Magneto-Electric Effect on Guided Waves in Functionally Graded Piezoelectric–Piezomagnetic Fan-Shaped Cylindrical Structures
Abstract
:1. Introduction
2. Mathematics and Formulation
3. Numerical Results
3.1. Comparison with Rectangular Bar
3.2. Convergence Confirmation
3.3. The Magneto-Electric Effect
3.4. The Influence of the Graded Functions
3.5. The Influence of the Geometric Size
3.6. Waves at High Frequencies
3.7. The Stress, Electric, and Magnetic Displacement Distribution
3.8. The Poynting Vector
4. Conclusions
- (1)
- If the radius-thickness ratio is bigger than 1000, fan-shaped cylindrical structures could be treated as a rectangular bar.
- (2)
- The variation in geometric size of the cross-section has remarkable influence on wave characteristics. The cut-off frequencies have a negative relationship with the cross-section area of the fan-shaped cylindrical structures.
- (3)
- For the FGPP fan-shaped cylindrical structures, the magneto-electric effect could be adjusted via altering the geometric size.
- (4)
- The phase velocities for higher modes at high frequencies approximatively approach a value which is below the shear velocity, and they also increase with the increase of β.
- (5)
- For the big wavenumber case, the Poynting vector distributions are concentrated in the region with more material of smaller elasticity modulus, and the Poynting vector distributions are also concentrated near the boundaries, especially near the corner.
Author Contributions
Funding
Conflicts of Interest
Appendix A
References
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M,J | Mode1 | Mode2 | Mode3 |
---|---|---|---|
4,4 | 1054.86 | 1221.42 | 2564.77 |
4,5 | 1054.80 | 1221.34 | 2563.99 |
4,6 | 1054.79 | 1221.34 | 2563.12 |
5,4 | 1054.24 | 1220.87 | 2562.70 |
5,5 | 1054.19 | 1220.79 | 2561.84 |
5,6 | 1054.19 | 1220.79 | 2561.10 |
6,4 | 1054.27 | 1220.83 | 2560.59 |
6,5 | 1054.23 | 1220.75 | 2559.78 |
6,6 | 1054.22 | 1220.75 | 2559.17 |
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Zhang, B.; Yu, J.; Elmaimouni, L.; Zhang, X. Magneto-Electric Effect on Guided Waves in Functionally Graded Piezoelectric–Piezomagnetic Fan-Shaped Cylindrical Structures. Materials 2018, 11, 2174. https://doi.org/10.3390/ma11112174
Zhang B, Yu J, Elmaimouni L, Zhang X. Magneto-Electric Effect on Guided Waves in Functionally Graded Piezoelectric–Piezomagnetic Fan-Shaped Cylindrical Structures. Materials. 2018; 11(11):2174. https://doi.org/10.3390/ma11112174
Chicago/Turabian StyleZhang, Bo, Jiangong Yu, Lahoucine Elmaimouni, and Xiaoming Zhang. 2018. "Magneto-Electric Effect on Guided Waves in Functionally Graded Piezoelectric–Piezomagnetic Fan-Shaped Cylindrical Structures" Materials 11, no. 11: 2174. https://doi.org/10.3390/ma11112174