952 | 0.811 | 0.895 | 1.011 | 0.963 |
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Huang, Y.; Li, L.; Xu, Z.; Li, C.; Mao, K. Free Vibration Analysis of Functionally Gradient Sandwich Composite Plate Embedded SMA Wires in Surface Layer. Appl. Sci. 2020, 10, 3921. https://doi.org/10.3390/app10113921
Huang Y, Li L, Xu Z, Li C, Mao K. Free Vibration Analysis of Functionally Gradient Sandwich Composite Plate Embedded SMA Wires in Surface Layer. Applied Sciences. 2020; 10(11):3921. https://doi.org/10.3390/app10113921
Chicago/Turabian StyleHuang, Yizhe, Lin Li, Zhichao Xu, Chaopeng Li, and Kuanmin Mao. 2020. "Free Vibration Analysis of Functionally Gradient Sandwich Composite Plate Embedded SMA Wires in Surface Layer" Applied Sciences 10, no. 11: 3921. https://doi.org/10.3390/app10113921
APA StyleHuang, Y., Li, L., Xu, Z., Li, C., & Mao, K. (2020). Free Vibration Analysis of Functionally Gradient Sandwich Composite Plate Embedded SMA Wires in Surface Layer. Applied Sciences, 10(11), 3921. https://doi.org/10.3390/app10113921