Mutual Interactions of Lamb Waves in Nonlinear Elastic Plates
Abstract
:1. Introduction
- (1)
- As the characteristics of the nonlinear modulation are practically important for its applications, the mutual interactions of Lamb waves in nonlinear elastic plates are studied in this study;
- (2)
- The Lamb wave mutual interaction theory can be utilized to guide nonlinear mode selection;
- (3)
- The fatigue damage in the metal plate can be detected by the Lamb wave mutual interaction.
2. Nonlinear Modulation Generation of Lamb Waves
2.1. Lamb Wave Propagation
2.2. The Dispersion Property
2.3. Mutual Interaction
3. Nonzero Power Flux
- (1)
- Symmetric–symmetric or antisymmetric–antisymmetric mutual interactions.
- (2)
- Symmetric–antisymmetric mutual interaction.
4. Synchronism Condition
5. Experimental Research
5.1. Experimental Setup
5.2. Experimental Results
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Nonlinear Forcing Terms
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Secondary Mode Type | v | ||
---|---|---|---|
Symmetric | {S 0 A} | ||
Antisymmetric | {A 0 S} |
Fundamental Wave Field | Secondary Modulation |
---|---|
Symmetric–symmetric | Symmetric |
Antisymmetric–antisymmetric | |
Symmetric–antisymmetric | Antisymmetric |
No. | Waves | Primary Mode | Frequency | Synchronism | Theoretical Modulation |
---|---|---|---|---|---|
1 | a | S0 | 195 kHz | Only for fb + fa | S0 mode at 468 kHz |
b | S0 | 273 kHz | |||
2 | a | S0 | 210 kHz | Only for fb − fa | S0 mode at 246 kHz |
b | S0 | 456 kHz | |||
3 | a | A0 | 20 kHz | Both fb + fa and fb − fa | A0 mode at 170 kHz and 130 kHz |
b | S0 | 150 kHz | |||
4 | a | A0 | 40 kHz | None | None |
b | S0 | 150 kHz |
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Ma, S.; Zhang, G.; Hou, H.; Wang, L. Mutual Interactions of Lamb Waves in Nonlinear Elastic Plates. Metals 2022, 12, 2175. https://doi.org/10.3390/met12122175
Ma S, Zhang G, Hou H, Wang L. Mutual Interactions of Lamb Waves in Nonlinear Elastic Plates. Metals. 2022; 12(12):2175. https://doi.org/10.3390/met12122175
Chicago/Turabian StyleMa, Shuyi, Guixian Zhang, Hongfeng Hou, and Lidong Wang. 2022. "Mutual Interactions of Lamb Waves in Nonlinear Elastic Plates" Metals 12, no. 12: 2175. https://doi.org/10.3390/met12122175